Patent Publication Number: US-2022233275-A1

Title: Method and system for braces removal from dentition mesh

Description:
TECHNICAL FIELD 
     The disclosure relates generally to manipulation of elements that are represented by a three-dimensional mesh and more particularly to methods and apparatus for tooth crown surface characterization in a surface contour image that has been obtained using reflectance imaging. 
     BACKGROUND 
     Three-dimensional (3-D) imaging and 3-D image processing are of growing interest to dental/orthodontic practitioners for computer-aided diagnosis, for prosthesis design and fabrication, and for overall improved patient care. For cephalometric measurement and analysis, 3-D imaging and 3-D image processing offer significant advantages in terms of flexibility, accuracy, and repeatability. 3-D cephalometric analysis overcomes some of the shortcomings associated with conventional methods of two-dimensional (2-D) cephalometric analysis, such as 2-D geometric errors of perspective projection, magnification, and head positioning in projection, for example. 3-D cephalometrics has been shown to yield objective data that is more accurate, since it is based on calculation rather than being largely dependent upon discrete measurements, as is the case with 2-D cephalometrics. 
     Early research using 3-D cephalometrics methods employed 3-D imaging and parametric analysis of maxillo-facial anatomical structures using cone beam computed tomography (CBCT) of a patient&#39;s head. Using CBCT methods, a significant role of the 3-D cephalometric analysis was to define mathematical models of maxillary and mandibular arches for which the axes of inertia were calculated for each tooth or group of teeth. This, in turn, required the segmentation of individual teeth from the acquired CBCT head volume of a patient. 
     Conventionally, during an orthodontic treatment procedure, multiple 2-D X-ray cephalogram acquisitions are used to assess treatment progress. Conventional 3-D cephalometric analysis can also be used for this purpose, requiring multiple CBCT scans. However, both 2-D and 3-D radiographic imaging methods expose the patient to ionizing radiation. Reducing overall patient exposure to radiation is desirable, particularly for younger patients. 
     Optical intraoral scans, in general, produce contours of dentition objects and have been helpful in improving visualization of teeth, gums, and other intra-oral structures. Surface contour characterization using visible or near-visible light can be particularly useful for assessment of tooth condition and has recognized value for various types of dental procedures, such as for restorative dentistry. This can provide a valuable tool to assist the dental practitioner in identifying various problems and in validating other measurements and observations related to the patient&#39;s teeth and supporting structures. Surface contour information can also be used to generate 3-D models of dentition components such as individual teeth; the position and orientation information related to individual teeth can then be used in assessing orthodontic treatment progress. With proper use of surface contour imaging, the need: for multiple 2-D or 3-D X-ray acquisitions of a patient&#39;s dentition can be avoided. 
     A number of techniques have been developed for obtaining surface contour information from various types of objects in medical, industrial, and other applications. Optical 3-dimensional (3-D) measurement methods provide shape and spatial information using light directed onto a surface in various ways. Among types of imaging methods used for contour imaging are fringe or structured light projection devices. Structured light projection imaging uses patterned or structured light and camera/sensor triangulation to obtain surface contour information for structures of various types. Once the structured light projection images are processed, a point cloud can be generated. A mesh can then be formed from the point cloud or a plurality of point clouds, in order to reconstruct at least a planar approximation to the surface. 
     Mesh representation can be particularly useful for showing surface structure of teeth and gums and can be obtained using a handheld camera and without requiring harmful radiation levels. However, when using conventional image processing approaches, mesh representation has been found to lack some of the inherent versatility and utility that is available using cone-beam computed tomography (CBCT) or other techniques that expose the patient to radiation. One area in which mesh representation has yielded only disappointing results relates to segmentation. Segmentation allows the practitioner to identify and isolate the crown and other visible portions of the tooth from gums and related supporting structure. Conventional methods for segmentation of mesh images can often be inaccurate and may fail to distinguish tooth structure from supporting tissues. 
     Various approaches for addressing the segmentation problem for mesh images have been proposed, such as the following:
         (i) A method described in the article “Snake-Based Segmentation of Teeth from Virtual Dental Casts” by Thomas Kronfeld et al. (in Computer-Aided Design &amp; applications, 7(a), 2010) employs an active contour segmentation method that attempts to separate every tooth and gum surface in a single processing iteration. The approach that is described, however, is not a topology-independent method and can fail, particularly where there are missing teeth in the jaw mesh.   (ii) An article entitled “Perception-based 3D Triangle Mesh Segmentation Using Fast Marching Watershed” by Page, D. L. et al. (in  Proc. CVPI  vol II 2003) describes using a Fast Marching Watershed method for mesh segmentation. The Fast Marching Watershed method that is described requires the user to enter seed points manually. The seed points must be placed at both sides of the contours of the regions under segmentation. The method then attempts to segment all regions in one step, using seed information. For jaw mesh segmentation, this type of method segments each tooth as well as the gum at the same time. This makes the method less desirable, because segmenting teeth from the gum region typically requires parameters and processing that differ from those needed for the task of segmenting teeth from each other. Using different segmentation strategies for different types of dentition components with alternate segmentation requirements would provide better performance.   (iii) For support of his thesis, “Evaluation of software developed for automated segmentation of digital dental models”, J. M. Moon used a software tool that decomposed the segmentation process into two steps: separation of teeth from gingival structure and segmentation of whole arch structure into individual tooth objects. The software tool used in Moon&#39;s thesis finds maximum curvature in the mesh and requires the user to manually choose a curvature threshold to obtain margin vertices that are used for segmenting the tooth. The software also requires the user to manually edit margins in order to remove erroneous segmentation results. Directed to analysis of shape and positional characteristics, this software tool does not employ color information in the separation of teeth regions from the gum regions.   (iv) U.S. Patent application 20030039389 A1 entitled “Manipulating a digital dentition model to form models of individual dentition components” by Jones, T. N. et al. discloses a method of separating portions of the dentition model representing the adjacent teeth.       

