Patent Publication Number: US-8126726-B2

Title: System and method for facilitating automated dental measurements and diagnostics

Description:
RELATED APPLICATIONS 
     The present application claims priority under 35 USC §120 to pending application Ser. No. 10/788,635 entitled “Dental Data Mining” filed on Feb. 27, 2004, and to application Ser. No. 11/379,198 entitled “Method and System for Providing Indexing and Cataloguing of Orthodontic Related Treatment Profiles and Options” filed Apr. 18, 2006, the disclosure of each of which are incorporated herein by reference for all purposes. 
     FIELD OF THE DISCLOSURE 
     The present disclosure relates, generally, to dental treatment, and in particular to a system and method for automated dental measurements and diagnostics of teeth malocclusion to facilitate dental treatment. 
     BACKGROUND 
     Accurate and complete measurements of teeth characteristics, and diagnostics based on such measurements are important in the growing field of computational orthodontics and other computer aided dental treatment systems. Although various techniques for impression-based computational orthodontics using three-dimensional (“3-D”) models have been developed, the associated dental measurements are manually performed in most instances. For example, such dental measurements are typically obtained by an orthodontic practitioner based in large part on that particular orthodontic practitioner&#39;s experience, knowledge and subjective perception. 
     In addition to be time consuming, such measurement techniques are susceptible to subjective analysis and human error. As a result, the reliability of such manual techniques is less than ideal and potentially hinders the orthodontic treatment process. Further, potentially beneficial indices for orthodontic and dental assessment, such as Peer Assessment Ratings (PAR) indices, American Board of Orthodontics (ABO) discrepancy indices, and ABO objective grading systems and the like are not used as often as possible due to the difficulty in manual measurements and hand calculations. For example, the PAR index has traditionally been calculated by hand on dental casts using specially configured rulers, a very time consuming approach, significantly influenced by subjective perceptions and thus prone to inaccuracies and error. 
     In view of the foregoing, it would be desirable to have methods and systems for providing optimum, objective diagnostics and treatment planning, as well as improved dental treatment evaluation and research. 
     SUMMARY OF THE DISCLOSURE 
     A computer-implemented method for automated dental measurements in one embodiment includes acquiring a digital model of a patient&#39;s teeth, automatically detecting reference data and features based on the digital model, and automatically computing dental measurements based on said reference data and features, where the dental measurements are associated with an occlusal characteristic of the patient. An apparatus for performing automated dental measurements in one embodiment includes one or more processors, and a memory coupled to the one or more processors, the memory configured for storing instructions which, when executed by the one or more processors, causes the one or more processors to acquire a digital model of the patient&#39;s teeth, automatically detect reference data and features based on said digital model, and automatically compute dental measurements based on said reference data and features, where the dental measurements are associated with an occlusal characteristic of the patient. 
     These and other features and advantages of the present disclosure will be understood upon consideration of the following detailed description of the disclosure and the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1A  shows one exemplary dental data mining system; 
         FIG. 1B  shows an analysis of the performance of one or more dental appliances; 
         FIG. 1C  shows various Movement Type data used in one embodiment of the data mining system; 
         FIG. 1D  shows an analysis of the performance of one or more dental appliances; 
         FIGS. 1E-1F  show various embodiments of a clusterizer to generate treatment plans; 
         FIG. 2A  is a flowchart of a process of specifying a course of treatment including a subprocess for calculating aligner shapes in accordance with the invention; 
         FIG. 2B  is a flowchart of a process for calculating aligner shapes; 
         FIG. 3  is a flowchart of a subprocess for creating finite element models; 
         FIG. 4  is a flowchart of a subprocess for computing aligner changes; 
         FIG. 5A  is a flowchart of a subprocess for calculating changes in aligner shape; 
         FIG. 5B  is a flowchart of a subprocess for calculating changes in aligner shape; 
         FIG. 5C  is a flowchart of a subprocess for calculating changes in aligner shape; 
         FIG. 5D  is a schematic illustrating the operation of the subprocess of  FIG. 5B ; 
         FIG. 6  is a flowchart of a process for computing shapes for sets of aligners; 
         FIG. 7  is an exemplary diagram of a statistical root model; 
         FIG. 8  shows exemplary diagrams of root modeling; 
         FIG. 9  show exemplary diagrams of CT scan of teeth; 
         FIG. 10  shows an exemplary user interface showing teeth; 
         FIG. 11  is a block diagram of the overall system for practicing the various embodiments of the present invention; 
         FIG. 12  illustrates a tabular representation of the indexing system stored in the storage unit of  FIG. 11  in accordance with one embodiment of the present invention; 
         FIG. 13  illustrates a representation of possible treatment goals for any given orthodontic case in one aspect of the present invention; 
         FIG. 14  illustrates a matrix representation for the possible treatment goals shown in  FIG. 13  formatted in accordance with the tabular representation shown in  FIG. 12  in accordance with one embodiment of the present invention; 
         FIG. 15  illustrates the lower arch length category for use in the indexing system in accordance with one embodiment of the present invention; 
         FIG. 16  illustrates the selection process display for use in the indexing system for the identified primary concern as “buck teeth” in accordance with one embodiment of the present invention; 
         FIG. 17  illustrates an exemplary selection process display  1700  for capturing one component of the sagittal dimension discrepancy for the patient&#39;s right side in one embodiment of the present invention; 
         FIG. 18  illustrates an exemplary selection process display  1700  for capturing one component of the sagittal dimension discrepancy for the patient&#39;s left side in one embodiment of the present invention; 
         FIG. 19  illustrates an exemplary selection process display  1900  for capturing one component of the vertical dimension in one embodiment of the present invention; 
         FIG. 20  illustrates an exemplary selection process display  2000  for capturing one component of the horizontal/transverse dimension in one embodiment of the present invention; 
         FIG. 21 , an exemplary selection process display  2100  for capturing one component of the arch length discrepancy category in accordance with one embodiment of the present invention; 
         FIG. 22  illustrates an exemplary selection process display  2200  for capturing another component of the arch length discrepancy category in accordance with one embodiment of the present invention; 
         FIG. 23  illustrates an exemplary patient summary display  2300  displayed on terminal  1101  for use in the indexing system in accordance with one embodiment of the present invention; 
         FIG. 24  illustrates a patient database  2400  in accordance with one embodiment of the present invention; 
         FIG. 25  illustrates the selection process for representative components for use in the indexing system in accordance with an embodiment of the present invention; 
         FIG. 26  illustrates an exemplary series of database addresses generated by combining the initial condition address with the treatment goal address in one embodiment of the present invention; 
         FIG. 27  illustrates an exemplary database for a patient in another embodiment of the present invention; 
         FIG. 28  is a flowchart illustrating the procedure for identifying a dentition profile using the indexing system in accordance with one embodiment of the present invention; 
         FIG. 29A  is a flowchart illustrating an exemplary method for automated dental measurements and diagnostics of teeth malocclusion to facilitate dental treatment in accordance with an exemplary embodiment of the present disclosure; 
         FIG. 29B  is a block diagram of an exemplary system for automated dental measurements and diagnostics of teeth malocclusion to facilitate dental treatment in accordance with an exemplary embodiment of the present disclosure; 
         FIG. 29C  is a flowchart illustrating an exemplary method for automated dental measurements and diagnostics of teeth malocclusion to facilitate dental treatment in accordance with another exemplary embodiment of the present disclosure; 
         FIG. 30  is a flowchart illustrating an exemplary method for automated dental measurements and diagnostics of teeth malocclusion to facilitate dental treatment in accordance with another exemplary embodiment of the present disclosure; 
         FIG. 31  is a block diagram of an exemplary system for automated dental measurements and diagnostics of teeth malocclusion to facilitate dental treatment in accordance with an exemplary embodiment of the present disclosure; and 
         FIGS. 32A-32J  illustrate a graphical representations of automated orthontic related measurements in accordance with exemplary embodiments of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     The present disclosure may be described herein in terms of various components and processing steps. It should be appreciated that such components and steps may be realized by any number of hardware and software components configured to perform the specified functions. For example, the present disclosure may employ various electronic control devices, visual display devices, input terminals and the like, which may carry out a variety of functions under the control of one or more control systems, microprocessors or other control devices. In addition, the present disclosure may be practiced in any number of orthodontic or dental contexts and the exemplary embodiments relating to a system and method for automated dental measurements and diagnostics of teeth malocclusion to facilitate dental treatment as described herein are merely a few of the exemplary applications for the disclosure. For example, the principles, features and methods discussed may be applied to any application or process in which automated measurements of anatomical, topological or other characteristics is desirable. 
     It should be noted that for illustrative purposes, the various exemplary methods and systems may be described in connection with a single tooth of a patient; however, it should be understood that such exemplary methods and systems may be suitably implemented on more than one tooth and/or all teeth within a patient, such as molars, bicuspids, canines and incisors within a patient. For example, the exemplary methods and systems may be suitably implemented by performing a particular process, operation or step on one or more teeth before proceeding to a subsequent process, operation or step, or by performing all or essentially all processes, operations or steps on a particular tooth before proceeding to another tooth, or any combination thereof. In addition, such processes, steps or operations may be suitably performed at various stages of treatment of a patient, from initial stages through any intermediate and/or final stages. 
     Digital treatment plans are now possible with 3-dimensional orthodontic treatment planning tools such as ClinCheck®. from Align Technology, Inc. or other software available from eModels and OrthoCAD, among others. These technologies allow the clinician to use the actual patient&#39;s dentition as a starting point for customizing the treatment plan. The ClinCheck®. technology uses a patient-specific digital model to plot a treatment plan, and then use a scan of the achieved treatment outcome to assess the degree of success of the outcome as compared to the original digital treatment plan as discussed in U.S. patent application Ser. No. 10/640,439, filed Aug. 21, 2003 and U.S. patent application Ser. No. 10/225,889 filed Aug. 22, 2002. The problem with the digital treatment plan and outcome assessment is the abundance of data and the lack of standards and efficient methodology by which to assess “treatment success” at an individual patient level. To analyze the information, a dental data mining system is used. 
       FIG. 1A  shows one exemplary dental data mining system. In this system, dental treatment and outcome data sets  1  are stored in a database or information warehouse  2 . The data is extracted by data mining software  3  that generates results  4 . The data mining software can interrogate the information captured and/or updated in the database  2  and can generate an output data stream correlating a patient tooth problem with a dental appliance solution. Note that the output of the data mining software can be most advantageously, self-reflexively, fed as a subsequent input to at least the database and the data mining correlation algorithm. 
     The result of the data mining system of  FIG. 1A  is used for defining appliance configurations or changes to appliance configurations for incrementally moving teeth. The tooth movements will be those normally associated with orthodontic treatment, including translation in all three orthogonal directions, rotation of the tooth centerline in the two orthogonal directions with rotational axes perpendicular to a vertical centerline (“root angulation” and “torque”), as well as rotation of the tooth centerline in the orthodontic direction with an axis parallel to the vertical centerline (“pure rotation”). 
     In one embodiment, the data mining system captures the 3-D treatment planned movement, the start position and the final achieved dental position. The system compares the outcome to the plan, and the outcome can be achieved using any treatment methodology including removable appliances as well as fixed appliances such as orthodontic brackets and wires, or even other dental treatment such as comparing achieved to plan for orthognathic surgery, periodontics, restorative, among others. 
     In one embodiment, a teeth superimposition tool is used to match treatment files of each arch scan. The refinement scan is superimposed over the initial one to arrive at a match based upon tooth anatomy and tooth coordinate system. After teeth in the two arches are matched, the superimposition tool asks for a reference in order to relate the upper arch to the lower arch. When the option “statistical filtering” is selected, the superimposition tool measures the amount of movement for each tooth by first eliminating as reference the ones that move (determined by the difference in position between the current stage and the previous one) more than one standard deviation either above or below the mean of movement of all teeth. The remaining teeth are then selected as reference to measure movement of each tooth. 
       FIG. 1B  shows an analysis of the performance of one or more dental appliances. “Achieved” movement is plotted against “Goal” movement in scatter graphs, and trend lines are generated. Scatter graphs are shown to demonstrate where all “scattered” data points are, and trend lines are generated to show the performance of the dental appliances. In one embodiment, trend lines are selected to be linear (they can be curvilinear); thus trend lines present as the “best fit” straight lines for all “scattered” data. The performance of the Aligners is represented as the slope of a trend line. The Y axis intercept models the incidental movement that occurs when wearing the Aligners. Predictability is measured by R 2  that is obtained from a regression computation of “Achieved” and “Goal” data. 
       FIG. 1C  shows various Movement Type data used in one embodiment of the data mining system. Exemplary data sets cover Expansion/Constriction (+/−X Translation), Mesialization/Distalization (+/−Y Translation), Intrusion (−Z Translation), Extrusion (+Z Translation), Tip/Angulation (X Rotation), Torque/Inclination (Y Rotation), and Pure Rotation (Z Rotation). 
       FIG. 1D  shows an analysis of the performance of one or more dental appliances. For the type of motion illustrated by  FIG. 1D , the motion achieved is about 85% of targeted motion for that particular set of data. 
     As illustrated saliently in  FIG. 1D , actual tooth movement generally lags targeted tooth movement at many stages. In the case of treatment with sequences of polymer appliances, such lags play an important role in treatment design, because both tooth movement and such negative outcomes as patient discomfort vary positively with the extent of the discrepancies. 
     In one embodiment, clinical parameters in steps such as  170  ( FIG. 2A) and 232  ( FIG. 2B ) are made more precise by allowing for the statistical deviation of targeted from actual tooth position. For example, a subsequent movement target might be reduced because of a large calculated probability of currently targeted tooth movement not having been achieved adequately, with the result that there is a high probability the subsequent movement stage will need to complete work intended for an earlier stage. Similarly, targeted movement might overshoot desired positions especially in earlier stages so that expected actual movement is better controlled. This embodiment sacrifices the goal of minimizing round trip time in favor of achieving a higher probability of targeted end-stage outcome. This methodology is accomplished within treatment plans specific to clusters of similar patient cases. 
     Table 1 shows grouping of teeth in one embodiment. The sign convention of tooth movements is indicated in Table 2. Different tooth movements of the selected 60 arches were demonstrated in Table 3 with performance sorted by descending order. The appliance performance can be broken into 4 separate groups: high (79-85%), average (60-68%), below average (52-55%), and inadequate (24-47%). Table 4 shows ranking of movement predictability. Predictability is broken into 3 groups: highly predictable (0.76-0.82), predictable (0.43-0.63) and unpredictable (0.10-0.30). For the particular set of data, for example, the findings are as follows: 
     1. Incisor intrusion, and anterior intrusion performance are high. The range for incisor intrusion is about 1.7 mm, and for anterior intrusion is about 1.7 mm. These movements are highly predictable. 
     2. Canine intrusion, incisor torque, incisor rotation and anterior torque performance are average. The range for canine intrusion is about 1.3 mm, for incisor torque is about 34 degrees, for incisor rotation is about 69 degrees, and for anterior torque is about 34 degrees. These movements are either predictable or highly predictable. 
     3. Bicuspid tipping, bicuspid mesialization, molar rotation, and posterior expansion performance are below average. The range for bicuspid mesialization is about 1 millimeter, for bicuspid tipping is about 19 degrees, for molar rotation is about 27 degrees and for posterior expansion is about 2.8 millimeters. Bicuspid tipping and mesialization are unpredictable, whereas the rest are predictable movements. 
     4. Anterior and incisor extrusion, round teeth and bicuspid rotation, canine tipping, molar distalization, and posterior torque performance are inadequate. The range of anterior extrusion is about 1.7 millimeters, for incisor extrusion is about 1.5 mm, for round teeth rotation is about 67 degrees, for bicuspid rotation is about 63 degrees, for canine tipping is about 26 degrees, for molar distalization is about 2 millimeters, and for posterior torque is about 43 degrees. All are unpredictable movements except bicuspid rotation which is predictable. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Studied groups of teeth 
               
            
           
           
               
            
               
                 Teeth 
               
               
                   
               
            
           
           
               
               
            
               
                 Incisors 
                 #7, 8, 9, 10, 23, 24, 25, 26 
               
               
                 Canines 
                 #6, 11, 22, 27 
               
               
                 Bicuspids 
                 #4, 5, 12, 13, 20, 21, 28, 29 
               
               
                 Molars 
                 #2, 3, 14, 15, 18, 19, 30, 31 
               
               
                 Anteriors 
                 #6, 7, 8, 9, 10, 11, 22, 23, 24, 25, 26, 27 
               
               
                 Posteriors 
                 #2, 3, 4, 5, 12, 13, 14, 15, 18, 19, 20, 21, 28, 29, 30, 31 
               
               
                 Round 
                 #4, 5, 6, 11, 12, 13, 20, 21, 22, 27, 28, 29 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 2 
               
