Abstract:
A pattern recognition system includes a hierarchical network of parametric pattern recognition components or algorithms of different types. During a &#34;training&#34; phase, distinctions among character types are gathered from a set of correctly labelled training samples. The structure of the component hierarchy is established by recursive training of various subsets of the original training set and, for each component, generation of a &#34;decision function&#34; that either (1) indicates a final classification by the present component the characters of the training, or (2) points to a component lower in the hierarchy, thereby establishing connectivity between components of the hierarchy. The training process continues, generating successively lower components in the hierarchy, until perfect classification is obtained on the training set. The hierarchy of components then is utilized to recognize characters or patterns from a set of unknown patterns or characters, by making successive &#34;passes&#34;, if necessary, on features extracted from each unknown character until the unknown character is classified.

Description:
A portion of the disclosure of this patent document contains material which is subject to copyright protection. The copyright owner has no objection to facsimile reproduction by anyone of the patent document or the patent disclosure, as it appears in the Patent and Trademark Office patent file or records, but otherwise reserves all copyright rights whatsoever. 
     CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is related to commonly assigned patent application &#34;Method and Apparatus for Generating Size and Orientation Invariant Shape Features&#34; by Steven L. Borowitz, Ser. No. 026,672, filed Mar. 13, 1987, now U.S. Pat. No. 4,802,230, issued Jan. 31, 1989 incorporated herein by reference. 
     BACKGROUND OF THE INVENTION 
     The invention relates to systems for pattern recognition which consist of a hierarchical network of parametric pattern recognition components to produce the efficiency of prior parametric pattern recognition systems and the power and flexibility of prior non-parametric recognition systems. 
     The statistical approach to character recognition involves extraction of &#34;features&#34; from pixel data obtained by scanning of a character and then feeding the extracted features into a statistical decision tree, which compares them to extracted features of preselected samples of various predefined character classes, and recognizes or rejects the character. The first step in the operation of a -parametric pattern recognition technique is feature extraction. Various techniques are known. Also, the technique developed by the assignee, described in the above Horowitz application, can be used. Typical pattern recognition systems utilize a &#34;training&#34; phase and a &#34;recognition&#34; phase. During the training phase, information representative of distinctions among character types is gathered from a set of correctly labeled &#34;training samples&#34; of characters and stored in a computer&#39;s memory in the form of numerical parameters and data structures. During the recognition phase, an unknown character, such as a hand written character, is assigned a classification based on information stored during the training phase. Training phases of parametric pattern recognition systems are well known, and may be found in such texts as &#34;Pattern Classification and Scene Analysis&#34;, Duda and Hart, John Wiley &amp; Sons, New York, 1973, and &#34;Pattern Recognition Principles&#34;, by Tou and Gonzalez, Addison-Wesley, Reading, Mass., 1974. Various pattern recognition techniques have been described, as in &#34;Computer-Oriented Approach to Pattern Recognition&#34;, W. S. Maisel, Academic Press, New York &amp; London, 1972. Utilization of decision tree components in character recognition is described in &#34;Isoetrp--An Interactive Clustering Algorithm With New Objectives&#34;, by C. Y. Suen, Pattern Recognition, Vol. 17, No. 2, p. 211-19, 1984, and &#34;Chinese Character Classification by Globally Trained Tree Classifier and Fourier Descriptors of Condensed Patterns&#34;, by Tang, Suen &amp; Wang, First International Conference on Computers and Applications, Beijing, China, 1984. Gaussian Discriminant Techniques for Parametric Pattern Recognition are very well known, and are described in the above Duda and Hart reference and the Tou and Gonzalez reference. 
     A significant problem of prior pattern recognition techniques is that they operate on the underlying assumption that class-conditional probability distributions of the extracted features have a Gaussian distribution. Although these prior parametric pattern recognition techniques have the major advantage that an arbitrarily large training set may be reduced to a tractable set of parameters by simple statistical estimation formulas, the assumptions of normality, class conditional independence, etc., of the probability distributions of features are often very incorrect. For example, a small percentage of people might, when writing, produce enough momentum in their hands to create a &#34;new&#34; feature in a particular letter. Also, some writers may write a particular letter in various ways, depending on what letter was last written. This results in substantially greater error rates than would be expected if the feature probability distribution data conforms to a Gaussian distribution. 
     Other prior pattern recognition techniques, referred to as non-parametric methods, such as the &#34;nearest-neighbor&#34; rule or the &#34;method of potential functions&#34;, are not constrained by the assumption that the probability distributions of extracted features are Gaussian. However, these techniques require far more computation and storage space for the data. The size of the data structure that summarizes the decision rules is proportional to the size of the training set, rather than independent of it as in parametric pattern recognition techniques. 
     Thus, there is an unmet need for an improved character recognition technique that provides the accuracy and flexibility of prior non-parametric pattern recognition strategies, the convenience and computational ease of prior parametric pattern recognition techniques, and the capability to operate on any size of character set. 