     While conventional methods for tooth segmentation exhibit some level of success in a limited set of test cases, none of these methods appears to be robust and commercially viable. In addition, conventional methods do not appear to be able to properly segment orthodontic braces and brackets that frequently appear in scanned dentition mesh models. 
     At different intervals during the orthodontic treatment process, it is desirable to remove the physical bracket braces from the teeth before performing intraoral scanning in order to obtain a clear 3D view of the teeth mesh model for progress assessment. However, due to factors such as de-bonding, staining, and plaque accumulation on rough surfaces of the tooth, the enamel can be damaged by removing the braces. The enamel thickness lost during bracket removal has been estimated to be approximately 150 micron. To prevent damage and enamel loss, there would be advantages in forgoing removal of the brace features if possible. One solution is to scan the dentition/dental arch without removing the physical braces from the teeth, and clean up the dental arch mesh by mesh manipulation. 
     U.S. Pat. No. 8,738,165 to Cinader Jr. et al., entitled “Methods of preparing a virtual dentition model and fabricating a dental retainer therefrom”, discloses a virtual model of a dental patient&#39;s dentition provided by obtaining a digital data file of the patient&#39;s teeth and orthodontic appliances connected to the teeth, and combined with data from the data file with other data that represents surfaces of the teeth underlying the appliances. In the &#39;165 disclosure, the virtual model is used in preparing a physical model of the patient&#39;s current dentition that can be used to make a dental retainer. The &#39;165 disclosure also notes editing tools used in image manipulating software to remove the data representing the orthodontic appliances. Image manipulating software described in the &#39;165 disclosure is “Geomagic Studio” (from Geomagic, Inc. of Research Triangle Park, N.C.), in which portions of an image are identified and deleted by a technician using a computer mouse or other input device. The U.S. Pat. No. 8,738,165 disclosure further mentions software known as “ZBrush” (from Pixologic, Inc. of Los Angeles, Calif.) used to digitally/manually fine-tune and sculpt the combined data. These methods can require considerable operator skill and results can be highly subjective. 
     There is, then, a need for improved methods and/or apparatus, preferably with little or no human intervention, for segmentation of mesh representations of tooth and gum structures including bracket removal for tooth/crown surface reconstruction. 
     SUMMARY 
     An aspect of this application is to advance the art, of tooth segmentation and/or manipulation in relation to volume imaging and visualization used in medical and dental applications. 
     Another aspect of this application is to address, in whole or in part, at least the foregoing and other deficiencies in the related art. It is another aspect of this application to provide, in whole or in part, at least the advantages described herein. 
     Certain exemplary method and/or apparatus embodiments according to the present disclosure can address particular needs for improved visualization and assessment of 3D dentition models, where brace representations have been removed or reduced and tooth surfaces added or restored for clarity. Restored 3D dentition models can be used with internal structures obtained using CBCT and other radiographic volume imaging methods or can be correlated to reflectance image data obtained from the patient. 
     These objects are given only by way of illustrative example, and such objects may be exemplary of one or more embodiments of the application. Other desirable objectives and advantages inherently achieved by exemplary method and/or apparatus embodiments may occur or become apparent to those skilled in the art. The invention is defined by the appended claims. 
     According to one aspect of the disclosure, there is provided a method for generating a digital model of reconstructed dentition that can include obtaining a 3-D digital mesh model of the patient&#39;s dentition including braces, teeth, and gingival, modifying the 3-D digital mesh dentition model by removing wire portions of the braces therefrom, modifying the 3-D digital mesh dentition model by removing bracket portions of the braces therefrom, approximating teeth surfaces of the modified 3-D digital mesh dentition model previously covered by the wire portions and the bracket portions of the braces, and displaying, storing, or transmitting over a network to another computer, the reconstructed 3-D digital mesh dentition model. 
     According to another aspect of the disclosure, there is provided a method for generating a digital model of a patient&#39;s dentition, the method executed at least in part by a computer that can include acquiring a 3-D digital mesh that is representative of the patient&#39;s dentition along a dental arch, wherein the digital mesh includes braces, teeth, and gingival tissue; modifying the 3-D digital mesh to generate a digital mesh dentition model by: (i) processing the digital mesh and automatically detecting one or more initial bracket positions from the acquired mesh; (ii) processing the initial bracket positions to identify bracket areas for braces that lie against tooth surfaces; (iii) identifying one or more brace wires extending between brackets; (iv) removing one or more brackets and one or more wires from the dentition model; (v) forming a reconstructed tooth surface within the digital mesh dentition model where the one or more brackets have been removed; and displaying, storing, or transmitting over a network to another computer, the modified 3-D digital mesh dentition model. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The foregoing and other objects, features, and advantages of the invention will be apparent from the following more particular description of the embodiments of the invention, as illustrated in the accompanying drawings. Elements of the drawings are not necessarily to scale relative to each other. 
         FIG. 1  is a schematic diagram that shows components of an imaging apparatus for surface contour imaging of a patient&#39;s teeth and related structures. 
         FIG. 2  shows schematically how patterned light is used for obtaining surface contour information using a handheld camera or other portable imaging device. 
         FIG. 3  shows an example of surface imaging using a pattern with multiple lines of light. 
         FIG. 4  shows a point cloud generated from structured light imaging, such as that shown in  FIG. 3 . 
         FIG. 5  shows a polygon mesh in the simple form of a triangular mesh. 
         FIG. 6A  is a logic flow diagram that shows a hybrid sequence for mesh segmentation according to an embodiment of the present disclosure. 
         FIG. 6B  is a logic flow diagram that shows a workflow sequence for hybrid segmentation of the tooth according to an embodiment of the present disclosure. 
         FIG. 7A  shows an example of a poorly segmented tooth. 
         FIG. 7B  shows an example of an improved segmentation. 
         FIG. 8A  shows an example of a seed line trace pattern. 
         FIG. 8B  shows an example of a block line trace pattern. 
         FIGS. 9A, 9B and 9C  show operator interface screens for review and entry of markup instructions for refining tooth mesh segmentation processing according to certain embodiments of the present disclosure. 
         FIG. 10  is a logic flow diagram that shows a sequence for bracket removal from the tooth mesh surface according to an exemplary embodiment of the application. 
         FIG. 11  shows an example of a dentition mesh containing teeth, brackets and gingival. 
         FIG. 12  is a diagram that shows exemplary resultant separated teeth from a 3D dentition mesh according to an exemplary embodiment of the application. 
         FIGS. 13A-13C  shows an example of removing a bracket from a tooth surface of a 3D dentition mesh and reconstructing the tooth surface afterwards. 
         FIGS. 13D and 13E  are diagrams that show a hole on tooth mesh surface where a bracket is removed and an initial patch approximated to fill the hole. 
         FIG. 13F  is a diagram that shows an initial arrangement of triangles in a tooth surface mesh patch and a modified arrangement of triangles for a tooth surface mesh patch. 
         FIG. 13G  shows an exemplary corrected 3D dentition mesh. 
         FIG. 14  is a logic flow diagram that shows an exemplary sequence for automatic braces and brackets detection and removal by processing logic according to an embodiment of the present disclosure. 
         FIG. 15  is a logic flow diagram showing a process for bracket area detection. 
         FIG. 16  shows images for a sequence that follows steps given in  FIG. 15 . 
         FIG. 17  shows exemplary coarse brackets obtained using the described sequence. 
         FIG. 18  shows braces wire detection. 
         FIG. 19  shows an arrangement of vertices for mask generation. 
         FIG. 20  shows the pruning operation for masks that can inaccurately extend to the opposite side in schematic representation. 
         FIG. 21  shows a post-processing sequence. 
         FIG. 22  shows an exemplary Fast Marching process. 
         FIG. 23  shows exemplary Fast March computation for arrival time from different seed-points along mask boundaries. 
         FIG. 24  shows results of using a sequence of different approaches for refinement of bracket regions according to an embodiment of the present disclosure. 
         FIG. 25  shows steps of an optional refinement of bracket regions using a convex hull computation. 
         FIG. 26  shows fine tuned bracket regions obtained using the described sequence. 
         FIG. 27  shows the recovered tooth surface following bracket removal. 
         FIG. 28  is a logic flow diagram that shows a sequence for bracket removal from the tooth mesh surface according to another exemplary embodiment of the application. 
         FIG. 29  shows an operator interface screen embodiment for review and entry of delineation instructions for separating brackets from tooth mesh according to one exemplary embodiment of the application.  FIG. 29  also shows an example of a closed contour or snake encircling a bracket. 
         FIG. 30  shows an example of highlighted mesh vertices within a closed contour. 
         FIG. 31  shows an example of a reconstructed tooth surface after the bracket is removed. 
         FIGS. 32-34  are diagrams that shows respectively, an example of dentition model with brackets, the same dentition model with brackets identified, and reconstructed teeth after brackets are removed according to one exemplary embodiment of the application. 
         FIG. 35A  is a diagram that shows an example of a dentition mesh containing teeth, bridged brackets and gingival tissue. 
         FIG. 35B  is a diagram that shows an example dentition mesh with bridges (e.g., wires) between brackets broken according to exemplary embodiments of the application. 
         FIG. 35C  is a diagram that shows an example dentition mesh illustrating detection of bridges (e.g., wires). 