               
                   
               
               
                 Sign convention of tooth movements 
               
               
                 Type of Movement 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                 X translation 
                 (−) is lingual 
                 (+) is buccal 
               
               
                 (Expansion/ 
               
               
                 Constriction) 
               
               
                 X rotation (Tipping) 
               
               
                 Upper &amp; Lower 
                 (−) is distal 
                 (+) is mesial 
               
               
                 right quadrants 
               
               
                 Upper &amp; Lower 
                 (−) is mesial 
                 (+) is distal 
               
               
                 left quadrants 
               
               
                 Y translation 
               
               
                 (Mesialization/ 
               
               
                 Distalization) 
               
               
                 Upper left &amp; Lower 
                 (−) is distal 
                 (+) is mesial 
               
               
                 right quadrants 
               
               
                 Upper right &amp; Lower 
                 (−) is mesial 
                 (+) is distal 
               
               
                 left quadrants 
               
               
                 Y rotation 
                 (−) is lingual crown 
                 (+) is buccal crown 
               
               
                 (Torquing) 
               
               
                 Z translation 
                 (−) is intrusion 
                 (+) is extrusion 
               
               
                 (Intrusion/Extrusion) 
               
               
                 Z rotation 
                 (−) is clockwise 
                 (+) is counterclockwise 
               
               
                   
                   
                 (Pure Rotation) 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 3 
               
             
            
               
                   
               
               
                 Ranking of Performance Index of movement 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                   
                 Performance 
                 Side 
                 Predict- 
               
               
                 Group 
                 Movement 
                 Model 
                 Index 
                 Effect 
                 ability 
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 Incisor 
                 Intrusion 
                 Linear 
                 85% 
                 0.03 
                 0.82 
               
               
                 Anterior 
                 Intrusion 
                 Linear 
                 79% 
                 0.03 
                 0.76 
               
               
                 Canine 
                 Intrusion 
                 Linear 
                 68% 
                 −0.10 
                 0.43 
               
               
                 Incisor 
                 Torque 
                 Linear 
                 67% 
                 0.21 
                 0.63 
               
               
                 Anterior 
                 Torque 
                 Linear 
                 62% 
                 0.15 
                 0.56 
               
               
                 Incisor 
                 Rotation 
                 Linear 
                 61% 
                 −0.09 
                 0.76 
               
               
                 Bicuspid 
                 Tipping 
                 Linear 
                 55% 
                 0.35 
                 0.27 
               
               
                 Molar 
                 Rotation 
                 Linear 
                 52% 
                 0.11 
                 0.58 
               
               
                 Posterior 
                 Expansion 
                 Linear 
                 52% 
                 0.11 
                 0.48 
               
               
                 Bicuspid 
                 Mesialization 
                 Linear 
                 52% 
                 0.00 
                 0.30 
               
               
                 Bicuspid 
                 Rotation 
                 Linear 
                 47% 
                 0.28 
                 0.63 
               
               
                 Molar 
                 Distalization 
                 Linear 
                 43% 
                 0.02 
                 0.20 
               
               
                 Canine 
                 Tipping 
                 Linear 
                 42% 
                 0.10 
                 0.28 
               
               
                 Posterior 
                 Torque 
                 Linear 
                 42% 
                 1.50 
                 0.28 
               
               
                 Round 
                 Rotation 
                 Linear 
                 39% 
                 −0.14 
                 0.27 
               
               
                 Anterior 
                 Extrusion 
                 Linear 
                 29% 
                 −0.02 
                 0.13 
               
               
                 Incisor 
                 Extrusion 
                 Linear 
                 24% 
                 0.02 
                 0.10 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 4 
               
             
            
               
                   
               
               
                 Ranking of movement predictability 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                   
                 Performance 
                 Side 
                 Predict- 
               
               
                 Group 
                 Movement 
                 Model 
                 Index 
                 Effect 
                 ability 
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 Incisor 
                 Intrusion 
                 Linear 
                 85% 
                 0.03 
                 0.82 
               
               
                 Anterior 
                 Intrusion 
                 Linear 
                 79% 
                 0.03 
                 0.76 
               
               
                 Incisor 
                 Rotation 
                 Linear 
                 61% 
                 −0.09 
                 0.76 
               
               
                 Incisor 
                 Torque 
                 Linear 
                 67% 
                 0.21 
                 0.63 
               
               
                 Bicuspid 
                 Rotation 
                 Linear 
                 47% 
                 0.28 
                 0.63 
               
               
                 Molar 
                 Rotation 
                 Linear 
                 52% 
                 0.11 
                 0.58 
               
               
                 Anterior 
                 Torque 
                 Linear 
                 62% 
                 0.15 
                 0.56 
               
               
                 Posterior 
                 Expansion 
                 Linear 
                 52% 
                 0.11 
                 0.48 
               
               
                 Canine 
                 Intrusion 
                 Linear 
                 68% 
                 −0.10 
                 0.43 
               
               
                 Bicuspid 
                 Mesialization 
                 Linear 
                 52% 
                 0.00 
                 0.30 
               
               
                 Canine 
                 Tipping 
                 Linear 
                 42% 
                 0.10 
                 0.28 
               
               
                 Posterior 
                 Torque 
                 Linear 
                 42% 
                 1.50 
                 0.28 
               
               
                 Bicuspid 
                 Tipping 
                 Linear 
                 55% 
                 0.35 
                 0.27 
               
               
                 Round 
                 Rotation 
                 Linear 
                 39% 
                 −0.14 
                 0.27 
               
               
                 Molar 
                 Distalization 
                 Linear 
                 43% 
                 0.02 
                 0.20 
               
               
                 Anterior 
                 Extrusion 
                 Linear 
                 29% 
                 −0.02 
                 0.13 
               
               
                 Incisor 
                 Extrusion 
                 Linear 
                 24% 
                 0.02 
                 0.10 
               
               
                   
               
            
           
         
       
     
     In one embodiment, data driven analyzers may be applied. These data driven analyzers may incorporate a number of models such as parametric statistical models, non-parametric statistical models, clustering models, nearest neighbor models, regression methods, and engineered (artificial) neural networks. Prior to operation, data driven analyzers or models are built using one or more training sessions. The data used to build the analyzer or model in these sessions are typically referred to as training data. As data driven analyzers are developed by examining only training examples, the selection of the training data can significantly affect the accuracy and the learning speed of the data driven analyzer. One approach used heretofore generates a separate data set referred to as a test set for training purposes. The test set is used to avoid overfitting the model or analyzer to the training data. Overfitting refers to the situation where the analyzer has memorized the training data so well that it fails to fit or categorize unseen data. Typically, during the construction of the analyzer or model, the analyzer&#39;s performance is tested against the test set. The selection of the analyzer or model parameters is performed iteratively until the performance of the analyzer in classifying the test set reaches an optimal point. At this point, the training process is completed. An alternative to using an independent training and test set is to use a methodology called cross-validation. Cross-validation can be used to determine parameter values for a parametric analyzer or model for a non-parametric analyzer. In cross-validation, a single training data set is selected. Next, a number of different analyzers or models are built by presenting different parts of the training data as test sets to the analyzers in an iterative process. The parameter or model structure is then determined on the basis of the combined performance of all models or analyzers. Under the cross-validation approach, the analyzer or model is typically retrained with data using the determined optimal model structure. 
     In one embodiment, the data mining software  3  ( FIG. 1A ) can be a “spider” or “crawler” to grab data on the database  2  ( FIG. 1A ) for indexing. In one embodiment, clustering operations are performed to detect patterns in the data. In another embodiment, a neural network is used to recognize each pattern as the neural network is quite robust at recognizing dental treatment patterns. Once the treatment features have been characterized, the neural network then compares the input dental information with stored templates of treatment vocabulary known by the neural network recognizer, among others. The recognition models can include a Hidden Markov Model (HMM), a dynamic programming model, a neural network, a fuzzy logic, or a template matcher, among others. These models may be used singly or in combination. 
     Dynamic programming considers all possible paths of M “frames” through N points, subject to specified costs for making transitions from any point i to any given frame k to any point j at the next frame k+1. Because the best path from the current point to the next point is independent of what happens beyond that point, the minimum total cost [i(k), j(k+1)] of a path through i(k) ending at j(k+1) is the cost of the transition itself plus the cost of the minimum path to i(k). Preferably, the values of the predecessor paths can be kept in an M×N array, and the accumulated cost kept in a 2×N array to contain the accumulated costs of the possible immediately preceding column and the current column. However, this method requires significant computing resources. 
     Dynamic programming requires a tremendous amount of computation. For the recognizer to find the optimal time alignment between a sequence of frames and a sequence of node models, it must compare most frames against a plurality of node models. One method of reducing the amount of computation required for dynamic programming is to use pruning. Pruning terminates the dynamic programming of a given portion of dental treatment information against a given treatment model if the partial probability score for that comparison drops below a given threshold. This greatly reduces computation. 
     Considered to be a generalization of dynamic programming, a hidden Markov model is used in the preferred embodiment to evaluate the probability of occurrence of a sequence of observations O(1), O(2), . . . O(t), . . . , O(T), where each observation O(t) may be either a discrete symbol under the VQ approach or a continuous vector. The sequence of observations may be modeled as a probabilistic function of an underlying Markov chain having state transitions that are not directly observable. 
     In the preferred embodiment, the Markov model is used to model probabilities for sequences of treatment observations. The transitions between states are represented by a transition matrix A=[a(i,j)]. Each a(i,j) term of the transition matrix is the probability of making a transition to state j given that the model is in state i. The output symbol probability of the model is represented by a set of functions B=[b(j), where the b(j) term of the output symbol matrix is the function that when evaluated on a specified value O(t) returns the probability of outputting observation O(t), given that the model is in state j. The first state is always constrained to be the initial state for the first time frame of the Markov chain, only a prescribed set of left to right state transitions are possible. A predetermined final state is defined from which transitions to other states cannot occur. 
     In one embodiment, transitions are restricted to reentry of a state or entry to one of the next two states. Such transitions are defined in the model as transition probabilities. For example, a treatment pattern currently having a frame of feature signals in state 2 has a probability of reentering state 2 of a(2,2), a probability a(2,3) of entering state 3 and a probability of a(2,4)=1−a(2,2)−a(2,3) of entering state 4. The probability a(2,1) of entering state 1 or the probability a(2,5) of entering state 5 is zero and the sum of the probabilities a(2,1) through a(2,5) is one. Although the preferred embodiment restricts the flow graphs to the present state or to the next two states, one skilled in the art can build an HMM model with more flexible transition restrictions, although the sum of all the probabilities of transitioning from any state must still add up to one. 
     In each state j of the model, the current feature frame may be identified with one of a set of predefined output symbols or may be labeled probabilistically. In this case, the output symbol probability b(j) (O(t)) corresponds to the probability assigned by the model that the feature frame symbol is O(t). The model arrangement is a matrix A=[a(i,j)] of transition probabilities and a technique of computing B=[b(j) (O(t))]. 
     In one embodiment, the Markov model is formed for a reference pattern from a plurality of sequences of training patterns and the output symbol probabilities are multivariate Gaussian function probability densities. The dental treatment information traverses through the feature extractor. During learning, the resulting feature vector series is processed by a parameter estimator, whose output is provided to the hidden Markov model. The hidden Markov model is used to derive a set of reference pattern templates, each template representative of an identified pattern in a vocabulary set of reference treatment patterns. The Markov model reference templates are next utilized to classify a sequence of observations into one of the reference patterns based on the probability of generating the observations from each Markov model reference pattern template. During recognition, the unknown pattern can then be identified as the reference pattern with the highest probability in the likelihood calculator. 
     The HMM template has a number of states, each having a discrete value. However, as treatment pattern features may have a dynamic pattern in contrast to a single value, the addition of a neural network at the front end of the HMM in an embodiment provides the capability of representing states with dynamic values. The input layer of the neural network comprises input neurons. The outputs of the input layer are distributed to all neurons in the middle layer. Similarly, the outputs of the middle layer are distributed to all output neurons, which output neurons correspond one-to one with internal states of the HMM. However, each output has transition probabilities to itself or to other outputs, thus forming a modified HMM. Each state of the thus formed HMM is capable of responding to a particular dynamic signal, resulting in a more robust HMM. Alternatively, the neural network can be used alone without resorting to the transition probabilities of the HMM architecture. 
     The output streams or results  4  of  FIG. 1A  are used as feedback in improving dental appliance design and/or usage by doctors. For example, the data mining results can be used to evaluate performance based on staging approaches, to compare appliance performance indices based on treatment approaches, and to evaluate performance comparing different attachment shapes and positions on teeth. 
     The ability to study tooth-specific efficacy and product performance for large clusters of treatment outcomes enables statistically significant comparisons to be made between two or more populations of cases. In the event that the two clusters studied contain differences in treatment approach, appliance design, or manufacturing protocol, the differences seen in the performance of the product as exhibited by the data output, can be attributed to the approach, design, or manufacturing protocol. The end result is a feedback mechanism that enables either the clinician or the manufacturer the ability to optimize the product design and usage based on performance data from a significantly large sample size using objective measurable data. 
     The theory of orthodontic treatment is not universally agreed upon, and actual treatment and outcomes are subject to additional uncertainties of measurement of patient variables, of relationships to unmeasured patient variables, as well as of varying patient compliance. As a result, different clinicians might prefer different treatment plans for a single patient. Thus, a single treatment plan may not be accepted by every clinician since there is no universally accepted “correct” treatment plan. 
     The next few embodiments allow greater clinician satisfaction and greater patient satisfaction by tailoring treatment parameters to preferences of clinicians. The system detects differences in treatment preferences by statistical observation of the treatment histories of clinicians. For example, clinicians vary in how likely they would be to perform bicuspid extraction in cases with comparable crowding. Even when there is not a sufficient record of past treatments for a given clinician, clustering may be performed on other predictor variables such as geographical location, variables related to training, or size and nature of practice, to observe statistically significant differences in treatment parameters. 
     Data mining can discover statistically significant patterns of different treatment outcomes achieved by different clinicians for comparable patients. For example, patient cases clustered together might have systematically fewer complications with one clinician as compared to another. Such a difference detected by the data mining tool might be used as a flag for feedback to the more poorly performing clinician as well as a flag for solicitation of treatment differences used by the better performing clinician. 
     In one embodiment, clustering techniques are used with previously completed cases to categorize treatment complications and outcomes. Probability models of risk are then built within each cluster. New cases are then allocated to the same clusters based on similarity of pre-treatment variables. The risks within each cluster of patients with completed treatments are then used with new cases to predict treatment outcomes and risks of complications. High-risk patients are then flagged for special attention, possibly including additional steps in treatment plan or additional clinical intervention. 
     In another embodiment, practitioners are clustered into groups by observed clinician treatment preferences, and treatment parameters are adjusted within each group to coincide more closely with observed treatment preferences. Practitioners without observed histories are then assigned to groups based on similarity of known variables to those within clusters with known treatment histories. 
       FIG. 1E  shows an exemplary process for clusterizing practices. First, the process clusterizes treatment practice based on clinician treatment history such as treatment preferences, outcomes, and demographic and practice variables ( 20 ). Next, the system models preferred clinical constraints within each cluster ( 22 ). Next, the system assigns clinicians without treatment history to clusters in  20  based on demographic and practice variables ( 24 ). In one embodiment, the system performs process  100  (see  FIG. 2A ) separately within each cluster, using cluster-specific clinical constraints ( 26 ). Additionally, the system updates clusters and cluster assignments as new treatment and outcome data arrives ( 28 ). 
       FIG. 1F  shows another embodiment of a data mining system to generate proposed treatments. First, the system identifies/clusterizes patient histories having detailed follow-up (such as multiple high-resolution scans), based on detailed follow-up data, diagnosis, treatment parameters and outcomes, and demographic variables ( 40 ). Within each cluster, the system models discrepancies between intended position and actual positions obtained from follow-up data ( 42 ). Further, within each cluster, the system models risk for special undesirable outcomes ( 44 ). At a second tier of clustering, patient histories with less detailed follow-up data are clusterized based on available variables. The second-tier clustering is partial enough that each of the larger number of second tier clusters can either be assigned to clusters calculated in  40  or else considered a new cluster ( 46 ). The system refines step  42  models with additional records from step  46  clusters ( 48 ). It can also refine step  44  models with additional records from step  48  clusters ( 50 ). At a third tier of clustering, the system then assigns new patients to step  46  clusters based on diagnosis, demographic, and initial physical ( 52 ). Within each step  52  cluster, the system models expected discrepancies between intended position and actual positions ( 54 ). From step  54 , the system uses revised expected position information where relevant (including  232  and  250 ,  FIG. 2B ) ( 67 ). Additionally, within each step  52  cluster, the system models risk for undesirable outcomes ( 56 ). From step  56 , the system also flags cases that require special attention and clinical constraints (as in  204  and  160 ,  FIGS. 2B and 2A ) ( 69 ). The process then customizes treatment plan to each step  52  cluster ( 58 ). Next, the system iteratively collects data ( 61 ) and loops back to identify/clusterize patient histories ( 40 ). Additionally, clusters can be revised and reassigned ( 63 ). The system also continually identifies clusters without good representation for additional follow-up analysis ( 65 ). 
     In clinical treatment settings, it is not cost-effective to obtain or process the full high-resolution data possible at every stage of tooth movement. For example:
         Patients may use several appliances between visits to clinicians.   A given patient may submit only one set of tooth impressions.   Radiation concerns may limit the number of CT or X-Ray scans used.   Clinicians generally do not have the time to report detailed spatial information on each tooth at each visit.       

     Due to these and other limitations, treatment planning is necessarily made based on partial information. 
     In one embodiment, missing information is approximated substantially by matching predictive characteristics between patients and a representative sample for which detailed follow-up information is collected. In this case, patients are flagged based on poorly anticipated treatment outcomes for requests for follow-up information, such as collection and analysis of additional sets of tooth impressions. Resulting information is then used to refine patient clusters and treatment of patients later assigned to the clusters. 
     In general, patient data is scanned and the data is analyzed using the data mining system described above. A treatment plan is proposed by the system for the dental practitioner to approve. The dental practitioner can accept or request modifications to the treatment plan. Once the treatment plan is approved, manufacturing of appliance(s) can begin. 
       FIG. 2A  illustrates the general flow of an exemplary process  100  for defining and generating repositioning appliances for orthodontic treatment of a patient. The process  100  includes the methods, and is suitable for the apparatus, of the present invention, as will be described. The computational steps of the process are advantageously implemented as computer program modules for execution on one or more conventional digital computers. 
     As an initial step, a mold or a scan of patient&#39;s teeth or mouth tissue is acquired ( 110 ). This step generally involves taking casts of the patient&#39;s teeth and gums, and may in addition or alternately involve taking wax bites, direct contact scanning, x-ray imaging, tomographic imaging, sonographic imaging, and other techniques for obtaining information about the position and structure of the teeth, jaws, gums and other orthodontically relevant tissue. From the data so obtained, a digital data set is derived that represents the initial (that is, pretreatment) arrangement of the patient&#39;s teeth and other tissues. 
     The initial digital data set, which may include both raw data from scanning operations and data representing surface models derived from the raw data, is processed to segment the tissue constituents from each other (step  120 ). In particular, in this step, data structures that digitally represent individual tooth crowns are produced. Advantageously, digital models of entire teeth are produced, including measured or extrapolated hidden surfaces and root structures. 
     The desired final position of the teeth—that is, the desired and intended end result of orthodontic treatment—can be received from a clinician in the form of a prescription, can be calculated from basic orthodontic principles, or can be extrapolated computationally from a clinical prescription (step  130 ). With a specification of the desired final positions of the teeth and a digital representation of the teeth themselves, the final position and surface geometry of each tooth can be specified (step  140 ) to form a complete model of the teeth at the desired end of treatment. Generally, in this step, the position of every tooth is specified. The result of this step is a set of digital data structures that represents an orthodontically correct repositioning of the modeled teeth relative to presumed-stable tissue. The teeth and tissue are both represented as digital data. 
     Having both a beginning position and a final position for each tooth, the process next defines a tooth path for the motion of each tooth. In one embodiment, the tooth paths are optimized in the aggregate so that the teeth are moved in the quickest fashion with the least amount of round-tripping to bring the teeth from their initial positions to their desired final positions. (Round-tripping is any motion of a tooth in any direction other than directly toward the desired final position. Round-tripping is sometimes necessary to allow teeth to move past each other.) The tooth paths are segmented. The segments are calculated so that each tooth&#39;s motion within a segment stays within threshold limits of linear and rotational translation. In this way, the end points of each path segment can constitute a clinically viable repositioning, and the aggregate of segment end points constitute a clinically viable sequence of tooth positions, so that moving from one point to the next in the sequence does not result in a collision of teeth. 
     The threshold limits of linear and rotational translation are initialized, in one implementation, with default values based on the nature of the appliance to be used. More individually tailored limit values can be calculated using patient-specific data. The limit values can also be updated based on the result of an appliance-calculation (step  170 , described later), which may determine that at one or more points along one or more tooth paths, the forces that can be generated by the appliance on the then-existing configuration of teeth and tissue is incapable of effecting the repositioning that is represented by one or more tooth path segments. With this information, the subprocess defining segmented paths (step  150 ) can recalculate the paths or the affected subpaths. 
     At various stages of the process, and in particular after the segmented paths have been defined, the process can, and generally will, interact with a clinician responsible for the treatment of the patient (step  160 ). Clinician interaction can be implemented using a client process programmed to receive tooth positions and models, as well as path information from a server computer or process in which other steps of process  100  are implemented. The client process is advantageously programmed to allow the clinician to display an animation of the positions and paths and to allow the clinician to reset the final positions of one or more of the teeth and to specify constraints to be applied to the segmented paths. If the clinician makes any such changes, the subprocess of defining segmented paths (step  150 ) is performed again. 
     The segmented tooth paths and associated tooth position data are used to calculate clinically acceptable appliance configurations (or successive changes in appliance configuration) that will move the teeth on the defined treatment path in the steps specified by the path segments (step  170 ). Each appliance configuration represents a step along the treatment path for the patient. The steps are defined and calculated so that each discrete position can follow by straight-line tooth movement or simple rotation from the tooth positions achieved by the preceding discrete step and so that the amount of repositioning required at each step involves an orthodontically optimal amount of force on the patient&#39;s dentition. As with the path definition step, this appliance calculation step can include interactions and even iterative interactions with the clinician (step  160 ). The operation of a process step  200  implementing this step will be described more fully below. 
     Having calculated appliance definitions, the process  100  can proceed to the manufacturing step (step  180 ) in which appliances defined by the process are manufactured, or electronic or printed information is produced that can be used by a manual or automated process to define appliance configurations or changes to appliance configurations. 
       FIG. 2B  illustrates a process  200  implementing the appliance-calculation step ( FIG. 2A , step  170 ) for polymeric shell aligners of the kind described in above-mentioned U.S. Pat. No. 5,975,893. Inputs to the process include an initial aligner shape  202 , various control parameters  204 , and a desired end configuration for the teeth at the end of the current treatment path segment  206 . Other inputs include digital models of the teeth in position in the jaw, models of the jaw tissue, and specifications of an initial aligner shape and of the aligner material. Using the input data, the process creates a finite element model of the aligner, teeth and tissue, with the aligner in place on the teeth (step  210 ). Next, the process applies a finite element analysis to the composite finite element model of aligner, teeth and tissue (step  220 ). The analysis runs until an exit condition is reached, at which time the process evaluates whether the teeth have reached the desired end position for the current path segment, or a position sufficiently close to the desired end position (step  230 ). If an acceptable end position is not reached by the teeth, the process calculates a new candidate aligner shape (step  240 ). If an acceptable end position is reached, the motions of the teeth calculated by the finite elements analysis are evaluated to determine whether they are orthodontically acceptable (step  232 ). If they are not, the process also proceeds to calculate a new candidate aligner shape (step  240 ). If the motions are orthodontically acceptable and the teeth have reached an acceptable position, the current aligner shape is compared to the previously calculated aligner shapes. If the current shape is the best solution so far (decision step  250 ), it is saved as the best candidate so far (step  260 ). If not, it is saved in an optional step as a possible intermediate result (step  252 ). If the current aligner shape is the best candidate so far, the process determines whether it is good enough to be accepted (decision step  270 ). If it is, the process exits. Otherwise, the process continues and calculates another candidate shape (step  240 ) for analysis. 
     The finite element models can be created using computer program application software available from a variety of vendors. For creating solid geometry models, computer aided engineering (CAE) or computer aided design (CAD) programs can be used, such as the AutoCAD®. software products available from Autodesk, Inc., of San Rafael, Calif. For creating finite element models and analyzing them, program products from a number of vendors can be used, including the PolyFEM product available from CADSI of Coralville, Iowa, the Pro/Mechanica simulation software available from Parametric Technology Corporation of Waltham, Mass., the I-DEAS design software products available from Structural Dynamics Research Corporation (SDRC) of Cincinnati, Ohio, and the MSC/NASTRAN product available from MacNeal-Schwendler Corporation of Los Angeles, Calif. 
       FIG. 3  shows a process  300  of creating a finite element model that can be used to perform step  210  of the process  200  ( FIG. 2 ). Input to the model creation process  300  includes input data  302  describing the teeth and tissues and input data  304  describing the aligner. The input data describing the teeth  302  include the digital models of the teeth; digital models of rigid tissue structures, if available; shape and viscosity specifications for a highly viscous fluid modeling the substrate tissue in which the teeth are embedded and to which the teeth are connected, in the absence of specific models of those tissues; and boundary conditions specifying the immovable boundaries of the model elements. In one implementation, the model elements include only models of the teeth, a model of a highly viscous embedding substrate fluid, and boundary conditions that define, in effect, a rigid container in which the modeled fluid is held. Note that fluid characteristics may differ by patient clusters, for example as a function of age. 
     A finite element model of the initial configuration of the teeth and tissue is created (step  310 ) and optionally cached for reuse in later iterations of the process (step  320 ). As was done with the teeth and tissue, a finite element model is created of the polymeric shell aligner (step  330 ). The input data for this model includes data specifying the material of which the aligner is made and the shape of the aligner (data input  304 ). 
     The model aligner is then computationally manipulated to place it over the modeled teeth in the model jaw to create a composite model of an in-place aligner (step  340 ). Optionally, the forces required to deform the aligner to fit over the teeth, including any hardware attached to the teeth, are computed and used as a figure of merit in measuring the acceptability of the particular aligner configuration. Optionally, the tooth positions used are as estimated from a probabilistic model based on prior treatment steps and other patient information. In a simpler alternative, however, the aligner deformation is modeled by applying enough force to its insides to make it large enough to fit over the teeth, placing the model aligner over the model teeth in the composite model, setting the conditions of the model teeth and tissue to be infinitely rigid, and allowing the model aligner to relax into position over the fixed teeth. The surfaces of the aligner and the teeth are modeled to interact without friction at this stage, so that the aligner model achieves the correct initial configuration over the model teeth before finite element analysis is begun to find a solution to the composite model and compute the movement of the teeth under the influence of the distorted aligner. 
       FIG. 4  shows a process  400  for calculating the shape of a next aligner that can be used in the aligner calculations, step  240  of process  200  ( FIG. 2B ). A variety of inputs are used to calculate the next candidate aligner shape. These include inputs  402  of data generated by the finite element analysis solution of the composite model and data  404  defined by the current tooth path. The data  402  derived from the finite element analysis includes the amount of real elapsed time over which the simulated repositioning of the teeth took place; the actual end tooth positions calculated by the analysis; the maximum linear and torsional force applied to each tooth; the maximum linear and angular velocity of each tooth. From the input path information, the input data  404  includes the initial tooth positions for the current path segment, the desired tooth positions at the end of the current path segment, the maximum allowable displacement velocity for each tooth, and the maximum allowable force of each kind for each tooth. 
     If a previously evaluated aligner was found to violate one or more constraints, additional input data  406  can optionally be used by the process  400 . This data  406  can include information identifying the constraints violated by, and any identified suboptimal performance of, the previously evaluated aligner. Additionally, input data  408  relating to constraints violated by, and suboptimal performance of previous dental devices can be used by the process  400 . 
     Having received the initial input data (step  420 ), the process iterates over the movable teeth in the model. (Some of the teeth may be identified as, and constrained to be, immobile.) If the end position and dynamics of motion of the currently selected tooth by the previously selected aligner is acceptable (“yes” branch of decision step  440 ), the process continues by selecting for consideration a next tooth (step  430 ) until all teeth have been considered (“done” branch from step  430  to step  470 ). Otherwise (“no” branch from step  440 ), a change in the aligner is calculated in the region of the currently selected tooth (step  450 ). The process then moves back to select the next current tooth (step  430 ) as has been described. 
     When all of the teeth have been considered, the aggregate changes made to the aligner are evaluated against previously defined constraints (step  470 ), examples of which have already been mentioned. Constraints can be defined with reference to a variety of further considerations, such as manufacturability. For example, constraints can be defined to set a maximum or minimum thickness of the aligner material, or to set a maximum or minimum coverage of the aligner over the crowns of the teeth. If the aligner constraints are satisfied, the changes are applied to define a new aligner shape (step  490 ). Otherwise, the changes to the aligner are revised to satisfy the constraints (step  480 ), and the revised changes are applied to define the new aligner shape (step  490 ). 
       FIG. 5A  illustrates one implementation of the step of computing an aligner change in a region of a current tooth (step  450 ). In this implementation, a rule-based inference engine  456  is used to process the input data previously described (input  454 ) and a set of rules  452   a - 452   n  in a rule base of rules  452 . The inference engine  456  and the rules  452  define a production system which, when applied to the factual input data, produces a set of output conclusions that specify the changes to be made to the aligner in the region of the current tooth (output  458 ). 
     Rules  452   a  . . .  452   n  have the conventional two-part form: an if-part defining a condition and a then-part defining a conclusion or action that is asserted if the condition is satisfied. Conditions can be simple or they can be complex conjunctions or disjunctions of multiple assertions. An exemplary set of rules, which defines changes to be made to the aligner, includes the following: if the motion of the tooth is too fast, add driving material to the aligner opposite the desired direction of motion; if the motion of the tooth is too slow, add driving material to overcorrect the position of the tooth; if the tooth is too far short of the desired end position, add material to overcorrect; if the tooth has been moved too far past the desired end position, add material to stiffen the aligner where the tooth moves to meet it; if a maximum amount of driving material has been added, add material to overcorrect the repositioning of the tooth and do not add driving material; if the motion of the tooth is in a direction other than the desired direction, remove and add material so as to redirect the tooth. 
     In an alternative embodiment, illustrated in  FIGS. 5B and 5C , an absolute configuration of the aligner is computed, rather than an incremental difference. As shown in  FIG. 5B , a process  460  computes an absolute configuration for an aligner in a region of a current tooth. Using input data that has already been described, the process computes the difference between the desired end position and the achieved end position of the current tooth ( 462 ). Using the intersection of the tooth center line with the level of the gum tissue as the point of reference, the process computes the complement of the difference in all six degrees of freedom of motion, namely three degrees of translation and three degrees of rotation (step  464 ). Next, the model tooth is displaced from its desired end position by the amounts of the complement differences (step  466 ), which is illustrated in  FIG. 5B . 
       FIG. 5D  shows a planar view of an illustrative model aligner  60  over an illustrative model tooth  62 . The tooth is in its desired end position and the aligner shape is defined by the tooth in this end position. The actual motion of the tooth calculated by the finite element analysis is illustrated as placing the tooth in position  64  rather than in the desired position  62 . A complement of the computed end position is illustrated as position  66 . The next step of process  460  ( FIG. 5B ) defines the aligner in the region of the current tooth in this iteration of the process by the position of the displaced model tooth (step  468 ) calculated in the preceding step ( 466 ). This computed aligner configuration in the region of the current tooth is illustrated in  FIG. 5D  as shape  68  which is defined by the repositioned model tooth in position  66 . 
     A further step in process  460 , which can also be implemented as a rule  452  ( FIG. 5A ), is shown in  FIG. 5C . To move the current tooth in the direction of its central axis, the size of the model tooth defining that region of the aligner, or the amount of room allowed in the aligner for the tooth, is made smaller in the area away from which the process has decided to move the tooth (step  465 ). 
     As shown in  FIG. 6 , the process  200  ( FIG. 2B ) of computing the shape for an aligner for a step in a treatment path is one step in a process  600  of computing the shapes of a series of aligners. This process  600  begins with an initialization step  602  in which initial data, control and constraint values are obtained. 
     When an aligner configuration has been found for each step or segment of the treatment path (step  604 ), the process  600  determines whether all of the aligners are acceptable (step  606 ). If they are, the process is complete. Otherwise, the process optionally undertakes a set of steps  610  in an attempt to calculate a set of acceptable aligners. First, one or more of the constraints on the aligners is relaxed (step  612 ). Then, for each path segment with an unacceptable aligner, the process  200  ( FIG. 2B ) of shaping an aligner is performed with the new constraints (step  614 ). If all the aligners are now acceptable, the process  600  exits (step  616 ). 