         FIG. 36  shows example results of bracket removal and surface reconstruction after breaking the bridge wires according to exemplary embodiments of the application. 
         FIG. 37  is a logic flow diagram that shows a sequence for bridged bracket removal from the tooth mesh surface according to an embodiment of the present disclosure. 
         FIG. 38  is a logic flow diagram that shows a sequence for bridged bracket removal from the tooth mesh surface according to another embodiment of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS 
     The following is a detailed description of exemplary embodiments, reference being made to the drawings in which the same reference numerals identify the same elements of structure in each of the several figures. 
     Where they are used, the terms “first”, “second”, and so on, do not necessarily denote any ordinal or priority relation, but may be used for more clearly distinguishing one element or time interval from another. 
     The term “exemplary” indicates that the description is used as an example, rather than implying that it is ideal or preferred. 
     The term “in signal communication” as used in the application means that two or more devices and/or components are capable of communicating with each other via signals that travel over some type of signal path. Signal communication may be wired or wireless. The signals may be communication, power, data, or energy signals which may communicate information, power, and/or energy from a first device and/or component to a second device and/or component along a signal path between the first device and/or component and second device and/or component. The signal paths may include physical, electrical, magnetic, electromagnetic, optical, wired, and/or wireless connections between the first device and/or component and second device and/or component. The signal paths may also include additional devices and/or components between the first device and/or component and second device and/or component. 
     In the context of the present disclosure, the terms “pixel” and “voxel” may be used interchangeably to describe an individual digital image data element, that is, a single value representing a measured image signal intensity. Conventionally an individual digital image data element is referred to as a voxel for 3-dimensional or volume images and a pixel for 2-dimensional (2-D) images. For the purposes of the description herein, the terms voxel and pixel can generally be considered equivalent, describing an image elemental datum that is capable of having a range of numerical values. Voxels and pixels have attributes of both spatial location and image data code value. 
     “Patterned light” is used to indicate light that has a predetermined spatial pattern, such that the light has one or more features such as one or more discernable parallel lines, curves, a grid or checkerboard pattern, or other features having areas of light separated by areas without illumination. In the context of the present disclosure, the phrases “patterned light” and “structured light” are considered to be equivalent, both used to identify the light that is projected onto the head of the patient in order to derive contour image data. 
     In the context of the present disclosure, the terms “viewer”, “operator”, and “user” are considered to be equivalent and refer to the viewing practitioner, technician, or other person who views and manipulates a contour image that is formed from a combination of multiple structured, light images on a display monitor. 
     A “viewer instruction”, “operator instruction”, or “operator command” can be obtained from explicit commands entered by the viewer or may be implicitly obtained or derived based on some other user action, such as making an equipment setting, for example. With respect to entries entered on an operator interface, such as an interface using a display monitor and keyboard, for example, the terms “command” and “instruction” may be used interchangeably to refer to an operator entry. 
     In the context of the present disclosure, a single projected line of light is considered a “one dimensional” pattern, since the line has an almost negligible width, such as when projected from a line laser, and has a length that is its predominant dimension. Two or more of such lines projected side by side, either simultaneously or in a scanned arrangement, provide a two-dimensional pattern. In exemplary embodiments, lines of light can be linear, curved or three-dimensional. 
     The terms “3-D model”, “point cloud”, “3-D surface”, and “mesh” may be used synonymously in the context of the present disclosure. The dense point cloud is formed using techniques familiar to those skilled in the volume imaging arts for forming a point cloud and relates generally to methods that identify, from the point cloud, vertex points corresponding to surface features. The dense point cloud is thus generated using the reconstructed contour data from one or more reflectance images. Dense point cloud information serves as the basis for a polygon model at high density for the teeth and gum surface. 
     According to the present disclosure, the phrase “geometric primitive” refers to basic 2-D geometric shapes that can be entered by the operator in order to indicate areas of an image. By way of example, and not limitation, geometric primitives can include lines, curves, points, and other open shapes, as well as closed shapes that can be formed by the operator, such as circles, closed curves, rectangles and squares, polygons, and the like. 
     Embodiments of the present disclosure provide exemplary methods and/or apparatus that can help to eliminate the need for multiple CBCT scans for visualization of tooth and jaw structures. Exemplary methods and/or apparatus embodiments can be used to combine a single CBCT volume with optical intraoral scans that have the capability of tracking the root position at various stages of orthodontic treatment, for example. To achieve this, the intraoral scans are segmented so that exposed portions, such as individual tooth crowns, from the intraoral scan can be aligned with the individual tooth and root structure segmented from the CBCT volume. 
       FIG. 1  is a schematic diagram showing an imaging apparatus  70  for projecting and imaging using structured light patterns  46 . Imaging apparatus  70  uses a handheld camera  24  for image acquisition according to an embodiment of the present disclosure. A control logic processor  80 , or other type of computer that may be part of camera  24  controls the operation of an illumination array  10  that generates the structured light and controls operation of an imaging sensor array  30 . Image data from surface  20 , such as from a tooth  22 , is obtained from imaging sensor array  30  and stored in a memory  72 . Control logic processor  80 , in signal communication with camera  24  components that acquire the image, processes the received image data and stores the mapping in memory  72 . The resulting image from memory  72  is then optionally rendered and displayed on a display  74 . Memory  72  may also include a display buffer for temporarily storing display  74  image content. 
     In structured light projection imaging of a surface, a pattern of lines is projected from illumination array  10  toward the surface of an object from a given angle. The projected pattern from the surface is then viewed from another angle as a contour image, taking advantage of triangulation in order to analyze surface information based on the appearance of contour lines. Phase shifting, in which the projected pattern is incrementally shifted spatially for obtaining additional measurements at the new locations, is typically applied as part of structured light projection imaging, used in order to complete the contour mapping of the surface and to increase overall resolution in the contour image. 
     The schematic diagram of  FIG. 2  shows, with the example of a single line of light L, how patterned light is used for obtaining surface contour information using a handheld camera or other portable imaging device. A mapping is obtained as an illumination array  10  directs a pattern of light onto a surface  20  and a corresponding image of a line L′ is formed on an imaging sensor array  30 . Each pixel  32  on imaging sensor array  30  maps to a corresponding pixel  12  on illumination array  10  according to modulation by surface  20 . Shifts in pixel position, as represented in  FIG. 2 , yield useful information about the contour of surface  20 . It can be appreciated that the basic pattern shown in  FIG. 2  can be implemented in a number of ways, using a variety of illumination sources and sequences and using one or more different types of sensor arrays  30 . Illumination array  10  can utilize any of a number of types of arrays used for light modulation, such as a liquid crystal array or digital micromirror array, such as that provided using the Digital Light Processor or DLP device from Texas Instruments, Dallas, Tex. This type of spatial light modulator is used in the illumination path to change the light pattern as needed for the mapping sequence. 
     By projecting and capturing images that show structured light patterns that duplicate the arrangement shown in  FIGS. 1 and 2  multiple times, the image of the contour line on the camera simultaneously locates a number of surface points of the imaged object. This can speed the process of gathering many sample points, while the plane of light (and usually also the receiving camera) is laterally moved in order to “paint” some or all of the exterior surface of the object with the plane of light. 
       FIG. 3  shows surface imaging using a pattern with multiple lines of light. Incremental shifting of the line pattern and other techniques help to compensate for inaccuracies and confusion that can result from abrupt transitions along the surface, whereby it can be difficult to positively identify the segments that correspond to each projected line. In  FIG. 3 , for example, it can be difficult to determine whether line segment  16  is from the same line of illumination as line segment  18  or adjacent line segment  19 . 
     By knowing the instantaneous position of the camera and the instantaneous position of the line of light within an object-relative coordinate system when the image was acquired, a computer and software can use triangulation methods to compute the coordinates of numerous illuminated surface points. As the plane is moved to intersect eventually with some or all of the surface of the object, the coordinates of an increasing number of points are accumulated. As a result of this image acquisition, a point cloud of vertex points or vertices can be identified and used to represent the extent of a surface within a volume. By way of example,  FIG. 4  shows a dense point cloud  50  generated from a structured light imaging apparatus, CS 3500 3-D camera made by Carestream Heath, Inc., Rochester N.Y., USA, using results from patterned illumination such as that shown in  FIG. 3 . The point cloud  50  models physical location of sampled points on tooth surfaces and other intraoral surfaces or, more generally, of surfaces of a real-world object. Variable resolution can be obtained. The example of  FIG. 4  shows an exemplary 100 micron resolution. The points in the point cloud represent actual, measured points on the three dimensional surface of an object. 