     Aligners may be unacceptable for a variety of reasons, some of which are handled by the process. For example, if any impossible movements were required (decision step  620 ), that is, if the shape calculation process  200  ( FIG. 2B ) was required to effect a motion for which no rule or adjustment was available, the process  600  proceeds to execute a module that calculates the configuration of a hardware attachment to the subject tooth to which forces can be applied to effect the required motion (step  640 ). Because adding hardware can have an effect that is more than local, when hardware is added to the model, the outer loop of the process  600  is executed again (step  642 ). 
     If no impossible movements were required (“no” branch from step  620 ), the process transfers control to a path definition process (such as step  150 ,  FIG. 2A ) to redefine those parts of the treatment path having unacceptable aligners (step  630 ). This step can include both changing the increments of tooth motion, i.e., changing the segmentation, on the treatment path, changing the path followed by one or more teeth in the treatment path, or both. After the treatment path has been redefined, the outer loop of the process is executed again (step  632 ). The recalculation is advantageously limited to recalculating only those aligners on the redefined portions of the treatment path. If all the aligners are now acceptable, the process exits (step  634 ). If unacceptable aligners still remain, the process can be repeated until an acceptable set of aligners is found or an iteration limit is exceeded (step  650 ). At this point, as well as at other points in the processes that are described in this specification, such as at the computation of additional hardware (step  640 ), the process can interact with a human operator, such as a clinician or technician, to request assistance (step  652 ). Assistance that an operator provides can include defining or selecting suitable attachments to be attached to a tooth or a bone, defining an added elastic element to provide a needed force for one or more segments of the treatment path, suggesting an alteration to the treatment path, either in the motion path of a tooth or in the segmentation of the treatment path, and approving a deviation from or relaxation of an operative constraint. 
     As was mentioned above, the process  600  is defined and parameterized by various items of input data (step  602 ). In one implementation, this initializing and defining data includes the following items: an iteration limit for the outer loop of the overall process; specification of figures of merit that are calculated to determine whether an aligner is good enough (see  FIG. 2B , step  270 ); a specification of the aligner material; a specification of the constraints that the shape or configuration of an aligner must satisfy to be acceptable; a specification of the forces and positioning motions and velocities that are orthodontically acceptable; an initial treatment path, which includes the motion path for each tooth and a segmentation of the treatment path into segments, each segment to be accomplished by one aligner; a specification of the shapes and positions of any anchors installed on the teeth or otherwise; and a specification of a model for the jaw bone and other tissues in or on which the teeth are situated (in the implementation being described, this model consists of a model of a viscous substrate fluid in which the teeth are embedded and which has boundary conditions that essentially define a container for the fluid). 
       FIG. 7  is an exemplary diagram of a statistical root model. As shown therein, using the scanning processes described above, a scanned upper portion  701  of a tooth is identified. The scanned upper portion, including the crown, is then supplemented with a modeled 3D root. The 3D model of the root can be statistically modeled. The 3D model of the root  702  and the 3D model of the upper portion  700  together form a complete 3D model of a tooth. 
       FIG. 8  shows exemplary diagrams of root modeling, as enhanced using additional dental information. In  FIG. 8 , the additional dental information is X-ray information. An X-ray image  710  of teeth is scanned to provide a 2D view of the complete tooth shapes. An outline of a target tooth is identified in the X-Ray image. The model  712  as developed in  FIG. 7  is modified in accordance with the additional information. In one embodiment, the tooth model of  FIG. 7  is morphed to form a new model  714  that conforms with the X-ray data. 
       FIG. 9  shows an exemplary diagram of a CT scan of teeth. In this embodiment, the roots are derived directly from a high-resolution CBCT scan of the patient. Scanned roots can then be applied to crowns derived from an impression, or used with the existing crowns extracted from Cone Beam Computed Tomography (CBCT) data. A CBCT single scan gives 3D data and multiple forms of X-ray-like data. PVS impressions are avoided. 
     In one embodiment, a cone beam x-ray source and a 2D area detector scans the patient&#39;s dental anatomy, preferably over a 360 degree angular range and along its entire length, by any one of various methods wherein the position of the area detector is fixed relative to the source, and relative rotational and translational movement between the source and object provides the scanning (irradiation of the object by radiation energy). As a result of the relative movement of the cone beam source to a plurality of source positions (i.e., “views”) along the scan path, the detector acquires a corresponding plurality of sequential sets of cone beam projection data (also referred to herein as cone beam data or projection data), each set of cone beam data being representative of x-ray attenuation caused by the object at a respective one of the source positions. 
       FIG. 10  shows an exemplary user interface showing the erupted teeth, which can be shown with root information in another embodiment. Each tooth is individually adjustable using a suitable handle. In the embodiment of  FIG. 10 , the handle allows an operator to move the tooth in three-dimensions with six degrees of freedom. 
     The teeth movement is guided in part using a root-based sequencing system. In one embodiment, the movement is constrained by a surface area constraint, while in another embodiment, the movement is constrained by a volume constraint. 
     In one embodiment, the system determines a surface area for each tooth model. The system then sums all surface areas for all tooth models to be moved. Next, the system sums all surface areas of all tooth models on the arch. For each stage of teeth movement, the system checks that a predetermined area ratio or constraint is met while the tooth models are moved. In one implementation, the constraint can be to ensure that the surface areas of moving teeth are less than the total surface areas of teeth on an arch supporting the teeth being moved. If the ratio is greater than a particular number such as 50%, the system indicates an error signal to an operator to indicate that the teeth should be moved on a slower basis. 
     In another embodiment, the system determines the volume for each tooth model. The system then sums the volumes for all tooth models being moved. Next, the system determines the total volume of all tooth models on the arch. For each stage of teeth movement, the system checks that a predetermined volume ratio or constraint is met while the tooth models are moved. In one implementation, the constraint can be to ensure that the volume for moving teeth is less than the volume of all teeth on an arch supporting the teeth being moved. If the ratio is greater than a particular number such as 50%, the system indicates an error signal to an operator to indicate that the teeth should be moved on a slower basis. 
     Optionally, other features are added to the tooth model data sets to produce desired features in the aligners. For example, it may be desirable to add digital wax patches to define cavities or recesses to maintain a space between the aligner and particular regions of the teeth or jaw. It may also be desirable to add digital wax patches to define corrugated or other structural forms to create regions having particular stiffness or other structural properties. In manufacturing processes that rely on generation of positive models to produce the repositioning appliance, adding a wax patch to the digital model will generate a positive mold that has the same added wax patch geometry. This can be done globally in defining the base shape of the aligners or in the calculation of particular aligner shapes. One feature that can be added is a rim around the gumline, which can be produced by adding a digital model wire at the gumline of the digital model teeth from which the aligner is manufactured. When an aligner is manufactured by pressure fitting polymeric material over a positive physical model of the digital teeth, the wire along the gumlines causes the aligner to have a rim around it providing additional stiffness along the gumline. 
     In another optional manufacturing technique, two sheets of material are pressure fit over the positive tooth model, where one of the sheets is cut along the apex arch of the aligner and the other is overlaid on top. This provides a double thickness of aligner material along the vertical walls of the teeth. 
     The changes that can be made to the design of an aligner are constrained by the manufacturing technique that will be used to produce it. For example, if the aligner will be made by pressure fitting a polymeric sheet over a positive model, the thickness of the aligner is determined by the thickness of the sheet. As a consequence, the system will generally adjust the performance of the aligner by changing the orientation of the model teeth, the sizes of parts of the model teeth, the position and selection of attachments, and the addition or removal of material (e.g., adding wires or creating dimples) to change the structure of the aligner. The system can optionally adjust the aligner by specifying that one or more of the aligners are to be made of a sheet of a thickness other than the standard one, to provide more or less force to the teeth. On the other hand, if the aligner will be made by a stereo lithography process, the thickness of the aligner can be varied locally, and structural features such as rims, dimples, and corrugations can be added without modifying the digital model of the teeth. 
     The system can also be used to model the effects of more traditional appliances such as retainers and braces and therefore be used to generate optimal designs and treatment programs for particular patients. 
       FIG. 11  is a block diagram of the overall indexing system  1100  for practicing the various embodiments of the present invention. The indexing system  1100  in one embodiment includes a terminal  1101 , which may be configured as a personal computer, workstation, or mainframe, and which includes a user interface input device  1103  and a user interface output device  1105 , a storage unit  1107 , and a central server  1109 . 
     Referring to  FIG. 11 , the user interface input device  1103  may include a keyboard and may further include a pointing devices and/or a scanner, including x-ray or intra-oral scanner. The pointing device may be an indirect pointing device such as a mouse, trackball, touchpad, or graphics tablet, or a direct pointing device such as a touchscreen incorporated into the user interface output device  1105 . Other types of user interface input devices, such as voice recognition systems, may be used within the scope of the present invention. 
     Referring again to  FIG. 11 , the user interface output device  1105  may include a printer and a display subsystem, which includes a display controller and a display device coupled to the controller. The display device may be a cathode ray tube (CRT), a flat-panel device such as a liquid crystal display, or a projection device. The display subsystem may also provide nonvisual display such as audio output. 
     The indexing system  1100  shown in  FIG. 11  also includes the data storage unit  1107  which is configured to, under the access and control of either a central server  1109  or a client application, to maintain the basic programming and data constructs that provide the functionality of the present invention. Software is stored in storage unit  1107  which may include a memory unit and file storage unit. The memory unit may include a main random access memory (RAM) for storage of instructions and data during program execution and a read-only memory (ROM) in which fixed instructions are stored. 
     The file storage unit of the data storage unit  1107  may provide persistent (nonvolatile) storage for program and data files, and typically includes at least one hard disk drive and at least one CD-ROM drive (with associated removable media). There may also be other devices such as a floppy disk drive and optical drives (all with their associated removable media). Additionally, the file storage unit may include drives of the type with removable media cartridges, such as hard disk cartridges and flexible disk cartridges. One or more of the drives may be located at a remote location, such as in central server  1109  on a local area network or at a site on the Internet&#39;s World Wide Web or the entire system may be a stand-alone software application resident on the user&#39;s system. 
     In one aspect of the present invention, the central server  1109  may be configured to communicate with the terminal  1101  and data storage unit  1107  to access software stored in the data storage unit  1107  based on and in response to the input received from terminal  1101 , and to perform additional processing based on procedures and/or routines in accordance with the instructions or input information received from the terminal  1101 . 
     Referring back to  FIG. 11 , the indexing system  1100  in accordance with one embodiment of the present invention organizes orthodontic needs by the most common configurations of orthodontic discrepancies in the different dimensions: sagittal, vertical, horizontal/transverse, and arch length. The categories may be expanded to specifically capture other components such as facial profile, individual dental configurations, dynamic functional relationships, and surrounding soft tissue conditions; however, discrepancies in these four categories capture a significant portion of orthodontic related dental problems or concerns. Within each category, there may be a predetermined number of individual components to characterize the potential conditions for that dimension. For each condition, a predetermined combination of different possible conditions may be created. This collection of predefined combinations for each component, where each component belongs to one of the four main categories described, in one embodiment defines a matrix such that any patient at any time point may be defined as a specific address within the matrix. Both the matrix and address matrix may be stored in storage unit  1107 . 
       FIG. 12  illustrates an exemplary tabular representation of the indexing system matrix stored in the storage unit  1107  of  FIG. 11  in accordance with one embodiment of the present invention. The exemplary table  1200  of  FIG. 12  illustrates a simplified version of the possible conditions for one component within each of the four categories. 
     Referring to  FIG. 12 , the table  1200  includes a category field  1201 , a reference component field  1202 , and the pre-defined options field  1203 . Table  1200  also includes a number of options field  1204 . The category field  1201  in one embodiment includes the categories for which reference dentition condition information is stored. In the exemplary embodiment, the categories may include: sagittal, vertical, horizontal, and arch length. In this exemplary embodiment, the reference component field  1202  includes one common component within each dimension by which malocclusion is judged. The common pre-defined options field  1203  includes the various levels of malocclusion for that dimension of the category. For example, the common malocclusions for the right canine component of the sagittal category are: Full class 2+(greater than full cusp Class 2), Full (Cusp) Class 2, Partial Class 2 (also called end-on Class 2), and so on. Within each dimensional component selection is also a selection for “normal.” 
     Referring to  FIG. 12 , the number of options field  1204  in one embodiment includes the number of possible reference conditions in each category, and also a total number of possible combinations of reference conditions. For example, the sagittal category has seven (7) possible reference conditions for the canine relationship component and the vertical category has seven (7) reference conditions for the anterior overbite component. The example shown yields 7×7×7×7=2401 possible combinations of reference conditions for the four components, as shown in table  1200  of  FIG. 12 . In one embodiment, each of these 2,401 patient case combinations is stored in a database in storage unit  1107  ( FIG. 11 ), for example, by the central server  1109 . Since there can be numerous components used to describe each of the four main orthodontic dimensions and not just one component per dimension as illustrated, in practice, the total number of combinations that can be used to describe a patient may be substantially higher, but at the same time, will be a finite number such that it may be indexed, catalogued, and queried as described in  FIG. 11 . 
     In reference to the index table  1200  illustrated in  FIG. 12 , an identifier may be composed of a four-position, or “four-bit” matrix: ABCD. In this four-bit matrix, in one embodiment of the present invention, the “A” position in the matrix corresponds to the sagittal dimension, the “B” position in the matrix corresponds to the vertical dimension, the “C” position in the matrix corresponds to the horizontal dimension, and the “D” position in the matrix corresponds to the arch length dimension. 
     The actual number or letter in the position of each “bit” of the matrix may be associated with the corresponding condition within the category. For example, referring again to the exemplary table  1200  of  FIG. 12 , an identifier of 3256 represents: a right canine partial Class 2, with moderate anterior deep bite, upper midline to the left 0-1 mm, and lower moderate crowding. This “3256” identifier corresponds to an address in an indexing database stored in storage unit  1107  which has stored in the database, related clinical information for the particular pairing of “3256” to a user-defined treatment goal (for example, discussed in further detail below with reference to  FIG. 14 ). 
     Dental Characterization Database 
     Referring back to  FIG. 11 , the indexing system  1100  in one embodiment of the present invention may also be used to represent one or more teeth within a patient&#39;s dentition. Typically an adult patient&#39;s dentition includes 32 teeth. Dentists usually characterize five surfaces of each tooth: mesial, occlusal/incisal, distal, buccal/facial, and lingual. Each of these surfaces may be natural or covered by a restoration such as silver amalgam, composite, porcelain, gold, or metal crown. The tooth may also be missing or have been treated with a root canal or an implant. These combinations may be represented with an indexing system for the initial dentition, target dentition (treatment goal), and final dentition which is the outcome of the treatment. 
     For each tooth in a patient&#39;s dentition, there may be a number of possible conditions based on the characteristics of the tooth, such as the surface of the tooth and whether the tooth as been treated or is missing. The combinations of different possible conditions of the teeth define a matrix. An exemplary embodiment of the present invention includes a 32-position address within the matrix, where each position in the address corresponds to a tooth in a patient&#39;s dentition and includes a sub-address in which alphanumeric characters or other representations represent the current condition of the tooth. 
     A “5-bit” sub-address for each tooth includes positions 12345 where each of the positions “1” to “5” represents one of the five surfaces of the tooth. In particular, position 1 of the sub-address corresponds to the mesial surface of the tooth, position 2 of the sub-address corresponds to the occlusal or incisal surface of the tooth, position 3 of the sub-address corresponds to the distal surface of the tooth, position 4 of the sub-address corresponds to buccal or facial surface of the tooth, and position 5 of the sub-address corresponds to the lingual surface of the tooth. 
     Moreover, each of the following characters “A” to “N” corresponds to a condition of the particular surface of the tooth in the sub-address. 
     
       
         
           
               
               
             
               
                   
               
             
            
               
                 A = amalgam 
                 H = porcelain crown with root canal 
               
               
                 B = composite 
                 I = amalgam with root canal 
               
               
                 C = porcelain veneer 
                 J = composite with root canal 
               
               
                 D = gold 
                 K = gold crown with implant 
               
               
                 E = porcelain crown 
                 L = porcelain crown with implant 
               
               
                 F = gold crown 
                 M = missing 
               
               
                 G = gold crown with root canal 
                 N = natural 
               
               
                   
               
            
           
         
       
     
     For example, consider the following patient identifier 1:NNABN. The identifier 1:NNABN would represent: tooth number 1 of a 32-bit address which has a natural mesial surface (subaddress position 1), an occlusal amalgam (subaddress position 2), a natural distal surface (subaddress position 3), a buccal/facial composite (subaddress position 4), and a natural lingual surface (subaddress position 5). 
     In an exemplary embodiment of patient&#39;s initial dentition, target dentition (treatment goal), and final dentition, such example may be configured as: 
     TotalAddress=SubAddress1:SubAddress2:SubAddress3 
     SubAddress1=Teeth 1-32 initial 
     SubAddress2=Teeth 1-32 target 
     SubAddress3=Teeth 1-32 current, timepoint today 
     whereby each of the of the 1-32 may further include an addition sub-matrix of 1-5 surfaces as previously described. 
     In this manner, dentists may easily query their practice database to determine how much dental work has been done and remains to be done. They can also track trends of use in their practice and what are the most common procedures in the practice. The patient matrix may also be used in forensics for patient identification purposes, as well as for national security and other security purposes. 
       FIG. 13  illustrates an exemplary tabulation of the possible treatment goals of the indexing system treatment goal matrix stored in the storage unit  1107  of  FIG. 111  in accordance with one embodiment of the present invention. Four examples of treatment goals are the following: 
     Treatment Goal 1: Pre-restorative set-up—the objective of this goal is to better position specific teeth for the purpose of improved placement of dental restorations such as crowns, bridges, and implants. Some of the patient&#39;s dental components may be left as is (untreated) if they do not contribute to the purpose of improvement of the restorative goal. 
     Treatment Goal 2: Esthetic alignment—the objective of this goal is to align the patient&#39;s anterior teeth for the purpose of improved esthetics. Generally speaking, the patient&#39;s bite may be left as is (untreated) if it does not contribute to the purpose of improving the esthetic component of the patient&#39;s smile. 
     Treatment Goal 3: Anterior function improvement—the objective of this goal is to improve the anterior function of the teeth while also improving the anterior esthetic component. Generally speaking, the patient&#39;s posterior occlusion may be left as is if it does not contribute to the improvement of the canine function and/or anterior esthetics. 
     Treatment Goal 4: Optimal set-up—the objective of this goal is to make the entire bite close to “textbook” ideal, including both the canine and molar function. 
       FIG. 14  illustrates an expanded version of  FIG. 13  using the characteristics as defined by the tabulation shown in  FIG. 12 . More specifically, each of the four treatment goals identified in  FIG. 13  may be further refined and formatted according to the tabulation and indexing shown in  FIG. 12  to describe the target objective of treatment in greater detail according to each individual component. 
     For example, for the treatment goal 1 for pre-restorative set-up, an example of this goal according to the 4-bit matrix format in  FIG. 12  may be XXX4 where the “X” is the patient&#39;s existing relationship for that component left untreated, and only the fourth digit is planned for treatment. Furthermore, for the treatment goal 2 for esthetic alignment, an example of this goal according to the 4-bit matrix format in  FIG. 2  may be XX44 where “X” is the patient&#39;s existing relationship for that component left untreated, and only the third and fourth digits (representing the transverse and arch length components, respectively) are planned for treatment. 
     In addition, for treatment goal 3 for anterior function improvement, an example of this goal according to the 4-bit matrix format in  FIG. 12  may be 4X44 whereby “X” is the patient&#39;s existing relationship for that component left untreated. In this example, only the second digit component (corresponding to the vertical dimension) is not planned for treatment. Finally, for treatment goal 4 for optimal set-up, an example of this goal according to the 4-bit matrix defined in  FIG. 12 , may be 4444. 
     There are various ways to generate an identifier which represents a patient&#39;s unique problem or case type. Traditionally, the method has been to describe and define a characteristic and have the trained individual subjectively identify the condition or “label” which best represents the patient&#39;s condition. To reduce the variability in this method requires calibration and/or objective measures to define each of the labels. 
     Another method involves using a visual image-based interface. To characterize a patient&#39;s dentition, a user compares the patient&#39;s dentition to images of reference dentition conditions which depict the severity of malocclusion, or lack thereof. The user then identifies where the patient&#39;s dentition condition falls within a range of reference conditions depicting malocclusion and selects the image that either best represents the patient, or selects a relative position of the patient&#39;s condition from a continuous gradient of patient image depictions of the specific problem. The visual image interface can be presented to the user without any descriptions or labels to avoid any pre-conceived biases associated with the label. 
     Visual images have been previously described in the ICON indexing system for example, to describe an esthetic component of the patient. In the ICON system, the assessor selects 1 of 10 images which best represents the patient&#39;s anterior esthetic component. Through calibration, multiple users are then able to determine a patient&#39;s esthetic component with reasonable consistency. The use of a visual interface to capture every component of the patient&#39;s orthodontic dental condition however, has not previously been described as an interface for creation of a digital patient database. 
       FIG. 15  illustrates the lower arch length component  1500  for use in the indexing system in accordance with one embodiment of the present invention. This illustration of the lower arch length component  1500  is an exemplary visual scale allowing the user to select an image which is similar to the patient&#39;s dentition condition. Referring to  FIG. 5 , there are shown seven images of the lower arch, each representing a possible reference condition for the lower arch length category. In this exemplary embodiment, images  1501 - 1507  represents the 7 images corresponding to the individual fields for the “Lower Arch Length” component of “Arch Length” dimension of  FIG. 12 . The user simply selects which of the seven images is best represented in the patient. Or they may be able to select where in between two adjacent images the patient can be best described. They do not need to know what the technical label or term is; they simply need to select an image or area between two images based on direct comparison of the existing condition to the pictures presented. 
     In the exemplary embodiment shown in  FIG. 15 , each of the seven images  1501 - 1507  has a corresponding predefined alphanumeric character. Thus, when an image is selected, the associated predefined alphanumeric character is added to the identifier address of the patient. By labeling each category with an alphanumeric character, the patient&#39;s dentition may be characterized through alphanumeric addressing. The output to the user may explain the specific details of their selection in greater detail, including the technical description and treatment options associated with such a condition. In an alternate embodiment, an alphanumeric character may be generated when the user selects the area in between adjacent images, representing that the patient&#39;s condition falls in between the condition of the adjacent images selected. The user interface may also be a combination of both direct selection of the image as well as in-between selection of images. 
     Referring now to  FIG. 16 , an exemplary doctor and patient information display  1600  for the indexing system  1100  is illustrated in accordance with one embodiment of the present invention. This display  600  includes information input by a user into fields  1601 - 1603  to identify a patient. In particular, a patient&#39;s name is input into field  1601 , a patient&#39;s gender is input into field  1602 , and a patient&#39;s primary concern(s) is input into field  1603 . The preferred embodiment of field  1603  is a check-box selection of pre-defined possible conditions which can then be catalogued according to the selections of the user. It will be appreciated that other patient information may be added. Once the patient information has been entered, a user can select a predefined input command or button to move onto the next display, which is illustrated in  FIG. 17 . 
     Referring to  FIG. 17 , an exemplary selection process display  1700  is shown for the sagittal dimension (matrix address position “A” in FIG.  12 )—right buccal, right canine/cuspid component. A series of images of reference dentition conditions  1701 - 1703  are displayed in conjunction with buttons  1704  allowing the images to be scrolled to the left or right. A user clicks the left or right arrow buttons  1704  to select the image of the reference dentition condition that best reflects the patient&#39;s current condition specifically at the location(s) indicated by the focusing arrows indicated in  1702 . In this exemplary embodiment, a user clicks the left or right arrow buttons to select the cuspid (canine) relationship that is similar to a patient&#39;s current occlusion. 
     Once the selection is made, the next button  1705  is pressed to move onto the next screen. The exemplary selection process display  1700  also includes buttons  1706 - 1709  to allow a user to go back, access a glossary, ask for advice, and save the information, respectively. 
     Referring to  FIG. 18 , an exemplary selection process display  1800  is shown for the sagittal category—left buccal, left cuspid component. A series of images of reference dentition conditions  1801 - 1803  are displayed in association with buttons  804  allowing the images to be scrolled to the left or right. A user clicks the left or right arrow buttons  804  to select the image of the reference dentition condition that best reflects the patient&#39;s current condition. In this exemplary embodiment, a user clicks the left or right arrow buttons to select the cuspid relationship that is similar to a patient&#39;s current occlusion. 
     Once the selection is made, the next button  1805  is pressed to move onto the next display which is illustrated in  FIG. 19 . The exemplary selection process display  1800  also includes buttons  1806 - 1809  to allow a user to go back, access a glossary, ask for advice, and save the information, respectively. 
     Referring to  FIG. 19 , an exemplary selection process display  1900  is shown for the vertical dimension (matrix address position “B” in FIG.  12 )—anterior overbite component. A series of images of reference conditions  1901 - 1903  are displayed in conjunction with buttons  1904  allowing the images to be scrolled to the left or right. A user clicks the left or right arrow buttons  1904  to select the image of the reference dentition condition that best reflects the patient&#39;s current condition. In this exemplary embodiment, a user clicks the left or right arrow buttons  1904  to select the anterior vertical overbite relationship component that is similar to a patient&#39;s degree of open or deep bite. 
     Once the selection is made, the next button  1905  is pressed to move onto the next display, which is illustrated in  FIG. 20 . The exemplary selection process display  1900  also includes buttons  1906 - 1909  to allow a user to go back, access a glossary, ask for advice, and save the information, respectively. 
     Referring to  FIG. 20 , an exemplary selection process display  2000  is shown for the horizontal/transverse dimension (matrix address position “C” in FIG.  12 )—upper and lower midline components. An image  1010  representing a reference dentition condition is altered by clicking the upper arrows  2001 - 2002  corresponding to the upper arch of the image  2010 , and by clicking the lower arrows  2003 - 2004  corresponding to the lower arch of the image  1010  to best match the midline of the image  2010  to a patient&#39;s midline component relationship. Once the selection is made, the next button  2005  is pressed to move onto the next display, which is illustrated in  FIG. 21 . The exemplary selection process display  2000  of  FIG. 20  also includes buttons  2006 - 2009  to allow a user to go back, access a glossary, ask for advice, and save the information, respectively. 
     Referring to  FIG. 21 , an exemplary selection process display  2100  is shown for the upper arch length category. An image of a reference dentition condition  2101  and descriptions of reference dentition conditions  2102 ,  2103  are displayed in association with buttons  2104  allowing the reference dentition condition image and descriptions to be scrolled to the left or right. A user clicks the left or right arrow buttons  2104  to select the image or description of the reference dentition condition that best reflects the patient&#39;s current condition. In this exemplary embodiment, a user clicks the left or right arrow buttons  2104  to select the image or description of the reference dentition condition that is similar to a patient&#39;s upper arch length from the occlusal view. In this particular embodiment, if there is both crowding and spacing present, a user is instructed to use the net amount of crowding or spacing, but it may be possible to have each aspect captured independently. 
     Again, once the selection is made, the next button  2105  is pressed to move onto the next display which is illustrated in  FIG. 22 . The exemplary selection process display  2100  also includes buttons  2106 - 2109  to allow a user to go back, access a glossary, ask for advice, and save the information, respectively. 
     Referring to  FIG. 22 , an exemplary selection process display  2200  is shown for the arch length dimension (matrix position “D” in FIG.  12 )—lower arch length component. An image of a reference dentition condition  2201  and descriptions of reference dentition conditions  2202 ,  2203  are displayed in association with buttons  2204  allowing the reference dentition condition image and descriptions to be scrolled to the left or right. A user clicks the left or right arrow buttons  2204  to select the image or description of the reference dentition condition that best reflects the patient&#39;s current condition for the lower arch length component of arch length. In this exemplary embodiment, a user clicks the left or right arrow buttons  2204  to select the image or description of the reference dentition condition that is similar to a patient&#39;s lower arch length from the occlusal view. In this example, if both crowding and spacing are present, the user is instructed to use the net amount of crowding or spacing. It may be possible however to capture crowding and spacing independently in order to derive the net discrepancy. 
     Once the selection is made, the next button  2205  is pressed to move onto the next display, which is illustrated in  FIG. 23 . The exemplary selection process display  2200  of  FIG. 22  also includes buttons  2206 - 2209  to allow a user to go back, access a glossary, ask for advice, and save the information, respectively. 
       FIG. 23  illustrates an exemplary patient summary tabulation  1300  for output display on terminal  1101  for use in the indexing system in accordance with one embodiment of the present invention. The exemplary patient summary display  2300  is generated from the information input from previous displays 1600-2200, as illustrated in corresponding  FIGS. 16-22 , respectively. Referring to  FIG. 23 , the selections made during the processes and displays described above and illustrated in conjunction with  FIGS. 16-22  are summarized as shown in the summary display  2300  in one embodiment of the present invention. 
     For example, for each reference dentition category including sagittal, vertical, horizontal and arch length, the corresponding malocclusion reference component (for example, right canine, anterior overbite, upper midline relative to lower midline, and lower arch length, respectively), and each of which is associated with a selected one of the pre-defined options (for example, right canine partial Class 2, moderate anterior deep bite, upper midline to left 0-1 mm, and lower moderate crowding, respectively). Also can be seen from  FIG. 23  is the selected value of the selected pre-defined options  1203  ( FIG. 12 ) as tabulated and illustrated in  FIG. 12 . The user is also able to edit the dentition condition information in each of the categories by selecting the corresponding “EDIT” button to go back to the page desired and reselecting the image corresponding to that category. 
     In this manner, in one embodiment of the present invention, the information input by the user during the selection process is indexed and catalogued in a patient database (for example, the database  2400  shown in  FIG. 24  below) of the indexing system  1100 . In one embodiment of the present invention, the selection process discussed in conjunction with  FIGS. 16-22  for the indexing and cataloguing is transparent to the user. The patient information input by the user in the selection process is used to generate both the summary display as illustrated in  FIG. 23  and an identifier representing the dentition conditions of the patient.  FIGS. 16-22  illustrate the selection process display  1600  for use in the indexing system  1100  for various categories in accordance with one embodiment of the present invention. This is the selection process for inputting a patient&#39;s dentition information. It will be appreciated that although  FIGS. 17-22  illustrate reference dentition conditions represented by pictorial images, the present invention is not intended to be limited to such representations. The reference dentition conditions may also be represented by symbols, icons, descriptions, graphs, 3-D objects, radiographs, forms, and other types of images. The reference conditions may also be user-defined through an interactive graphical image such that the user best recreates the condition observed in the patient as a means of input for the system. 
       FIG. 24  illustrates a patient database  2400  for use in the indexing system  1100  in accordance with one embodiment of the present invention. The patient database  2400  includes a patient field  2401 , an indexing database address field  2402 , and one or more category fields  2403 . In the exemplary database of  FIG. 24 , the category fields  2403  include a sagittal category field  2404 , a vertical category field  2405 , a horizontal category field  2406 , an upper arch length category field  2407 , a lower length category field  2408 , a rotation field  2409 , a vertical correction field  2410 , and a midline correction field  2411 . 
     Referring to  FIG. 24 , the patient field  2401  includes the patient name. The indexing database address field  2402  includes the patient identifier. This patient identifier corresponds to an address in the indexing database  1300 , for example, as shown in  FIG. 13 . The address in the indexing database  1300  is associated with treatment information for that particular diagnostic combination. The category fields  2403 , which in this exemplary embodiment are the sagittal category field  2404 , the vertical category field  2405 , the horizontal category field  2406 , the upper arch length category field  2407 , the lower length category field  2408 , the rotation field  2409 , the vertical correct field  2410 , and the midline correct field  2411 , include the patient&#39;s one or more dentition conditions in the respective categories. For example, referring to  FIG. 24 , patient L. Smith&#39;s dentition condition in the sagittal category field  2404  is “Class I”. Patient M. Jones&#39; dentition condition in the upper arch length category field  2407  is “normal”. The category fields  2403  also indicate whether the particular reference condition is eligible for treatment (for example, shown by the Y/N indicator). 
     In this manner, the patient identifier may be configured to represent the patient conditions. For example, referring to the indexing database address field  2402 , it is shown that L. Smith&#39;s identifier is “55772752”. Since the identifier includes eight positions, the identifier is an eight-position matrix. The number in each position of the identifier represents a particular condition within a particular category. In this exemplary embodiment, the first position of the identifier matrix represents the patient condition in the sagittal category. For example, the sagittal category field  2404  indicates that L. Smith has a “Class I” malocclusion. Thus, the number 5 in the first position of the identifier represents a “Class I” malocclusion in the sagittal category. 
     Referring back to  FIG. 24 , the second position of the identifier matrix represents the patient condition in the vertical category. For example, the vertical category field  2405  indicates that L. Smith has normal occlusion. Thus, the number 5 in the second position of the identifier represents a normal occlusion in the vertical category. The third position of the identifier matrix represents the patient condition in the horizontal category. For example, the horizontal category field  2406  indicates that L. Smith has a crossbite. Thus, the number 7 in the third position of the identifier represents crossbite in the horizontal category. 
     Moreover, the fourth position of the identifier matrix represents the patient condition in the upper arch length category. For example, the upper arch length category field  2407  indicates that L. Smith has moderate crowding. Thus, the number 7 in the fourth position of the identifier represents moderate crowding in the upper arch length category. In addition, the fifth position of the identifier matrix represents the patient condition in the lower arch length category. For example, the lower arch length category field  2408  indicates that L. Smith has moderate spacing. Thus, the number 2 in the fifth position of the identifier represents moderate spacing in the lower arch length category. 
     In addition, the sixth position of the identifier matrix represents the patient condition in the rotation category. For example, the rotation category field  2409  indicates that L. Smith has &lt;20° rotation. Thus, the number 7 in the sixth position of the identifier represents &lt;20° rotation in the rotation category. Further, the seventh position of the identifier matrix represents the patient condition in the vertical correction category. For example, the vertical correct category field  2410  indicates that L. Smith has no extrusion. Thus, the number 5 in the seventh position of the identifier represents no intrusion/extraction in the vertical correction category. 
     Finally, referring yet again to  FIG. 24 , the eighth position of the identifier matrix represents the patient condition in the midline correct category. For example, the midline correct category field  2411  indicates that L. Smith has &gt;2 mm midline correction. Thus, the number 2 in the eighth position of the identifier represents &gt;2 mm midline correct in the midline correction category. 
     In this manner, in one embodiment of the present invention, the conditions in the categories may be arranged in a predetermined order each associated with a numerical (for example “the number 2 in the eight position of the identifier representing greater than 2 mm midline correction in the midline correction category for patient L. Smith), or a predefined identifier such as, alphanumeric characters, symbols and the like. In a further embodiment, the conditions in the categories may be arranged in ascending order by difficulty and the categories are sorted in order of difficulty so that it is possible to define a matrix where 11111111 represents the mildest case and 33333333 is the most severe case in an eight position matrix identifier, for example as described above. Additionally, each index in the matrix is weighted to derive a composite score of the overall case. 
       FIG. 25  illustrates an alternate embodiment of the present invention for capturing an address in the selection process for use in the indexing system.  FIG. 25  illustrates the table  1200  of  FIG. 12  used directly as a graphical interface. In such embodiment, each reference condition as shown and illustrated in tabular format as rectangles may be represented as user input buttons with text which may be clicked to highlight and select the appropriate reference condition. The assumption for this type of interface is that the user understands the definitions of the text in order to select the appropriate button. When the buttons are pressed to select a particular reference condition, the selections are highlighted (shown in bold in  FIG. 25 ). Clicking any button twice will deselect the initial selection so that another selection can be made. In this manner, users who are more familiar with the various types of reference conditions may be able to input the information more quickly than through a visual-image based interface. In this example, the generated address would be “3256.” The “Selected Value” column on the right side of  FIG. 25  is in one embodiment, transparent to the user/patient, and not displayed to the user since the address has no relevance to the end user, and is important only for the database query. 
       FIG. 26  illustrates an exemplary series of database addresses generated by combining the initial condition address with the treatment goal address in one embodiment of the present invention. As indicated from the exemplary table  1200  of  FIG. 12 , there are 2,701 possible patient case combinations or addresses for four components of seven possible selection options each. Thus, an identifier address points to one of the 2,701 possible combinations in the database. Each identifier is associated with a field stored in a database of the storage unit  1107  ( FIG. 11 ). An identifier may be extended so that it represents the patient&#39;s condition at different time points. For example, the database may be structured such that time points for initial dentition, target dentition, and actual final dentition are captured as separate addresses. For example, consider the following address:
         ABCD: A*B*C*D*:A**B**C**D**       