     The surface structure can be approximated from the point cloud representation by forming a polygon mesh, in which adjacent vertices are connected by line segments. For a vertex, its adjacent vertices are those vertices closest to the vertex in terms of Euclidean distance. 
     By way of example,  FIG. 5  shows a 3-D polygon mesh model  60  in the simple form of a triangular mesh. A triangular mesh forms a basic mesh structure that can be generated from a point cloud and used as a digital model to represent a 3-D object by its approximate surface shape, in the form of triangular plane segments sharing adjacent boundaries. Methods and apparatus for forming a polygon mesh model, such as a triangular mesh or more complex mesh structure, are well known to those skilled in the contour imaging arts. The polygon unit of the mesh model, and relationships between neighboring polygons, can be used in embodiments of the present disclosure to extract features (e.g., curvatures, minimum curvatures, edges, spatial relations, etc.) at teeth boundaries. In intra-oral imaging, segmentation of individual components of the image content from a digital model can be of value to the dental practitioner in various procedures, including orthodontic treatment and preparation of crowns, implants, and other prosthetic devices, for example. Various methods have been proposed and demonstrated for mesh-based segmentation of teeth from gums and of teeth from each other. However, drawbacks of conventional segmentation solutions include requirements for a significant level of operator skill and a high degree of computational complexity. Conventional approaches to the problem of segmenting tooth components and other dentition features have yielded disappointing results in many cases. Exemplary method and apparatus embodiments according to the present disclosure address such problems with segmentation that can utilize the polygonal mesh data as a type of source digital model and can operate in more than one stage: e.g., first, performing an automated segmentation that can provide at least a close or coarse approximation of the needed segmentation of the digital model; and second, allowing operator interactions to improve, correct or clean up observed errors and inconsistencies in the automated results, which can yield highly accurate results that are difficult to achieve in a purely automated manner without significant requirements on operator time or skill level or on needed computer resources. This hybrid approach in exemplary method and apparatus embodiments can help to combine computing and image processing power with operator perception to check, correct, and refine results of automated processing. 
     The logic flow diagram of  FIG. 6A  shows a hybrid sequence for tooth mesh segmentation and generation of a digital model to identify individual features or intraoral components such as teeth from within the mouth according to an exemplary embodiment of the present disclosure. In an image acquisition step S 100 , a plurality of structured light images of the patient&#39;s dentition are captured, providing a set of contour images for processing. A point cloud generation step S 110  then generates a point cloud of the patient&#39;s dentition using the set of contour images. A polygon mesh generation step S 120  forms a polygon mesh by connecting adjacent points from point cloud results. A triangular mesh provides one type of polygon mesh that can be readily generated for approximating a surface contour; more complex polygon mesh configurations can alternately be used. 
     Continuing with the  FIG. 6A  sequence, given the polygon mesh, a segmentation step S 130  can be executed. For a dental contour image, for example, segmentation step S 130  can distinguish teeth from gum tissue, as well as distinguishing one tooth from another. Segmentation results can then be displayed, showing the results of this initial, automated segmentation processing. The automated segmentation step S 130  can provide an intermediate image. Thus automated step S 130  can perform the bulk of segmentation processing, but can further benefit from operator review and refinements of results. For its automatic processing, segmentation step S 130  can use any of a number of known segmentation techniques, such as fast-marching watershed algorithms, so-called snake-based segmentation, and other methods known to those skilled in the imaging arts, as noted earlier. 
       FIG. 6A  also shows an optional repeat loop that can enable viewer interaction with the intermediate image for refining the results of the automated segmentation processing, for example, using the basic apparatus shown in  FIG. 1 . An accept operator instructions step S 140  can be executed, during which the viewer indicates, on the displayed results, seed points, seed lines, block lines, boundary features, or other markings that identify one or more distinct features of the segmentation results to allow further segmentation refinement and processing. Viewer markup instructions cause segmentation step S 130  to be executed at least a second time, this second time using input markup(s) from entered viewer instructions. It can be appreciated that different segmentation algorithms can be applied at various stages of automated or manual processing. Final results of segmentation processing can be displayed, stored, and transmitted between computers, such as over a wired or wireless network, for example. 
     The process shown in  FIG. 6A  can thus allow automated segmentation to perform the coarse segmentation (e.g., first segmentation) that can be more easily accomplished, such as segmentation of teeth from gum tissue, for example. Thus, for example, tooth and gum partitioning can be automated. In one embodiment, tooth and gum partitioning can use an automated curvature-based method that computes curvature of vertices in the mesh, and then uses a thresholding algorithm to identify margin vertices having large negative curvature. Alternately, color-based segmentation can be used for tooth segmentation from the gums. This type of method can obtain average hue values from regions of the image and calculate threshold values that partition image content. 
     An exemplary embodiment of workflow for the hybrid tooth segmentation system is depicted in the logic flow diagram of  FIG. 6B . Upon receiving a dentition mesh such as the one described in Step S 120  and shown in  FIGS. 4 and 5 , the control logic processor  80  ( FIG. 1 ) initiates an automated segmentation step S 202  in which a fully automatic tooth segmentation tool is evoked to delineate teeth and gum regions and delineate individual teeth regions. The fully automatic tooth segmentation tool employs exemplary algorithms such as active contour models published in the literature or otherwise well-known to those skilled in the image processing arts. The delineation of teeth effectively produces individually segmented teeth; however, these generated teeth may contain poorly segmented intraoral components. A first checking step S 204  then checks for poorly segmented intraoral components. Checking for incorrect or incomplete segmentation in step S 204  can be accomplished either computationally, such as by applying trained artificial intelligence algorithms to the segmentation results, or by viewer interaction, such as following visual inspection by the viewer. By way of example,  FIG. 7A  shows an exemplary poorly segmented or mis-segmented tooth  302 . As shown in  FIG. 7A , a segmented tooth boundary  306  is not aligned with an actual tooth boundary  308 . 
     Still referring to the workflow process in  FIG. 6B , if checking Step S 204  identifies one or more poorly segmented teeth, either computationally or visually, a primary assisted segmentation step S 206  executes, activating a segmentation procedure that is also automated, but allows some level of operator adjustment. Primary assisted segmentation step S 206  applies an algorithm for segmentation that allows operator adjustment of one or more parameters in a parameter adjustment step S 210 . Another checking step S 208  executes to determine if additional segmentation processing is needed. The adjustable parameter can be altered computationally or explicitly by an operator instruction in step S 210 . Subsequent figures show an exemplary operator interface for parameter adjustment. 
     An exemplary algorithm employed in primary assisted segmentation Step S 206  can be a well-known technique, such as the mesh minimum curvature-based segmentation method. The adjustable parameter can be the threshold value of the curvature. With the help of the parameter adjustment in step S 210 , a correction of the poorly segmented tooth can be made.  FIG. 7B  shows an image of tooth  312  that, by comparison with  FIG. 7A , shows a segmented tooth boundary  316  now well aligned with the actual boundary. 
     However, as is clear from the exemplary workflow embodiment shown in  FIG. 6B , the delineation of teeth performed in Step S 206  may still produce poorly segmented intraoral components or features, so that a repeated segmentation process is helpful. The checking of poor segmentation in step S 208  can be accomplished either computationally, such as by applying artificial intelligence algorithms to the segmentation results, or more directly, by visual inspection performed by the user. In addition to the adjustable parameter adjusted in Step S 210 , the hybrid tooth segmentation system optionally allows the user to add exemplary geometric primitives such as seed lines on the tooth region and add blocking lines between the teeth or between the teeth and gum to aid the tooth segmentation process.  FIG. 8A  shows an exemplary seed line  406  for marking a tooth, added to a mesh image  62 .  FIG. 8B  shows an exemplary block line  408  for indicating space between two teeth, added to a mesh image  62 . 
     The three basic steps, Step S 206 , Step S 208  and Step S 210  in the  FIG. 6B  sequence constitute an exemplary primary segmentation loop  54  that follows the fully automatic segmentation of step S 202  and checking step S 204 . This exemplary primary segmentation loop  54  is intended to correct segmentation errors from the fully automated segmentation of automated segmentation step S 202 , as identified in step S 204 . Exemplary primary segmentation loop  54  can be executed one or more times, as needed. When exemplary primary segmentation loop  54  is successful, segmentation can be complete. 