     In this arrangement, the first four positions “A” to “D” of the matrix represent the patient&#39;s initial dentition (as previously described), positions “A*” to “D*” of the matrix represent the patient&#39;s target dentition or treatment goal, and positions “A**” to “D**” of the matrix represent the patient&#39;s actual final dentition or treatment outcome. Because the number of positions in the matrix may be variable, and since each position can include symbols, alphanumeric characters or other representations, the depth of individual patient cases that is stored is may be detailed and specific to the patient and/or the associated profile or condition. Using the 4 possible treatment outcomes illustrated in  FIG. 14  and the 2,701 possible combinations in  FIG. 12 , this equates to 2,701×4=10,804 possible paired combinations between initial and goal. 
       FIG. 27  illustrates an exemplary database for a patient with an index address of “3256” and the four possible treatment goals of 1 through 4. The resulting four combined addresses have different data for each of the parameters. This information is reported to the user either (1) upon completion of the case characterization, whereby all possible treatment goal options are presented to the user or (2) upon completion of the case characterization and selection of a single treatment goal, whereby only the information from this address-goal pair is presented to the user. 
     For each of these paired combinations, a combined address can be created, with database assets in a “digital mailbox” associated with each address. Assets for each digital mailbox can include, but is not limited to: treatment plan information related to the case-treatment goal pairing, such as a text description of the treatment condition and goals, treatment precautions, treatment length estimates, doctor skill set requirements, prescription data, sample case data, and case difficulty. This data may be generated using expert opinion, computational algorithms, and/or historical case content. 
     For example, with respect to  FIG. 23 , where the case is identified as a “3256” and using the 4 types of treatment goals as shown in  FIG. 14 , combining the two yields four distinct database addresses: 3256:1, 3256:2, 3256:3, and 3256:4. Each of the addresses can be populated with information specific to the case-treatment goal combination. All four options can be simultaneously displayed to the user as “treatment options” or the user can select a specific treatment goal and have a single specific resulting treatment option data displayed. It is also conceivable that the user may also select any number of specific goals, and each of the data associated with each goal selected is reported to the user depending on the initial condition parameters selected. 
       FIG. 28  illustrates a process  2800  for identifying a dentition problem or condition of a patient. The process  2800  is discussed more fully in conjunction with  FIGS. 16-27 . At step  2801 , the user starts by entering identification information such as doctor and patient name, in addition to patient chief concern(s) ( FIG. 16 ). In one embodiment, this comparison may be performed by the central server  1109  ( FIG. 11 ) based on information received, for example, from the terminal  1101 , and/or based on stored information retrieved from the data storage unit  1107 . This and other related transactions in the process may be performed over a data network such as the internet via a secure connection. The user then selects one of two user interfaces to input the patient&#39;s dental condition. The preferred method for the novice user is the visual-user interface ( FIG. 17-22 ) shown as step  2802 . The advanced user will likely prefer the alternative user interface ( FIG. 25 ) illustrated as step  2803 . 
     Referring to  FIG. 28 , at step  2804  an initial dentition condition of a patient in each category is compared to one or more reference conditions in the same category. After comparing the initial dentition condition of the patient in each category to one or more reference conditions for each respective category, at step  2804 , the selected reference condition similar to the initial patient condition in the same category is received. Thereafter, at step  2805 , the patient identifier is then generated based on the combination of alphanumeric characters corresponding to the selected reference conditions. Edits can be made to the inputs during the summary page review (step  2804 ) until the user is satisfied with the information submitted. 
     The output following the completion of the data input is a translation summary ( FIG. 23 ), which formats the user input into technically relevant and correct terminology. At the same time, the user input is also translated into a database address representing the current patient condition (FIG.  25 )—step  2805 . Once the database address is created, the user can choose to view all possible treatment options for this patient (OPTION  1 ), or specifically select a treatment goal and view the specific goal associated with the user&#39;s selection (OPTION  2 ). To view all the possible treatment options for the patient (OPTION  1 ), the database ( FIG. 27 ) is queried at step  2806 , and all data associated with the input address is presented to the user at step  2807  (END  1 ). 
     Referring back to  FIG. 28 , if the user desires to select a specific goal, the specific goal is first defined by the user through a selection interface at step  2808  ( FIG. 13 ), and the selection is then translated into a database address at step  2809  ( FIG. 14 ), and the two addresses (patient condition and treatment goal) merged to create a combined address or index at step  2810  ( FIG. 26 ). This combined address is then used to query the database at step  2811  ( FIG. 27 ) in order to produce data specific to a single patient condition-treatment goal combination at step  2812  (END  2 ). 
     For OPTION  2 , it may also be possible that the user can select multiple goals and only the data specific to those selected goals be produced for the user. Once the user has reached END  1  or END  2 , the user has the option to purchase the product for the purpose of any one of the selected treatment goals, by selecting a pre-populated or semi-populated treatment prescription which can be part of the output data presented to the user through this experience. 
     As discussed above, the user interface can provide one or more patient cases from the indexing database that matches the patient problem. Additionally, a range of patient cases from the indexing database that address specific components of the patient&#39;s problem can be provided. In this manner, in one embodiment of the present invention, search tools may be created to run statistics using the patient identifiers. For example, one search request may be to find all 131X cases. In this exemplary search request, X represents any character in the fourth position of the address. Thus, the search request would be to find all patient identifiers having “131” as the first 3 digits of their patient identifier address. 
     By labeling historically treated cases with this identification methodology, a catalog of orthodontic treatment can be created for future reference when planning treatment and assessing treatment outcomes. The result is a front-end user interface for capturing the description of an orthodontic condition and classifying the orthodontic condition in a systematic scalable way. Referring again to  FIG. 28 , once the identifier is generated at step  2805 , one or more treatment options can be determined using information generated from a database query. The generated one or more treatment options may be stored in the data storage unit  1107  ( FIG. 11 ), and also, be provided to the terminal  1101  for display on the display unit. 
     Given the diagnosis and treatment planning of orthodontic treatments can include a significant subjective component that may vary depending upon the doctor&#39;s preferences and level of training, the indexing system provides a comprehensive, robust, and a substantially objective approach to establishing the patient diagnosis, treatment goal, and treatment plan. The patient identifier of the present invention which represents the patient&#39;s case, as well as the target treatment goal and final outcome enables treatment outcome profiles to be objectively catalogued, and for the catalog to be evaluated based on probabilities and distributions. Indices such as prognosis and case difficulty can be assigned to matrix combinations, enabling similar cases to be treated like similarly successful cases. Treatment options may be correlated for completeness and ease of use. Treatment products, such as appliances, may be associated with specific matrix combinations so that their suggested use is more closely tied to a successful outcome. 
     Within the scope of the present invention, other embodiments for inputting a patient&#39;s dentition condition are also contemplated. For example, a configurable three-dimensional model may be used to input the information. In such embodiment, the user may recreate the patient dentition condition for the dimension. Alternatively, a three-dimensional graphics model may be staged to represent the entire range of possible reference conditions for any given dimension. In such embodiment, a user manipulates a slider to match a stage of the range which is closest to the actual patient condition. 
     It will also be appreciated that this method of objectively characterizing a case according to individual components is not limited to the time points of pre-treatment, treatment goal, and post-treatment, and that any time point during treatment and following treatment may be also catalogued in a similar fashion using the same input and database system. 
     It will also be appreciated that in this exemplary embodiment although only one reference condition is discussed as being selected for a particular category, the present invention is not intended to be so limiting. The selection of one or more reference conditions within each category is within the scope of the present invention. 
     Accordingly, a method for characterizing a dentition of a patient in one embodiment of the present invention includes comparing an initial patient condition in each of a plurality of dentition categories with one or more reference conditions in each of the plurality of dentition categories, where each of the one or more reference conditions has a corresponding representation, selecting at least one reference condition in one or more of the plurality of dentition categories, where each selected reference condition is similar to the initial patient condition in a same dentition category, and generating a patient identifier based on the corresponding representations of each selected reference condition. 
     In one aspect, the plurality of dentition categories may include at least two of: sagittal, vertical, horizontal, upper and arch length dimensions, or a number of a tooth in a dentition of a patient. 
     Moreover, the method may further include determining whether each initial patient condition is indicated for treatment based on treatment information corresponding to the selected reference condition, providing one or more treatment options for each initial patient condition indicated for treatment, where the one or more treatment options include one or more of a treatment description, a treatment goal, a time to complete the treatment, a difficulty level, and a skill level to complete the treatment, an example of the treatment option. 
     Further, in another aspect, the method may also include comparing at least a portion of the patient identifier with one or more reference identifiers, wherein each of the one or more reference identifiers includes an initial reference dentition and a final reference dentition, selecting at least one reference identifier from the one or more reference identifiers, wherein the selected reference identifier includes the portion of the patient identifier, and determining a final patient dentition based on the final reference dentition corresponding to the selected reference identifier. 
     A method for characterizing a dentition of a patient in accordance with another embodiment of the present invention includes receiving an initial dentition of a patient, generating an initial profile representing the initial dentition of the patient, identifying an initial malocclusion from the initial profile, and comparing at least a portion of the initial profile with one or more reference profiles of reference dentitions, where said one or more reference profiles includes a reference malocclusion substantially similar to the initial malocclusion at the beginning, during any treatment stage, or final outcome treatment position. 
     Also, the method may also include the step of selecting at least one of the one or more reference profiles, where said one or more reference profiles has a related final reference dentition. 
     Additionally, in a further aspect, the method also includes providing a target dentition of the patient based on the final reference dentition. 
     The step of generating an initial profile in one embodiment may include visually categorizing the initial dentition of the patient. 
     Moreover, the method may also include identifying one or more treatment options associated with the one or more reference profiles. 
     A system for providing an orthodontic profile indexing system in accordance with still another embodiment of the present invention includes a storage unit, and a controller unit operatively coupled to the storage unit, and configured to compare an initial patient condition in each of a plurality of dentition categories with one or more reference conditions in each of the plurality of dentition categories, where each of the one or more reference conditions has a corresponding representation, select at least one reference condition in one or more of the plurality of dentition categories, where each selected reference condition is similar to the initial patient condition in a same dentition category, and to generate a patient identifier based on the corresponding representations of each selected reference condition. 
     The controller unit may be configured to determine whether each initial patient condition is eligible for treatment based on treatment information corresponding to the selected reference condition, and to provide one or more treatment options for each initial patient condition eligible for treatment. 
     Also, the controller unit may be further configured to compare at least a portion of the patient identifier with one or more reference identifiers, where each of the one or more reference identifiers includes an initial reference dentition and a final reference dentition, to select at least one reference identifier from the one or more reference identifiers, where the selected reference identifier includes the portion of the patient identifier, and to determine a final patient dentition based on the final reference dentition corresponding to the selected reference identifier. 
     In addition, a terminal may be operatively coupled to the controller unit, and configured to transmit one or more of the initial patient condition, where the terminal may be further configured to include a display unit. 
     A system for characterizing a dentition of a patient in accordance with still another embodiment of the present invention includes a central controller unit configured to generate an initial profile representing the initial dentition of the patient, to identify an initial malocclusion from the initial profile, and to compare at least a portion of the initial profile with one or more reference profiles of reference dentitions, wherein said one or more reference profiles includes a reference malocclusion substantially similar to the initial malocclusion. 
     In another aspect, a user terminal may be operatively coupled to the central controller unit, the user terminal configured to transmit the initial dentition of the patient. 
     The central controller unit may be further configured to select at least one of the one or more reference profiles, wherein said one or more reference profiles has a related final reference dentition. 
     In addition, the central controller unit may be further configured to provide a target dentition of the patient based on the final reference dentition. 
     The central controller unit may be further configured to visually categorize the initial dentition of the patient. 
     Moreover, the central controller unit may be further configured to identify one or more treatment options associated with the one or more reference profiles. 
     In yet still a further aspect, a storage unit may be configured to store one or more of an initial profile an initial malocclusion, and a reference malocclusion. 
     The various processes described above including the processes performed by the central server  1109  ( FIG. 11 ) in the software application execution environment in the indexing system  1100  including the processes and routines described in conjunction with the Figures may be embodied as computer programs developed using an object oriented language that allows the modeling of complex systems with modular objects to create abstractions that are representative of real world, physical objects and their interrelationships. The software required to carry out the inventive process, which may be stored in the memory or data storage unit  1107  of the indexing system or internally (not shown) within the central server  1109 , may be developed by a person of ordinary skill in the art and may include one or more computer program products. 
     While the characterization of adult dentition has been discussed in conjunction with the embodiments described above, the various embodiments of the present invention may be used for the characterization of child dentitions. In addition, in accordance with the embodiments of the present invention, the various aspects of the present invention may be manually implemented by the user, for example, using print-out documentation, visual graphics, and/or photographic images of the conditions and/or treatment options, and further, may include, within the scope of the present invention, manual computation or calculation of the results. In this manner, within the scope of the present invention, the various embodiments discussed above in the context of a computerized system for implementing the aspects of the present invention, may be implemented manually. 
     In accordance with various aspects of the present disclosure, systems and methods for facilitating automated dental measurements and diagnostics of teeth malocclusion to facilitate dental treatment are provided. Such systems and methods may be practiced with minimum human intervention for measurement of tooth anatomy characteristics, crowding, spacing and/or to establish diagnosis for malocclusion aspects such as open bite, cross bite, AP classes and the like. For example, in accordance with an exemplary embodiment, with reference to  FIG. 29A , an exemplary method  2900  for facilitating automated dental measurements and diagnostics of teeth malocclusion is configured to acquire a digital model of a patient&#39;s teeth ( 2902 ), to automatically establish and/or detect reference data and/or features ( 2904 ), and to automatically compute dental measurements ( 2906 ). In accordance with other exemplary embodiments, for example with reference to  FIG. 29C , an exemplary automated system and method  2900  may also be configured to automatically detect malocclusions ( 2920 ) and/or to automatically compute orthodontic or dental indices ( 2930 ). 
     Such automated dental measurement and diagnostic techniques of method  1100  may be conducted with one or more computer-based systems through the use of one or more algorithms. For example, with reference to  FIG. 29B , an exemplary computerized system  2910  for facilitating automated dental measurements and diagnostics of teeth malocclusion may comprise one or more computer-based systems or modules, such as a system  2912  configured for storing digital data sets, computational modules  2914  configured for computing one or more dental measurements, and/or a system  2916  configured for compiling treatment cases data, such as may be used to facilitate later treatments of other patients. Systems  2912 ,  2914  and/or  2916  may comprise one or more microprocessors, memory systems and/or input/output devices for processing data and information, comprising one or more software algorithms configured for computing and/or performing other functions set forth herein. For example, exemplary computerized system  2910  may comprise memory or storage subsystems, processors, network interfaces, input/output devices and/or other components as disclosed in U.S. Pat. No. 6,767,208, entitled “System and Method for Positioning Teeth”, assigned to Align Technology, Inc., or any other computerized system components used for computational orthodontics. 
     The acquiring of a digital model of a patient&#39;s teeth ( 2902 ) may be achieved in various manners now known or hereinafter devised, such as any methodology or process for converting scanned data into a digital representation. Such a digital model includes modeling of the plurality of teeth of a patient, including relative positions of arches or other like indicia in digital models of teeth. Thus, such methodology or processes may include, for example, those disclosed in U.S. Pat. No. 5,975,893, entitled “Method and System for Incrementally Moving Teeth” assigned to Align Technology, Inc. For example, with reference to an overall method for producing the incremental position adjustment appliances for subsequent use by a patient to reposition the patient&#39;s teeth as set forth in U.S. Pat. No. 5,975,893, as a first step, a digital data set representing an initial tooth arrangement is obtained, referred to as the IDDS. Such an IDDS may be obtained in a variety of ways. For example, the patient&#39;s teeth may be scanned or imaged using well known technology, such as X-rays, three-dimensional x-rays, computer-aided tomographic images or data sets, magnetic resonance images, and the like. 
     Methods for digitizing such conventional images to produce data sets are well known and described in the patent and medical literature. By way of example, one approach is to first obtain a plaster cast of the patient&#39;s teeth by well known techniques, such as those described in “Graber, Orthodontics: Principle and Practice,” Second Edition, Saunders, Philadelphia, 1969, pp. 401-415. After the tooth casting is obtained, it may be digitally scanned using a conventional laser scanner or other range acquisition system to produce the IDDS. The data set produced by the range acquisition system may, of course, be converted to other formats to be compatible with the software that is used for manipulating images within the data set. General techniques for producing plaster casts of teeth and generating digital models using laser-scanning techniques are described, for example, in U.S. Pat. No. 5,605,459. In accordance with another exemplary embodiment, the acquiring of a digital model of a patient&#39;s teeth may also comprise such techniques as disclosed in U.S. Pat. No. 6,767,208, entitled “System and Method for Positioning Teeth”, assigned to Align Technology, Inc. Accordingly, any methodology or process for converting scanned data into a digital representation or otherwise for the acquiring of a digital model of a patient&#39;s teeth may be utilized to acquire digital model of the teeth ( 2902 ). 
     The automatic establishment and/or detection of reference data and/or features ( 2904 ) may comprise various steps and processes and provide various types of references and features. Such reference data and/or features may be automatically detected by system  2910  based on the digital acquisition of teeth, and are configured to allow the clinician to have various dental measurements automatically calculated to facilitate diagnosis and treatment. For example, system  2910  may automatically assess two-dimensional and three-dimensional digital scan data from the digital model to automatically identify selected reference data and features configured to facilitate desired measurements. Such selected reference data and features may be suitably recognized through databases, libraries and other like memory applications that comprise reference data and dental features characteristics that may enable the automatic recognition of such reference data and features through computer-implemented methods. 
     In accordance with an exemplary embodiment, with reference to an exemplary method  3000  illustrated in  FIG. 30 , after the acquisition of a digital model of teeth ( 3002 ), and based on the corresponding scanned data, the automatic establishment and/or detection of reference data and/or features ( 3004 ) may comprise the automatic establishment of reference objects ( 3042 ), the automatic establishment of reference frames ( 3044 ), the automatic detection of anatomical dental features ( 3046 ), and the automatic construction of orthodontic references ( 3048 ). Any of one or more of these such features, frames and references may then be used by system  3010  to automatically calculate suitable measurements. 
     The automatic establishment of reference objects ( 3042 ) comprises the determination of various reference entities (planes, regions, etc) for facilitating measurements of teeth position and/or metrics characteristics for teeth, and in particular, to enable system  3100  to automatically determine how far apart certain features, objects or other items are from one another. With reference to  FIG. 31 , a computerized system  3100 , such as system  3100 , may obtain or otherwise establish one or more reference objects. For example, a reference object may comprise an occlusal plane  3102 , which is an average plane of supporting planes which approximate the tips of central incisors and cusps of the first molars in such a way that all teeth points (except of the points of the canines) are on one of its sides, and/or an occlusal surface  3104 . For example, an occlusal plane may include an average plane of supporting planes that pass through at least three points including two tip points of the incisors. An example of occlusal plane is illustrated in  FIG. 32B . 
     Another reference object may be a facial axis of clinical crown (FACC)  3106  that comprises a geodesic curve on the facial part of the crown of a tooth between occlusal and gingival extremities (for incisors and canines and bicuspids) and a curve along the buccal groove for molars, thus having an occlusal endpoint and gingival endpoint. An example of the facial axis of clinical crown (FACC) is illustrated in  FIG. 32C . In addition, a reference object may comprise a curve through facial axis (FA) points  3108 , and/or an embrasure curve  3110  that comprises a curve through the facial axis points of the same arch. A facial axis (FA) point includes mid point of the facial axis of clinical crown (FACC), and an example is also illustrated in  FIG. 32C . 
     Another reference object may also comprise a middle plane of clinical crown (MPCC)  3112  that comprises a middle plane of a corresponding tooth that is transversal to the facial surface of the clinical crown. Referring to the Figures, an example of the middle plane of clinical crown (MPCC)  3112  is illustrated in  FIG. 32C . Moreover, reference objects may further comprise a facial axis (FA) line  3114  that comprises a tangent line to the FACC at the facial axis point, a facial plane of the clinical crown (FPCC)  3116  that comprises a tangent plane to the facial surface of a clinical crown at the facial axis (FA) point, and a facial normal (FN) line  3118  that comprises a normal line in the facial plane to the facial axis line at a facial axis (FA) point. Referring yet again to the Figures an example of facial axis (FA) line, a facial plane of the clinical crown (FPCC), and facial normal (FN) line are each illustrated in  FIG. 32C . 
     Still further, reference objects may comprise a center of resistance  3120  that is a conventional point through which passes every axis of tooth rotation, an arch form curve  3122 , an arch form template  3124  comprises the final positions of arch form curves for successfully treated cases, and/or an arch form ideal curve  3126  that comprises an arch form template curve that best fits an existing arch form (after appropriate scaling). Accordingly, the automatic establishment of reference objects ( 3042 ) may comprise the determination of various static reference, landmarks, and/or other like objects for facilitating measurements of metrics or characteristics for teeth. 
     The automatic establishment of reference frames ( 3044 ) comprises the establishing of reference frames to provide a dynamic assessment. In other words, in one embodiment, the automatic establishment of reference frames ( 3044 ) allows determination of how much the teeth are supposed to move, or have actually moved. For example, the establishing of frames based on the FACC for each tooth may be used to automatically assess teeth movement; however, the automatic establishment of reference frames ( 3044 ) may be based on any manner for establishing and/or using frames, with such determination being through computer-implemented methods herein. 
     Referring to  FIG. 30 , the automatic detection of anatomical dental features ( 3046 ) comprises the automatic detection of real landmarks associated with the digital teeth model. For example, automatic detection of anatomical dental features ( 3046 ) may comprise the automatic detection of landmarks such as cusps, ridges, grooves, contact points or any other physical reference points or landmarks associated with teeth. In addition, the automatic construction of orthodontic references ( 3048 ) may comprise the automatic construction of abstract landmarks, as opposed to real landmarks as automatically detected in ( 3046 ). For example, the automatic construction of orthodontic references ( 3048 ) may comprise the constructing of occlusal planes, arch boxes and/or any other abstract landmarks that may be suitably constructed. 
     Once any one or more of the reference objects, reference frames, dental features have been automatically established, detected and/or constructed, system  2910  may perform automatic computation of dental measurements. The automatic computation of dental measurements ( 3006 ) may comprise, for example, the computation of teeth dimensions and/or arch dimensions and the like based on one or more of the dental features, reference objects and/or frames established, detected and/or constructed in processes ( 3042 ), ( 3044 ), ( 3046 ) and ( 3048 ). In accordance with exemplary embodiments, such computation of dental measurements may be obtained by automatically performing point-to-point measurements, point-to-plane measurements, plane-to-plane measurements, point to curve or surface measurements, distance along a curve, angle between directions, angle between direction and plane, angle between planes measurements, area of surface, volume, or combinations thereof, and based upon which, performing automatic orthodontic measurements such as overjet and overbite measurements. 
     In one embodiment, the automatic computation of dental measurements ( 3006 ) may comprise the computation of numerous teeth dimensions, e.g., size, shape and other tooth characteristics, as well as the computation of arch dimensions and the like, e.g., the relative position of the teeth in the arch. For example, the automatic computation of dental measurements ( 3006 ) may comprise the computation of the angular relative position, such as crown angulation (tip), crown inclination (torque) and/or crown rotation (around the tooth axis). Crown angulation is the angle from a facial axis (FA) line and the projection the occlusal plane normal to the facial plane. An example of the crown angulation is shown in  FIG. 32F . Crown inclination is an angle between the projections of the facial axis (FA) line and the projection of the occlusal plane normal to the middle plane of the clinical crown (MPCC). An example of crown inclination is shown in  FIG. 32G . Crown Rotation is an angle between projection of the facial normal (FN) line onto the occlusal plane and the ideal arch form for a particular tooth. An example of crown rotation is shown in  FIG. 32H . 
     In addition, the automatic computation of dental measurements ( 3006 ) may comprise the computation of the translational relative position of each tooth with respect to the other teeth, such as the crown level and/or crown prominence. Crown level comprises the signed distance from the high point of the FACC to the occlusal plane, while crown prominence comprises the signed distance from the facial axis (FA) point to the ideal arch form for a tooth. An example of crown prominence is illustrated in  FIG. 32I . 
     The automatic computation of dental measurements ( 3006 ) may also comprise the computation of the relative overlap, e.g., the local overcrowding or how the teeth obstruct each other. Measurements of local overlap may be suitably applied from a tooth to one or both of any adjacent teeth, such as orthogonal order and/or overlap region. Orthogonal order measurement is an order of the tooth and an adjacent tooth in the direction orthogonal to the arch form, and may determine whether the tooth is in front of or behind the adjacent tooth. Overlap region of a tooth is the amount of overlap of a tooth on an adjacent tooth, as determined by projection on arch curve or facial plane of the tooth. 
     Another computational dental measurement may comprise the relative coherence that is a derivative of the angular relative position and translational relative position measurements. In particular, the relative coherence of two adjacent teeth is a difference of their relative positions with respect to the angular and translational components. 
     A further computational dental measurement includes tooth shape characteristics such as crown shapes that are important for the efficacy of the dental aligners with respect to the aligners&#39; grip that is associated with the tooth shape characteristics. For example, the mesial to distal width, the buccal to lingual width, the crown height (length of the crown in the direction of normal to the occlusal plane) and other like tooth characteristics, such as spline curve at around crown base (spline curve on the boundary of crown and gingival surface) may be automatically measured by system  2910 . More particularly, the mesial to distal width of a tooth may be defined as the distance between the horizontal extreme points of the tooth with respect to the facial plane of the clinical crown (FPCC), where the distance is measured in the direction of the middle plane normal. An example of the mesial to distal width is illustrated in  FIG. 32E . Moreover, the buccal to lingual width of a tooth may include the distance between the innermost and outermost points of the tooth with respect to the middle plane of the clinical crown (MPCC), where the distance is measured in the direction of the facial plane normal. An example of buccal to lingual width of a tooth is illustrated in  FIG. 32D . 
     The automatic computation of dental measurements ( 3006 ) may also comprise the computation of various other dental features such incisor, canine, pre-molar and molar characteristics. For example, the table below illustrates dental features and associated types of features that may be used for automatic dental measurement of misalignment and/or malocclusion, where the types of features include point features (described by center point and region around the center point, for example a cusp) and elongated features (described by center curve and region around the center curve, for example, groove and ridge): 
     
       
         
           
               
               
               
             
               
                   
                   
               
               
                   
                 Dental Features 
                 Type of Feature 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                 Incisor Features 
                 Incisal Ridge 
                 Elongated 
               
               
                   
                 Upper Incisal Occlusal Surface 
               
               
                 Canine Features 
                 Canine Cusp 
                 Point 
               
               
                   
                 Canine Ridge 
                 Elongated 
               
               
                 Pre-molar Features 
                 Buccal cusp 
                 Point 
               
               
                   
                 Lingual cusp 
                 Point 
               
               
                   
                 Central Groove 
                 Elongated 
               
               
                 Molar Features 
                 Mesiobuccal cusp 
                 Point 
               
               
                   
                 Mesiolingual cusp 
                 Point 
               
               
                   
                 Distobuccal cusp 
                 Point 
               
               
                   
                 Distolingual cusp 
                 Point 
               
               
                   
                 Central Groove 
                 Elongated 
               
               
                   
                 Buccal Groove 
                 Elongated 
               
               
                   
               
            
           
         
       
     
     Accordingly, the automatic computation of dental measurements ( 3006 ) may comprise the computation of teeth dimensions and/or arch dimensions and the like based on one or more of the static or dynamic dental features, reference objects and/or frames established, detected and/or constructed. 
     In particular embodiments, the automatic computation of dental measurements ( 3006 ) may further include the determination of dental alignment characteristics such as incisor ridge alignment angle, mandibular posterior alignment characteristic, maxillary posterior alignment characteristic, posterior marginal ridge relative height, buccolingual inclination distance of posterior tooth, and interproximal contacts. More specifically, the incisor ridge alignment angle may be determined by calculating the angle between the projection of the ridge into occlusal plane and the tangent to arch form template curve at the closest point. Mandibular posterior alignment characteristic shows the relative parallel alignment of the curve through the mesiobuccal and distobuccal cusps of the molars and buccal cusps of the premolars, to the arch form template curve. 
     Additionally, regarding the curve through central grooves of molars and premolar cusps of premolars, the maximally posterior alignment characteristic is ratio of the longest to the shortest distance between the referenced curve through central groove and arch form template respectively. Posterior marginal ridge relative height is the difference between the distances to occlusal plane of marginal ridges of adjacent teeth, whereas buccolingual inclination distance of posterior tooth is the biggest distance between the lingual cusps and occlusal plane. In addition, interproximal contacts of a tooth are a pair of distances between the tooth and its adjacent tooth. 
     Moreover, the automatic computation of dental measurements ( 3006 ) in further embodiments may comprise the automatic computation of bite characteristics including, for example, occlusal contacts and occlusal relationship along arch. More specifically, occlusal contact characteristics of mandibular premolar or molar are the set of distances of the buccal cusps to the central groove (occlusal surface) of the opposing tooth. Occlusal contact characteristics of maxillary premolar or molar are the set of distances of the lingual cusps to the central groove (occlusal surface) of the opposing tooth, and occlusal contact characteristics of mandibular anterior teeth (incisors and canines) are the distances from the ridges to occlusal surface of opposing anterior teeth. 
     The occlusal relationship along arch provides assessment of how far the bite is from Class I, Class II or Class III relationships. For example, occlusal relationship characteristics of Class I include the following measurements:
         Distance from maxillary canine cusp tip to the embrasure contact between mandibular canine and adjacent premolar (measured along the arch curve);   Distance from buccal cusp of the first maxillary premolar to the interproximal contact between mandibular premolars (measured along the arch curve);   Distance from buccal cusp of the second maxillary premolar to the interproximal contact between mandibular premolar and first molar (measured along the arch curve);   Distance from mesiobuccal cusp of the first maxillary molar to the buccal groove of mandibular first molar (measured along the arch curve);   Distance from mesiobuccal cusp of the second maxillary molar to the buccal groove of mandibular second molar (measured along the arch curve).       