     In some cases, however, additional segmentation processing beyond what is provided by primary segmentation loop  54  is needed. Segmentation processing can be complicated by various factors, such as tooth crowding, irregular tooth shapes, artifacts from scanning, indistinct tooth contours, and undistinguishable interstices among others. Where additional segmentation is needed, an exemplary secondary segmentation loop  56  can be used to provide more interactive segmentation approaches. The secondary segmentation loop  56  can include an interactive segmentation step S 212 , another checking step S 214 , and an operator markup step S 216 . Interactive segmentation step S 212  can activate a segmentation process that works with the operator for indicating areas of the image to be segmented from other areas. Interactive segmentation step S 212  can have an automated sequence, implemented by an exemplary algorithm such as a “fast march” method known to those skilled in the image segmentation arts. Step S 212  may require population of the tooth region images by operator-entered seeds or seed lines or other types of geometric primitives before activation or during processing. In certain exemplary embodiments, seed lines or other features can be automatically generated in Step S 100 , S 110  and S 120  when the dentition mesh is entered into the system for optional operator adjustment (e.g., subsequent operations such as secondary segmentation loop  56  or Step  212 ). In addition, the features, seeds or seed lines can be added to the segmentation process in operator markup Step S 216  by the user. The results from Step S 212  are subject to inspection by the user in Step S 216 . Results from the hybrid automated/interactive segmentation processing can then be displayed in a display step S 220 , as well as stored and transmitted to another computer. 
     Following the sequence of  FIG. 6B , some exemplary methods and apparatus of the present disclosure provide a hybrid tooth segmentation that provides the benefits of interactive segmentation with human-machine synergy. 
       FIGS. 9A-9C  show operator interface screens  52  for portions of a sequence for review and entry of markup instructions for refining mesh segmentation processing according to certain exemplary embodiments of the present disclosure. Interim mesh segmentation results are shown in a display area  86  on screen  52 . A number of controls  90  for adjustment of the segmentation process are available, such as an adjustment control  84  for setting a level for overall aggressiveness or other parameter or characteristic of the segmentation processing algorithm. Optional selection controls  88  allow the viewer to specify one or more segmentation algorithms to be applied. This gives the operator an opportunity to assess whether one particular type of segmentation algorithm or another appear to be more successful in performing the segmentation task for the given mesh digital model. The operator can compare results against the original and adjust parameters to view results of successive segmentation attempts, with and without operator markup. 
       FIG. 9A  also shows a trace pattern  96  that is entered as an operator seed line instruction for correcting or refining segmentation processing, as was shown previously with respect to  FIG. 8A . According to an embodiment of the present disclosure, an operator mark in the form of trace pattern  96  or other arbitrary marking/geometric can be used to provide seed points that indicate a specific feature for segmentation, such as a molar or other tooth feature that may be difficult to process for conventional segmentation routines. Seed marks can then be used as input to a fast marching algorithm or other algorithm type, as described previously. In some cases, for example, adjacent teeth may not be accurately segmented with respect to each other; operator markup can provide useful guidance for segmentation processing where standard segmentation logic does not perform well. As  FIG. 9A  shows, the operator can have controls  90  available that allow the entered markup to be cleared or provided to the segmentation processor. As  FIG. 9B  shows, color or shading can be used to differentiate various teeth or other structures identified by segmentation. Additional controls  90  can also be used to display individual segmented elements, such as individual teeth, for example. As  FIG. 9C  highlights, in some exemplary embodiments, individual controls  90  can be used individually or in combination. 
     In one embodiment, segmentation of individual teeth from each other can use curvature thresholds to compute margin and border vertices, then use various growth techniques to define the bounds of each tooth relative to margin detection. 
     In some exemplary embodiments, controls  90  can include, but are not limited to enter/adjust seed or boundary geometries, enter/adjust selected segmentation procedures, enter/adjust number of objects to segment, subdivide selected object, modify segmented object display, etc. 
     Bracket and Wires Removal with Reconstruction 
     The logic flow diagram of  FIG. 10  shows an exemplary embodiment of a workflow for bracket removal from a dentition 3D mesh according to an embodiment of the present disclosure. As shown in  FIG. 10 , a virtual or digital 3D dentition mesh model is obtained in an acquisition step S 1002 . For example, a digital 3D dentition mesh model can be obtained by using an intraoral scanner that employs structured light. 
       FIG. 11  is a diagram that shows an exemplary 3D dentition mesh that can be acquired in step S 1002  of  FIG. 10 . As shown in  FIG. 11 , 3D dentition mesh  1100  can include brackets  1102 , gingival tissue  1104  and teeth  1106 . Preferably, a result from the exemplary workflow process of  FIG. 10  will be a 3D dentition mesh including the teeth  1106  and gingival tissue  1104  from the 3D dentition mesh  1100 , but without the brackets  1102  and tooth surfaces previously covered by brackets  1102  and with the tooth surfaces accurately reconstructed. 
     As shown in  FIG. 10 , separation steps  1004  and  1006  constitute a tooth segmentation method for an obtained dentition 3D mesh. As described herein, in one embodiment steps S 1004  and S 1006  can be implemented by similar steps of a hybrid sequence for tooth mesh segmentation depicted in  FIG. 6A . Alternatively in another embodiment, steps S 1004  and S 1006  can be implemented by similar steps of a hybrid tooth segmentation method or system depicted in  FIG. 6B . Segmentation distinguishes each tooth from its neighboring teeth and from adjacent gingival tissue. 
     Continuing with the workflow in  FIG. 10  and with reference to  FIGS. 11, 12, and 13A, 13B, and 13C , brackets  1102  are automatically removed from the 3D dentition mesh  1100  (e.g., tooth surfaces) in a removal step S 1008 . In one exemplary embodiment, the separated (or segmented) teeth resulting from step S 1006  can individually undergo bracket removal and surface reconstruction described hereafter.  FIG. 12  is a diagram that shows exemplary resultant separated teeth  1202  contained within the 3D dentition mesh  1100 . 
     In removal step S 1008 , to automatically remove the brackets from surfaces of the separated teeth  1202 , each individually segmented tooth (or crown) is examined and processed. An exemplary segmented tooth  1202  with bracket  1302  to be removed is shown in  FIG. 13A . In one exemplary embodiment, an automatic bracket removal algorithm first detects boundaries of the bracket  1302 . Various approaches known to one skilled in the imaging arts can be used to detect bracket boundaries in the 3D dentition mesh  1100 . In one exemplary embodiment, bracket boundary detection can use an automated curvature-based algorithm that detects and computes the curvatures of vertices in the mesh of tooth surfaces, and then uses a thresholding algorithm to identify margin vertices that have large negative curvature values, indicative of a high degree of curvature. 
     As shown in  FIG. 13A , these identified margin vertices form a closed 3D curve or bracket boundary  1303  (or the boundary vertices of the bracket) that surrounds the bracket  1302 . Then, mesh vertices within the closed 3D boundary are removed in the 3D dentition mesh  1100 . As  FIG. 13B  shows, this results in a gap or hole  1304  on the tooth surface.  FIG. 13B  is a diagram that shows an exemplary segmented tooth  1202  with bracket  1302  removed. As shown in  FIG. 13B , small white patches can be present in the bracket hole  1304 ; these white patches do not belong to the bracket  1302  itself, but can be other artifacts behind the original bracket. These artifacts can become visible after the bracket  1302  has been removed from the 3D dentition mesh  1100  by an automatic bracket removal algorithm. 
     Referring again to the flow diagram of  FIG. 10 , in a reconstruction step S 1010 , tooth surfaces of the segmented tooth  1202  having the bracket removed are automatically reconstructed. Various approaches known to those skilled in the imaging arts can be used to fill holes in the 3D dentition mesh  1100 . An exemplary segmented tooth  1202  having automatically reconstructed tooth surface  1306  is shown in  FIG. 13C . In exemplary embodiments, hole-filling procedures (e.g., tooth or crown surface reconstruction) can include a first step to generate an initial patch to fill the hole and a second step to smooth the reconstructed mesh to obtain improved quality polygons (e.g., triangles) therein. 
       FIG. 13D  schematically shows a part of the 3D dentition mesh  1100  forming a 3D crown mesh surface after mesh portions representing a bracket are removed. A closed polygon  1303 ′ represents a boundary of the (removed) bracket. A region  1308  enclosed by the closed polygon  1303 ′ is the gap or hole left by bracket removal. First in step S 1010 , an initial patch is generated to fill the tooth surface or hole of region  1308  (e.g., within the closed polygon  1303 ′). In one embodiment, the initial patch contains a plurality of triangles  1310  arranged in an exemplary prescribed pattern such as one formed by connecting vertices in the closed polygon  1303 ′ to form the pattern shown in  FIG. 13E . Then, in reconstruction step S 1010 , polygons such as triangles  1310  of the initial patch can be further modified or optimized. One exemplary procedure of modifying or optimally arranging the triangles  1310  is illustrated in  FIG. 13F  where four points A, B, C, and D form two triangles ABD and CDB in the triangles  1310 , which are rearranged to become triangles ABC and CDA in an improved set of triangles  1310 ′. An improved triangle arrangement can reduce or avoid long, thin triangles. 
     In a second part of reconstruction step S 1010  of the  FIG. 10  sequence, the 3D mesh with the initial patch can be smoothed to obtain better quality. In one embodiment, the second part of step S 1010  can correct positions of points created in the initial patch using local information globally. Thus, the 3D mesh including the initial patch (e.g., triangles  1310 ,  1310 ′ within the hole of polygon  1303 ′) and the surrounding regions, such as triangles  1312  surrounding (or nearby) the hole  1308 ′ in  FIG. 13D  can be smoothed using a Laplacian smoothing method that adjusts the location of each mesh vertex to the geometric center of its neighbor vertices. 
     For example, an implementation of mesh smoothing is described by Wei Zhao et al. in “A robust hole-filling algorithm for triangular mesh” in  The Visual Computer  (2007) December 2007, Volume 23, Issue 12, pp 987-997, that can implement a patch refinement algorithm using the Poisson equation with Dirichlet boundary conditions. The Poisson equation is formulated as 
       Δ f =div( h ) f|   ∂Ω   =f*|   ∂Ω 
 
     wherein f is an unknown scalar function; 
     
       
         
           
             
               Δ 
               ⁢ 
               f 
             
             = 
             
               
                 
                   ∂ 
                   2 
                 
                 
                   ∂ 
                   
                     x 
                     2 
                   
                 
               
               ⁢ 
               
                 + 
                 
                   
                     
                       ∂ 
                       2 
                     
                     
                       ∂ 
                       
                         y 
                         2 
                       
                     
                   
                   ⁢ 
                   
                     + 
                     
                       
                         ∂ 
                         2 
                       
                       
                         ∂ 
                         
                           z 
                           2 
                         
                       
                     
                   
                 
               
             
           
         
       
     
     is a Laplacian operator; h is the guidance vector field; div(h) is the divergence of h; and f* is a known scalar function providing the boundary condition. The guidance vector field on a discrete triangle mesh as used in Wei Zhao&#39;s method is defined as a piecewise constant vector function whose domain is the set of all points on the mesh surface. The constant vector is defined for each triangle and this vector is coplanar with the triangle. 
     In a display step S 1012  of  FIG. 10 , the exemplary segmented tooth  1202  having automatically reconstructed tooth surface  1306  (see  FIG. 13C ) can be displayed. Although described for one exemplary segmented tooth  1202 , steps S 1008 , S 1010  and S 1012  can be repeatedly performed until all brackets are removed from 3D dentition mesh  1100 . In this manner, the resultant corrected 3D dentition mesh  1100  can be displayed in step S 1012  after each additional segmented tooth surface is corrected. Alternatively, steps S 1008  and S 1010  can be performed for all teeth in the 3D dentition mesh  1100 , before the resultant corrected 3D dentition mesh  1100  is displayed in step  1012 .  FIG. 13G  shows an exemplary corrected 3D dentition mesh  1316 . 
     Braces and Brackets Detection and Removal 
     Certain exemplary method and/or apparatus embodiments can provide automatic braces detection and removal by initial (e.g., coarse) bracket detection, subsequent wire detection, and refinement of detected (e.g., separated) initial brackets, which can then be removed from the initial 3D mesh and subsequently filled by various surface reconstruction techniques. 
     The logic flow diagram of  FIG. 14  shows an exemplary sequence for automatic braces and brackets detection and removal, without tooth segmentation as a pre-step, by processing logic according to an embodiment of the present disclosure. A coarse bracket detection step S 1302  provides estimated positions of brackets, using an approach such as that described subsequently. A brace wires detection step S 1304  then detects connecting wires that extend across the bracket region. A masks generation step S 1308  generates masks for the brackets; these masks narrow the search area for detection. A processing step S 1310  provides pruning and other morphological operations for further defining the masks. A Fast March application step S 1320  executes a fast march algorithm according to the defined mask region. A refinement step S 1330  performs the necessary refinement of detected bracket areas or regions using morphological operators. A fine tuning step S 1340  generates the fine-tuned bracket regions that are then used for removal steps. 
     Coarse Bracket Detection 
     Coarse bracket detection in step S 1302  can proceed as described in the flow diagram of  FIG. 15  and as shown visually in the sequence of  FIG. 16 . In a computation step S 1306 , the system computes a parabola  502  that is a suitable fit for the imaged dentition. This is typically executed from image content in a top view image  500  as shown, using curvature detection logic. Parabola  502  can be traced along the edges of teeth in the arch using the imaged content. Given this processing, in a side detection step S 1312 , a buccal side  504  or, alternately, the opposite lingual side of the arch is then identified. 
     With the lingual or buccal side  504  of the arch and parabola  502  located, one or more bracket areas or regions  506  disposed on that side can then be identified in a bracket areas detection step S 1324 . According to an embodiment of the present disclosure, bracket area  506  detection uses the following general sequence, repeated for points along parabola  502 :
         (i) Extend a normal outward toward the side from the generated parabola  502 ;   (ii) Detect a maximum length of the extended normals within a local neighborhood, such as within a predetermined number of pixels or calculated measurement;   (iii) Select nearby points on the mesh that lie within a predetermined distance from the detected maximum.
 
These substeps identify candidate bracket areas or regions  508  as shown in the example of  FIG. 16 . These candidate areas  508  can be processed in order to more accurately identify bracket features that lie against the teeth and to distinguish each bracket from the corresponding tooth surface.
       

     Once areas  508  have been identified, a decision step S 1328  determines whether or not post treatment is needed in order to correct for processing errors. If post treatment is not required, bracket areas have been satisfactorily defined. If post treatment is required, further processing is applied in a false detection correction step S 1332  to remove false positives and in a clustering step S 1344  to effect further clustering of bracket areas that are in proximity and that can be assumed to belong to the same bracket  510 .  FIG. 17  shows exemplary coarse brackets  510  obtained using the described coarse bracket detection sequence of  FIG. 15 . 
     Brace Wires Detection 
     Brace wires detection step S 1304  from the  FIG. 14  sequence can proceed as shown in  FIG. 18  and as described following. 
     Coarse brackets  510  may be connected by brace wires  512 . Processing can detect wire extending from each bracket region. It is useful to remove these wires in order to obtain improved bracket removal. 
     For each vertex V in the bracket region as shown in  FIGS. 18 and 19 , processing can perform a nearest neighbor search within a suitable radius, such as within an exemplary 5 mm radius, resulting in a set of neighbor vertices VN. Processing then checks the normal of each of the vertices in VN. 
     The detected wires can facilitate identification of the individual brackets. If it is determined that the normal for at least one vertex in VN points to the opposite direction of the normal of the vertex V (e.g. if the dot product of the two normal vectors &lt;−0.9), then V is considered a candidate vertex on the wire (or bridge). This can be measured, for example, because there is space between the wire feature and the tooth. This procedure can be applied to the entire mesh, resulting in a set that has a number of candidate vertices. 
     The set of candidate vertices is used to compute a plurality of connected regions. Each of the connected regions can be analyzed using a shape detection algorithm, such as principal component analysis PCA, familiar to those skilled in the imaging arts and used for shape detection, such as wire detection. 
       FIG. 18  shows results of wire detection for wires  512  extending between brackets. These detected wires can then be used to algorithmically identify and separate connected brackets. 
     Generating Initial Masks 
     With separated coarse brackets detected in some manner (either originally detected using step S 1302  or using the results from wire detection step S 1304 ), an initial mask can be generated for each individual coarse bracket. These initial masks can be helpful for narrowing the search area in Fast Marching brackets detection. In practice, a proper initial mask should be, adequately large enough to cover all the components (base, pad, slots, hook, band, etc.) that belong to a bracket. 
     Generating and processing initial masks from steps S 1308  and S 1310  in  FIG. 14  can be executed as follows. Referring to the schematic diagram of  FIG. 19 , this processing can generate a mask for each bracket. The mask is used to define the region of interest (ROI) for subsequent fast march bracket detection. 
     Processing for mask generation can use the following sequence, with reference to  FIG. 19 :
         (i) Jaw mesh orientation. The z axis is orthogonal to the bite plane.   (ii) Sorting. Brackets, separated by wire detection, in each dental arch are sorted and center, normal, and bi-normal features are computed for each bracket.   (iii) Identification. Each bracket type is identified as either lingual or buccal, on back molar or on other teeth. A suitable radius is set for mask generation for each bracket.   (iv) Radius search. A radius search is executed from the center of each initial bracket in order to generate an initial mask  520  for each bracket. The mask should be large enough to contain the bracket.       

     The centroid of each mask  520  is connected to each neighbor along the arch, as represented in flattened form in  FIG. 19 . 
     Processing Initial Masks 
     Processing initial masks in step S 1310  of  FIG. 14  performs a pruning operation that shapes the mask correctly for its corresponding bracket and removes areas where the initial mask is inaccurate and extends to opposite sides of the same tooth or extends between teeth.  FIG. 20  shows the pruning operation for masks that inaccurately extend to the opposite side in schematic representation at images  530 . Pruning results are shown in the example of image  532 . Pruning for masks that inaccurately extend across teeth, as shown in image  540 , is shown in image  542 . 
     Starting from one end of the dental arch, the bi-normal bn can be defined as the vector from a bracket&#39;s own center to that of the next bracket in the series that is formed by sorting all brackets that lie along the dental arch from one side to another. The cross product of the z-axis and bi-normal can be used to generate its normal as depicted in  FIG. 19 , showing the z-axis, normal n, and bi-normal bn of each bracket. 
     For pruning where masks extend to the opposite side as shown in schematic representation in  FIG. 20  at image  530  with pruning at image  532 , the following processing can be executed at each vertex in the mask:
         (i) Compute D normal , the dot product of the normal and bracket normal for each vertex:       

         D   normal   =&lt;N   vi   ,N   bracket &gt;         wherein N vi  is the normal of vertex v b  N bracket  is the bracket normal. (The notation &lt;a,b&gt; indicates dot product and can alternately be expressed as a·b.)   (ii) Remove the vertices whose D normal  value is below a predetermined threshold value (for example, below −0.1). This dot product value indicates vectors tending towards opposite directions.       
     For pruning where masks extend to neighboring teeth, as shown in schematic representation at image  540  in  FIG. 20  with pruning at image  542 , the following processing can be executed at each vertex in the mask:
         (i) Compute D binormal  for each vertex:       