     The following tables illustrate pairs of entities in the definition of Class I 
     
       
         
           
               
               
               
             
               
                   
                   
               
               
                   
                 Maxillary Buccal Cusp 
                 Mandibular Contact Point Between 
               
               
                   
                   
               
             
            
               
                   
                 Canine cusp tip 
                 Canine and adjacent premolar 
               
               
                   
                 First premolar 
                 Premolars 
               
               
                   
                 Second premolar 
                 Premolar and first molar 
               
               
                   
                   
               
            
           
         
       
     
                                             Maxillary Mesiobuccal Cusp   Mandibular Buccal Grove of                          First molar   First molar           Second molar   Second Molar                        
Further, occlusal relationship characteristics of Class II comprise the following measurements:
         Distance from mesiobuccal cusp of maxillary first molar to the embrasure or interproximal contact between mandibular second premolar and first molar (measured along the arch curve).   Distance from mesiobuccal cusp of maxillary second molar to the embrasure or interproximal contact between mandibular first molar and second molar (measured along the arch curve).       

     The following table illustrates pairs of entities in the definition of Class II: 
     
       
         
           
               
               
               
             
               
                   
                   
               
               
                   
                 Maxillary Mesiobuccal Cusp 
                 Mandibular Contact Point Between 
               
               
                   
                   
               
             
            
               
                   
                 First molar 
                 Second premolar and First molar 
               
               
                   
                 Second molar 
                 First Molar and Second Molar 
               
               
                   
                   
               
            
           
         
       
     
     Additionally, occlusal relationship characteristics of Class III comprise the following measurements:
         Mandibular premolars are extracted;   Distance from buccal cusp of maxillary second premolar to the buccal groove of mandibular first molar (measured along the arch curve).       

     The following table illustrates pairs of entities in the definition of Class III 
     
       
         
           
               
               
               
             
               
                   
                   
               
               
                   
                 Maxillary Buccal Cusp 
                 Mandibular Buccal Grove of 
               
               
                   
                   
               
             
            
               
                   
                 Second premolar 
                 First molar 
               
               
                   
                   
               
            
           
         
       
     
     In this manner, in particular embodiments, system  2910  may be configured to automatically calculate occlusal characteristics, such as, by performing computation of bite characteristics including, for example, occlusal contacts and occlusal relationship along arch. 
     In accordance with another exemplary embodiment, an automated method may also be configured to automatically detect malocclusions ( 3020 ). For example, the extent and amount of malocclusions such as crowding, spacing, overjet, open bite, cross bite, angle classes, occlusal contact and/or the like may be automatically determined from the various dental measurements computed ( 3006 ) and then suitably displayed by system  2910  to a clinician to facilitate dental treatment and planning. 
     For example, overjet as illustrated in one embodiment in  FIG. 32A , may be determined by the distance from the intersection point of a curve through the midpoints of mandibular incisal ridges with the middle plane on mandibular arch, to buccal surfaces of the maxillary incisors (in closed positions). Furthermore, overbite may be defined as a percentage of buccal surfaces of maxillary incisors that are above the curve through the midpoints of mandibular incisal ridges, as illustrated, for example, in  FIG. 32J . In this manner, in one embodiment, automatic determination of malocclusions may be achieved accurately, reliably and/or efficiently. 
     In accordance with further exemplary embodiments, an automated method may also be configured to automatically compute orthodontic or dental indices ( 3030 ), such as for the evaluation and assessment of malocclusions obtained under ( 3020 ). For example, the automatic computation of orthodontic or dental indices such as Peer Assessment Ratings (PAR) indices, ABO discrepancy indices, ABO objective grading systems and the like may also be realized based on the measurement results that are automatically computed ( 3006 ). The PAR index is a widely accepted standard for measuring and scoring the malocclusion of teeth in orthodontics, but has traditionally been a very time consuming approach, significantly influenced by subjective perceptions and thus prone to inaccuracies and error. However, using the automated diagnostic methods ( 3000 ), such errors, inaccuracies and time-delays are substantially reduced and/or eliminated. In accordance with an exemplary embodiment, system  2910  may automatically compute a PAR index by determination and assessment of measurements, such as finding anterior teeth contact points, determining posterior bite classes, detecting or measuring posterior open bite or cross bite, calculating anterior overjet and/or measuring midline discrepancies. 
     System  2910  may compute such indices to allow a clinician to efficiently assess the complexity of a case and/or measure the quality of treatment outcome during any stage of the treatment process. In addition, the use of such indices may allow treatment cases to be scored or evaluated before, during and/or after treatment. Comparisons may be suitably made between projected and actual treatment. In a further embodiment, system  2910  may be configured to compute the indices based upon information related to previously treated cases that include similar dental parameters to the patient&#39;s computed dental measurements ( 2906 ), including, for example, the patient&#39;s initial dental conditions and the determined orthodontic measurements. Additional detailed information related to indexing dental characteristics and associated treatments, for example, is described in pending application Ser. No. 11/379,198 entitled “Method and System for Providing Indexing and Cataloguing of Orthodontic Related Treatment Profiles and Options” assigned to the Assignee of the present application, and the disclosure of which is incorporated herein by reference for all purposes. 
     In the manner described above, in accordance with various aspects of the present disclosure, a system and method for facilitating automated dental measurements and diagnostics of teeth to facilitate dental treatment are provided, such as may be used for measurement and assessment of tooth anatomy characteristics, crowding, spacing and/or establish diagnosis for malocclusion aspects such as misalignment, open bite, cross bite, AP classes and the like, all realized with minimum human intervention. In accordance with an exemplary embodiment, an exemplary automated system and method are configured to acquire a digital model of a patient&#39;s teeth, automatically establish and/or detect reference data and features based on such digital model, and then automatically compute dental measurements based on such reference data and/or features. Such automated dental measurement and diagnostic techniques may be conducted with one or more computer-based systems through the use of one or more algorithms or computer codes. 
     The acquiring of a digital model of a patient&#39;s teeth may be achieved in various manners now known or hereinafter devised. In accordance with an exemplary embodiment, the automatic establishment and/or detection of reference data and features is based on the digital model data and may comprise the establishment of reference objects, the establishment of reference frames, the detection of anatomical dental features, and/or the construction of orthodontic features. The automatic computation of dental measurements may then be conducted based on one or more dental features and reference objects and frames. 
     In accordance with other exemplary embodiments, the automated system and method may also be configured to automatically detect malocclusion and/or to automatically compute orthodontic or dental indices. 
     Within the scope of the present disclosure, the various operational steps, as well as the components for carrying out the operational steps, may be implemented in alternate ways depending upon the particular application or in consideration of any number of cost functions associated with the operation of the system, e.g., various of the component and methodologies and/or steps may be deleted, modified, or combined with other components, methodologies and/or steps. Moreover, it is understood that various of the methods and steps disclosed herein, such as generating of IDDS, computation of measurements and/or indices may comprise any other techniques now known or hereinafter developed for facilitating such methods and steps. 
     Systems and methods are disclosed providing a database comprising a compendium of at least one of patient treatment history; orthodontic therapies, orthodontic information and diagnostics; employing a data mining technique for interrogating said database for generating an output data stream, the output data stream correlating a patient malocclusion with an orthodontic treatment; and applying the output data stream to improve a dental appliance or a dental appliance usage. 
     The achieved outcome, if measured, is usually determined using a set of standard criteria such as by the American Board of Orthodontics, against which the final outcome is compared, and is usually a set of idealized norms of what the ideal occlusion and bite relationship ought to be. Another method of determining outcome is to use a relative improvement index such as PAR, IOTN, and ICON to measure degrees of improvement as a result of treatment. 
     The present invention provides methods and apparatus for mining relationships in treatment outcome and using the mined data to enhance treatment plans or enhance appliance configurations in a process of repositioning teeth from an initial tooth arrangement to a final tooth arrangement. The invention can operate to define how repositioning is accomplished by a series of appliances or by a series of adjustments to appliances configured to reposition individual teeth incrementally. The invention can be applied advantageously to specify a series of appliances formed as polymeric shells having the tooth-receiving cavities, that is, shells of the kind described in U.S. Pat. No. 5,975,893. 
     A patient&#39;s teeth are repositioned from an initial tooth arrangement to a final tooth arrangement by making a series of incremental position adjustments using appliances specified in accordance with the invention. In one implementation, the invention is used to specify shapes for the above-mentioned polymeric shell appliances. The first appliance of a series will have a geometry selected to reposition the teeth from the initial tooth arrangement to a first intermediate arrangement. The appliance is intended to be worn until the first intermediate arrangement is approached or achieved, and then one or more additional (intermediate) appliances are successively placed on the teeth. The final appliance has a geometry selected to progressively reposition teeth from the last intermediate arrangement to a desired final tooth arrangement. 
     The invention specifies the appliances so that they apply an acceptable level of force, cause discomfort only within acceptable bounds, and achieve the desired increment of tooth repositioning in an acceptable period of time. The invention can be implemented to interact with other parts of a computational orthodontic system, and in particular to interact with a path definition module that calculates the paths taken by teeth as they are repositioned during treatment. 
     In general, in one aspect, the invention provides methods and corresponding apparatus for segmenting an orthodontic treatment path into clinically appropriate substeps for repositioning the teeth of a patient. The methods include providing a digital finite element model of the shape and material of each of a sequence of appliances to be applied to a patient; providing a digital finite element model of the teeth and related mouth tissue of the patient; computing the actual effect of the appliances on the teeth by analyzing the finite elements models computationally; and evaluating the effect against clinical constraints. Advantageous implementations can include one or more of the following features. The appliances can be braces, including brackets and archwires, polymeric shells, including shells manufactured by stereo lithography, retainers, or other forms of orthodontic appliance. Implementations can include comparing the actual effect of the appliances with an intended effect of the appliances; and identifying an appliance as an unsatisfactory appliance if the actual effect of the appliance is more than a threshold different from the intended effect of the appliance and modifying a model of the unsatisfactory appliance according to the results of the comparison. The model and resulting appliance can be modified by altering the shape of the unsatisfactory appliance, by adding a dimple, by adding material to cause an overcorrection of tooth position, by adding a ridge of material to increase stiffness, by adding a rim of material along a gumline to increase stiffness, by removing material to reduce stiffness, or by redefining the shape to be a shape defined by the complement of the difference between the intended effect and the actual effect of the unsatisfactory appliance. The clinical constraints can include a maximum rate of displacement of a tooth, a maximum force on a tooth, and a desired end position of a tooth. The maximum force can be a linear force or a torsional force. The maximum rate of displacement can be a linear or an angular rate of displacement. The apparatus of the invention can be implemented as a system, or it can be implemented as a computer program product, tangibly stored on a computer-readable medium, having instructions operable to cause a computer to perform the steps of the method of the invention. 
     Among the advantages of the invention are one or more of the following. Appliances specified in accordance with the invention apply no more than orthodontically acceptable levels of force, cause no more than an acceptable amount of patient discomfort, and achieve the desired increment of tooth repositioning in an acceptable period of time. The invention can be used to augment a computational or manual process for defining tooth paths in orthodontic treatment by confirming that proposed paths can be achieved by the appliance under consideration and within user-selectable constraints of good orthodontic practice. Use of the invention to design aligners allows the designer (human or automated) to finely tune the performance of the aligners with respect to particular constraints. Also, more precise orthodontic control over the effect of the aligners can be achieved and their behavior can be better predicted than would otherwise be the case. In addition, computationally defining the aligner geometry facilitates direct aligner manufacturing under numerical control. 
     A computer-implemented method for automated dental measurements in one embodiment includes acquiring a digital model of a patient&#39;s teeth, automatically detecting reference data or features based on the digital model, and automatically computing dental measurements based on said reference data or features, where the dental measurements are associated with an occlusal characteristic of the patient. 
     In one embodiment, automatically detecting reference data or features includes automatically establishing reference objects. 
     Further, automatically detecting reference data or features may include automatically establishing reference frames. 
     Also, automatically detecting reference data or features may include automatically detecting anatomical dental features. 
     Additionally, automatically detecting reference data or features may include automatically constructing orthodontic references. 
     Moreover, automatically establishing reference objects may include automatically establishing at least one of an occlusal plane, an occlusal surface, a facial axis of clinical crown (FACC), a curve through facial axis points, an embrasure curve, a middle plane of clinical crown (MPCC), a facial axis line (FA-line), a facial plane of the clinical crown (FPCC), a facial normal line (FN-line), a center of resistance, an arch form curve, an arch form template, or an arch form ideal curve. 
     The automatic establishing of reference frames in one aspect may include the establishing of frames to automatically determine the extent of movement of teeth. 
     Also, automatic establishing of reference frames may include the establishing of frames based on the FACC for each tooth. 
     The automatic detecting anatomical dental features may include the detection of at least one of cusps, ridges, grooves, and contact points for each tooth. 
     Additionally, the automatic constructing of orthodontic references may include the constructing of abstract landmarks. 
     The occlusal characteristic may include one or more of an overjet, an overbite, or a midline discrepancy. 
     The method in yet another embodiment may include automatic detection of the occlusal characteristic based on said dental measurements. 
     Additionally, the method may further include the automatic computation of orthodontic indices based on said dental measurements. 
     Also, the method may include the automatic computation of a PAR index based on said dental measurements. 
     In yet another aspect, the method may also include generating an instruction set associated with a configuration of sequential aligners for an orthodontic treatment. 
     The instruction set may be generated based on the computed dental measurements. 
     An apparatus for performing automated dental measurements in accordance with another embodiment includes one or more processors, and a memory coupled to the one or more processors, the memory configured for storing instructions which, when executed by the one or more processors, causes the one or more processors to acquire a digital model of the patient&#39;s teeth, automatically detect reference data or features based on said digital model, and automatically compute dental measurements based on said reference data or features, wherein the dental measurements are associated with an occlusal characteristic of the patient. 
     The memory may be further configured for storing instructions which, when executed by the one or more processors, causes the one or more processors to automatically detect reference data or features by automatically establishing reference objects. 
     The memory may be configured for storing instructions which, when executed by the one or more processors, causes the one or more processors to automatically detect reference data or features by automatically establishing reference frames. 
     In another aspect, the memory may be configured for storing instructions which, when executed by the one or more processors, causes the one or more processors to automatically detect reference data or features by automatically detecting anatomical dental features. 
     The memory may additionally be configured for storing instructions which, when executed by the one or more processors, causes the one or more processors to automatically detect reference data or features by automatically constructing orthodontic references. 
     In yet another aspect, the memory may be configured for storing instructions which, when executed by the one or more processors, causes the one or more processors to automatically establish reference objects by automatically establishing at least one of an occlusal plane, an occlusal surface, a facial axis of clinical crown (FACC), a curve through facial axis points, an embrasure curve, a middle plane of clinical crown (MPCC), a facial axis (FA) line, a facial plane of the clinical crown (FPCC), a facial normal (FN) line, a center of resistance, an arch form curve, an arch form template, or an arch form ideal curve. 
     The computerized modeling system in one aspect may be configured for the automatic establishing of reference frames by establishing of frames based on the FACC for each tooth. 
     Also, the memory may be further configured for storing instructions which, when executed by the one or more processors, causes the one or more processors to the automatically detect anatomical dental features by detecting of at least one of cusps, ridges, grooves, or contact points of a tooth. 
     Additionally, the memory may be configured for storing instructions which, when executed by the one or more processors, causes the one or more processors to automatically construct orthodontic references by constructing of occlusal planes and arch boxes. 
     The dental measurements may be associated with one or more of an overjet, an overbite, or a midline discrepancy. 
     In addition, the memory may be further configured for storing instructions which, when executed by the one or more processors, causes the one or more processors to automatically detect a malocclusion based on said dental measurements. 
     Moreover, in still another aspect, the memory may be configured for storing instructions which, when executed by the one or more processors, causes the one or more processors to automatically compute orthodontic indices based on the dental measurements. 
     In another embodiment, there is provided one or more storage devices having processor readable code embodied thereon, said processor readable code for programming one or more processors to perform a method for automated dental measurements, the method including acquiring a digital model of a patient&#39;s teeth, automatically detecting reference data or features based on the digital model, and automatically computing dental measurements based on said reference data or features, wherein the dental measurements are associated with an occlusal characteristic of the patient. 
     Various other modifications and alterations in the structure and method of operation of this disclosure will be apparent to those skilled in the art without departing from the scope and spirit of the disclosure. Although the disclosure has been described in connection with specific preferred embodiments, it should be understood that the disclosure as claimed should not be unduly limited to such specific embodiments. It is intended that the following claims define the scope of the present disclosure and that structures and methods within the scope of these claims and their equivalents be covered thereby.