         D   binormal   =&lt;N   vi   ,BN   bracket &gt;*Sgn(&lt; Dir   vi   ,BN   bracket &gt;)         wherein N vi  is the normal of vertex v i ; BN bracket  is the binormal of the bracket; Dir vi  is the direction from the bracket center to vertex v i ; and   Sgn(x) returns the +/− sign of (x).   (ii) Remove vertices whose D binormal  value is smaller than a threshold value (for example, smaller than −0.1).       
     After pruning, a post-processing procedure can be applied to each mask, as shown in the sequence of  FIG. 21 . An image  550  shows encircled gaps  556  that can be filled in order to complete masked regions. The remaining vertices after pruning are dilated to connect discontinuous regions and to fill regions that may have been inaccurately pruned. Dilation can be followed by an erosion process to remove regions of the mask lying between the teeth, as shown in encircled areas  552 ,  554 . An image  560  shows improvement to the encircled regions of image  550 . 
     There can be some small residual regions, as shown encircled in an area  572  in an image  570 , other than the main bracket mask region. These can be redundant areas, for example; these small regions can be detected and removed and only the largest connected region retained as the resultant initial mask. An image  580  shows the completed mask following both dilation and erosion processing. 
     Fast March Processing 
     Once well-pruned masks have been obtained, a Fast March algorithm can be applied within each mask, with boundaries of the mask used as seed vertices. Within the fast march algorithm, the arrival time for seed vertices can be set to 0. The arrival time for vertices within the mask can be computed with the common Fast Marching process, as shown schematically in  FIG. 22 . 
     Fast March processing uses a weighting or cost function in order to determine the most likely path between vertices in each masked region.  FIG. 22  shows different computations that can apply for paths between given vertices using Fast March methods.  FIG. 23  shows exemplary Fast March computation for arrival time from different seed-points along mask boundaries using the Fast March method. Masked regions  590  are shown, with grayscale- or color-encoded arrival times used for comparison as shown in image  595  in  FIG. 23 . 
     For Fast March processing, curvature values κ can be used. It should be noted that minimum κ values (for example, with negative values such as κ=−10) indicate very high curvature. The boundary of a bracket is characterized by a high absolute value of curvature. 
     The Fast Marching algorithm applies a speed function in order to compute the weight assigned to each edge in the graph. For bracket removal, there is a need for reduced edge weights in flat regions and larger edge weight values in highly curved regions. 
     The speed function for Fast Marching execution is based on normal difference of two neighbor vertices along an edge: D normal =∫ v     0     v     1   κ normal (s)·ds, where v 0  and v 1  are two neighbor vertices, the normal difference is equal to the integration of normal curvature κ normal  in the geodesic line on the mesh surface from v 0  to v 1 . The D normal  value is approximate to the averaged normal curvature of v 0  and v 1 , times the distance S from v 0  and v 1 : 
     
       
         
           
             
               
                 
                   
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     In implementing the speed function, the mean curvature can be used. The mean curvature is readily computed (as compared against a normal curvature) and operates without concern for possible differences in estimation for the propagating front stop at regions that are highly curved. The speed function is therefore defined as: 
     
       
         
           
             
               
                 
                   
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     wherein κ mean  is the mean curvature and w normal  is a weight value. 
     The speed function used for processing with masked Fast Marching can be defined as a normal difference of two neighbor vertices along the edge of an area being processed. Where vertices v 0  and v 1  are two neighboring vertices (that is, within nearest proximity of each other relative to the display medium), the normal difference is equal to the integration of normal curvature κ normal  in the geodesic line from vertex v 1  to v 2 . The normal difference is approximate to the average normal curvature of v 0  and v 1 , times a distance S from v 0  to v 1 . 
     Refining Detected Bracket Regions 
     Morphological processing can be used for final refinement of detected bracket regions.  FIG. 24  shows results of using a sequence of different approaches for refinement of bracket regions according to an embodiment of the present disclosure. An image  600  shows fast marching results for a typical image having brackets and braces. An image  610  shows results of image thresholding, well known to those skilled in the imaging arts. An image  620  shows results of a dilation and fill process. An image  630  shows results following image erosion, using a maximum-sized region. 
       FIG. 25  shows steps of an optional refinement of bracket regions using a convex hull computation. The following sequence can be used for convex hull processing:
         (i) compute the boundary of a bracket region in the mesh, as shown in an image  700 ; in the example shown, a large gap exists within the bracket region;   (ii) project the boundary vertices to the 2D PCA plane of the boundary as shown in an image  710 ;   (iii) compute the convex hull in the PCA plane, as shown in an image  720 ;   (iv) detect and record pairs of points that are connected, such as non-neighbor vertices as shown in an image  730 ;   (v) connect paired vertices in the original 3D boundary with geodesic lines to form a 2-manifold convex hull, as shown in an image  740 .
 
The resulting convex hull connects the gap that appears in image  700  and covers the full bracket.
       

       FIG. 26  shows the fine tuned bracket regions obtained using the described sequence. 
       FIG. 27  shows the recovered tooth surface following bracket definition and removal by applying, to the results in  FIG. 26 , the surface reconstruction process detailed in the preceding paragraphs and the sequence described with reference to  FIGS. 13A-14 . 
       FIG. 28  is a logic flow diagram that shows a workflow of another exemplary embodiment of the present disclosure for bracket removal on a 3D dentition mesh. Unlike the workflow shown in  FIG. 10 , the workflow shown in  FIG. 28  does not require tooth segmentation as a separate step. A 3D dentition mesh is received in an acquisition step S 1402 ; the received mesh contains teeth, brackets, and gingival tissue. Then, in an instruction step S 1404 , instructions are received from an operator regarding brackets in the 3D dentition mesh. 
       FIG. 29  is a diagram that displays an exemplary graphical user interface (GUI) that allows the user to input information to identify brackets in the 3D dentition mesh. As shown in  FIG. 29 , one exemplary GUI interface  1500  enables nodes to be placed by the user for a ‘snake’ operation, which automatically encircles bracket  1502  boundaries, based on the entered nodes. An exemplary bracket boundary  1503  generated by the automated ‘snake’ operation is shown in  FIG. 29 . The ‘snake’ is an active shape model that is frequently used in automatic object segmentation in image processing, for example by delineating an object outline from a possibly noisy 2D image. The active shape model of the snake is similar to that used in applications like object tracking, shape recognition, segmentation, edge detection and stereo matching. Methods using a snake active shape model or active contour model are well known to those skilled in the imaging arts. 
       FIG. 30  shows vertices  1602  encircled by the boundary  1503  being highlighted in the 3D dentition mesh after the user presses the ‘run’ command button  1504  in  FIG. 29 . Identified vertices  1602  are to be removed from the original 3D dentition mesh. In one exemplary embodiment, the GUI  1500  can let the user inspect the intermediate results for vertices  1602 , and if satisfied, the user presses the ‘cut’ button  1506 . The vertices  1602  change their highlight (e.g., color, texture, etc.) to indicate that these vertex features are to be removed from the original 3D dentition mesh. In one exemplary embodiment, pressing the ‘cut’ button  1506  causes processing to automatically remove the brackets from the teeth surface in a removal step S 1406  based on the operator instructions in step S 1404 . 
     After bracket removal, the tooth surfaces are filled or reconstructed in a reconstruction step S 1408 . In one exemplary embodiment, step S 1408  is performed when the user presses the ‘fill’ button  1506  in  FIG. 29  to reconstruct tooth surfaces and remove any holes or gaps caused by bracket removal. Step S 1408  can be performed using known algorithms such as described herein with respect to  FIG. 10 .  FIG. 31  shows an example of a reconstructed tooth surface  1702  after the bracket is removed. 
     The procedures shown in the  FIG. 28  sequence can be performed tooth by tooth, on a small group of adjacent teeth, or on all teeth simultaneously with respect to the 3D dentition mesh. 
       FIGS. 32-34  are diagrams that show sequential stages in the process leading to a complete, concurrent removal of all brackets from a 3D jaw mesh.  FIG. 32  is a diagram that shows a 3D dentition mesh  1800  with teeth, brackets and gingival tissue.  FIG. 33  is a diagram that shows the intermediate results of ‘snake’ cut operation with vertices  1802  that are to be removed shown in highlighted form.  FIG. 34  is a diagram that shows each of the final reconstructed teeth surfaces  1806  after all brackets are removed and all fill operations are completed. 
     It is noted that the above described user actions such as pressing the ‘cut’ button, pressing the ‘fill’ button and pressing the ‘run’ button are illustrative. In actual applications, these separate actions may not necessarily be sequentially initiated and can be accomplished automatically by computer software. 
     In some cases, 3D dentition models produced by an intraoral scanner may contain wires that bridge two neighboring brackets. In this situation, embodiments described previously may be insufficient for removal of the brackets and wires.  FIG. 35A  is a diagram that shows another exemplary dentition model. As shown in  FIG. 35A , dentition model  2100  includes brackets  2102 , gingival tissue  2104 , teeth  2106  and bridged brackets where a wire  2108  connects at least bracket  2110  and bracket  2112 . Generally, wires  2108  will connect all brackets  2102 . As shown in comparing  FIGS. 35A, 35B, and 35C , the wire  2108  can, once identified, be erased automatically or interactively according to exemplary methods and apparatus of the present disclosure. 
     In  FIG. 36 , an actual result  2204  for bridged brackets removal is shown. The surface reconstructed tooth  2210  and tooth  2212  in  FIG. 36  correspond to bracket  2110  and bracket  2112  in  FIG. 21A  before the brackets and wire  2108  are removed. 
       FIG. 37  is a logic flow diagram that shows an exemplary sequence for bridged bracket removal from tooth mesh surfaces according to an embodiment of the present disclosure. As shown in  FIG. 37 , a dentition model with bridged brackets is obtained in an acquisition step S 2302 , which is immediately followed by a cutting step S 2304  that includes automatically “breaking the bridge”. One exemplary detection embodiment that can be used to automatically break the bridge (or wire) is described as follows. 
     In a removal step S 2306 , given a vertex V in the dentition mesh model, processing logic performs a nearest neighbor search with an exemplary 5 mm radius resulting in a set of neighbor vertices VN. As described in the preceding sections, the system checks the normal of each of the vertices V in set VN. If it is found that there is at least one vertex in VN whose normal points to the opposite direction of the normal of V (e.g. if these two normal vectors&#39; dot product &lt;−0.9), then vertex V is on the wire (or bridge). An exemplary bridge (wire) detection result  2118  resulting from step S 2306  is shown in  FIG. 35C . These vertices of the 3D detention mesh detected in step S 2306  (e.g., associated with the wires  2108 ) are excluded or removed from the 3D detention mesh in the subsequent removal step S 2306  and reconstruction step S 2308 . 
     Removal step S 2306  employs either exemplary automatic or interactive methods to remove the disconnected brackets. The bracket removed tooth surface is reconstructed automatically in a reconstruction step S 2308  and the results are displayed for inspection in a display step S 2310 . For example, steps S 2306  and S 2308  can be performed as described above for  FIGS. 10 and 28 , respectively. 
       FIG. 38  is a logic flow diagram that shows another exemplary method embodiment for bridged brackets removal. As shown in  FIG. 38 , a dentition model with bridged brackets is acquired in an acquisition step S 2402 , which is immediately followed by an interaction step S 2404  of interactively “breaking the bridge”. In one exemplary embodiment, interactive operation effectively erases the thin wires with the assistance from a human by selecting and deleting mesh vertices that belong to the thin wires in step S 2404 . In one exemplary embodiment, step S 2404  can use a GUI with selectable operator actions to “clear”, “paint” (e.g., operator identify pixels showing wires), “auto paint”, “approve” (e.g., paint or auto paint), and “clear” to interactively break the bridges or remove the wires from the 3D dentition mesh based on the operator instructions. Then, a removal step S 2406  employs either automatic or interactive method to remove the disconnected brackets as previously described. The bracket removed tooth surfaces can be reconstructed automatically in a reconstruction step S 2408  as previously described. Then, the results are displayed for inspection in a display step S 2410 . 
     As described herein, exemplary method and/or apparatus embodiments to remove bridged brackets and restore teeth surfaces in a 3D dentition model are intended to be illustrative examples and the application is not so limited. For example, in one exemplary embodiment, bridged brackets can be removed and teeth surfaces restored by automatically identifying parts of a bracket and/or wire without human intervention in an obtained 3D dentition model by growing the identified parts into a region that covers the brackets and/or wires entirely (e.g., and preferably slightly beyond the brackets and/or wires boundaries). removing the region from the 3D dentition model surface, and restoring the removed region surfaces using hole filing techniques. In some exemplary embodiments, hole filling can fill portions of gingival tissue in addition to tooth surface portions. Surface data of the patient that were previously acquired, such as from a dentition mesh model obtained before braces were applied, can be used to generate the reconstructed tooth surface. 
     Consistent with one embodiment, the present disclosure can use a computer program with stored instructions that control system functions for image acquisition and image data processing for image data that is stored and accessed from an electronic memory. As can be appreciated by those skilled in the image processing arts, a computer program of an embodiment of the present invention can be utilized by a suitable, general-purpose computer system, such as a personal computer or workstation that acts as an image processor, when provided with a suitable software program so that the processor operates to acquire, process, transmit, store, and display data as described herein. Many other types of computer systems architectures can be used to execute the computer program of the present invention, including an arrangement of networked processors, for example. 
     The computer program for performing the method of the present invention may be stored in a computer readable storage medium. This medium may comprise, for example; magnetic storage media such as a magnetic disk such as a hard drive or removable device or magnetic tape; optical storage media such as an optical disc, optical tape, or machine readable optical encoding; solid state electronic storage devices such as random access memory (RAM), or read only memory (ROM); or any other physical device or medium employed to store a computer program. The computer program for performing the method of the present invention may also be stored on computer readable storage medium that is connected to the image processor by way of the internet or other network or communication medium. Those skilled in the image data processing arts will further readily recognize that the equivalent of such a computer program product may also be constructed in hardware. 
     It is noted that the term “memory”, equivalent to “computer-accessible memory” in the context of the present disclosure, can refer to any type of temporary or more enduring data storage workspace used for storing and operating upon image data and accessible to a computer system, including a database. The memory could be non-volatile, using, for example, a long-term storage medium such as magnetic or optical storage. Alternately, the memory could be of a more volatile nature, using an electronic circuit, such as random-access memory (RAM) that is used as a temporary buffer or workspace by a microprocessor or other control logic processor device. Display data, for example, is typically stored in a temporary storage buffer that is directly associated with a display device and is periodically refreshed as needed in order to provide displayed data. This temporary storage buffer can also be considered to be a memory, as the term is used in the present disclosure. Memory is also used as the data workspace for executing and storing intermediate and final results of calculations and other processing. Computer-accessible memory can be volatile, non-volatile, or a hybrid combination of volatile and non-volatile types. 
     It is understood that the computer program product of the present disclosure may make use of various image manipulation algorithms and processes that are well known. It will be further understood that the computer program product embodiment of the present invention may embody algorithms and processes not specifically shown or described herein that are useful for implementation. Such algorithms and processes may include conventional utilities that are within the ordinary skill of the image processing arts. Additional aspects of such algorithms and systems, and hardware and/or software for producing and otherwise processing the images or co-operating with the computer program product of the present invention, are not specifically shown or described herein and may be selected from such algorithms, systems, hardware, components and elements known in the art. 
     In this document, the terms “a” or “an” are used, as is common in patent documents, to include one or more than one, independent of any other instances or usages of “at least one” or “one or more.” In this document, the term “or” is used to refer to a nonexclusive or, such that “A or B” includes “A but not B,” “B but not A,” and “A and B,” unless otherwise indicated. In this document, the terms “including” and “in which” are used as the plain-English equivalents of the respective terms “comprising” and “wherein.” Also, in the following claims, the terms “including” and “comprising” are open-ended, that is, a system, device, article, or process that includes elements in addition to those listed after such a term in a claim are still deemed to fall within the scope of that claim. 
     Certain exemplary method and/or apparatus embodiments can provide automatic braces detection and removal by initial (e.g., coarse) bracket detection, subsequent wire detection, and refinement of detected (e.g., separated) initial brackets, which can then be removed from the initial 3D mesh. Exemplary embodiments according to the application can include various features described herein (individually or in combination). 
     While the invention has been illustrated with respect to one or more implementations, alterations and/or modifications can be made to the illustrated examples without departing from the spirit and scope of the appended claims. The presently disclosed embodiments are therefore considered in all respects to be illustrative and not restrictive. In addition, while a particular feature of the invention can have been disclosed with respect to one of several implementations, such feature can be combined with one or more other features of the other implementations as can be desired and advantageous for any given or particular function. The term “at least one of” is used to mean one or more of the listed items can be selected. The term “about” indicates that the value listed can be somewhat altered, as long as the alteration does not result in nonconformance of the process or structure to the illustrated embodiment. Other embodiments of the invention will be apparent to those skilled in the art from consideration of the specification and practice of the invention disclosed herein. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the invention being indicated by the following claims, and all changes that come within the meaning and range of equivalents thereof are intended to be embraced therein.