     SUMMARY OF THE INVENTION 
     It is an object of the invention to provide a pattern recognition system with increased accuracy over prior parametric pattern recognition techniques. 
     It is another object of the invention to provide a pattern recognition system which substantially increases accuracy over that of prior parametric pattern recognition techniques, yet avoids the computational complexity, cost, and large data storage capacity required of prior non-parametric pattern recognition systems. 
     It is another object of the invention to provide a pattern recognition system of the type described above wherein the size of the data structure representing the decision rule is independent of the size of the training set. 
     It is another object of the invention to provide a pattern recognition system wherein time and computational resources required during a training process are spent where they are most needed, on particularly difficult areas of the training process. 
     It is another object of the invention to provide a pattern recognition system of the type referred to above which achieves the benefits of both decision tree classification and Gaussian discriminant classification. 
     Briefly described, and in accordance with one embodiment thereof, the invention provides a system for statistical pattern or character recognition which reads an unknown pattern or character, extracts features from the unknown pattern or character, operates on the extracted features with a first classifier component and makes a decision whether the unknown pattern or character is within a first class, then determines if the first decision is a final decision that the unknown pattern or character is within the first class and, if so, reports that the unknown pattern is in the first class, and if it is not, selects a second classifier component; if the first decision is not a final decision, the system operates on the extracted features of the unknown pattern or character with the second classifier component and makes a second decision as to whether the unknown pattern or character is within the first class. The statistical pattern or character recognition system then repeats this process as many times as is needed to make a final decision as to whether the unknown pattern or character is within the first class; each decision that the unknown pattern or character is not within the first class results in selecting another classifier component lower in a hierarchy of classifier components. The system trains the first and second classifier components and any subsequent classifier components in the hierarchy with a training set of patterns or characters by selecting the first, second and other classifier components, extracting features from elements of the training set, and operating on the extracted features of the training set with the first classifier component to determine classes in which elements of the training set are classified, producing a first set of training elements of the training set which the first classifier component classifies into the first class, determines whether all of the first set of training elements are labelled as being included in the first class, and sets a decision indicator in the first classifier component to indicate that it can make a final decision that any other training component of the first set is in the first class. The training system recursively repeats the foregoing procedure for the second classifier component and any other classifier components lower in the hierarchy. The entire training procedure then is repeated for other sets of training elements and other classes. The components selected can be Gaussian discriminant components of decision tree components. 
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a block diagram useful in describing the training phase of a parametric pattern recognition component. 
     FIG. 2 is a block diagram useful in describing the recognition phase of a parametric pattern recognition component. 
     FIG. 3 is a diagram illustrating a hierarchy of parametric pattern recognition components in accordance with the present invention. 
     FIG. 4 is a diagram of a typical decision tree classifier. 
     FIG. 5 is a flow chart of a program HRECOGNIZE used in recognizing characters in accordance with the hierarchy shown in FIG. 3. 
     FIG. 6 is a flow chart of a program HTRAIN(i,T) used in training a hierarchical parametric pattern recognition component system as shown in FIG. 3. 
     FIG. 7 is a flow chart of a subroutine TREETRAIN called by the program of FIG. 6. 
     FIG. 8 is a flow chart of a subroutine TREE EDIT called by the subroutine of FIG. 7. 
     FIG. 9 is a flow chart of a subroutine EXPAND(i) called by the subroutine of FIG. 8. 
     FIG. 10 is a flow chart of a subroutine INTERACT(i) called by the subroutine of FIG. 9. 
     FIG. 10A is a flow chart of a subroutine CLUSTER PROCEDURE called by the subroutines of FIGS. 10 and 11. 
     FIG. 11 is a flow chart of a subroutine PARSECMD(y) called by the subroutine of FIG. 10. 
     FIG. 12 is a flow chart of a subroutine TREERECOGNIZE called by the program of FIG. 5. 
     FIG. 13 is a subroutine GAUSSTRAIN called by the program of Fi9. 6. 
     FIG. 14 is a flow chart of a subroutine GAUSSRECOGNIZE called by the program of FIG. 5. 
     FIG. 15 is a diagram useful in explaining isodata clustering and overlap. 
     FIG. 16 is a diagram useful in explaining the subroutine of FIG. 12. 
     FIG. 17 is a diagram useful in explaining basic feature extraction concepts. 
     FIG. 18 is a diagram of a system in which the character recognition system of the present invention can be incorporated. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
     The pattern recognition technique of the present invention is implemented in computer programs that run on the system shown in FIG. 18. In FIG. 18 a scanner 2 scans a hand drawn document 1 producing serial pixels which are filtered by noise filter 2A, the output of which is fed into a runlength encoder 2B. The runlength encoder 2B produces raw runlengths that are assembled or &#34;built&#34; into &#34;objects&#34; consisting of raw runlengths or horizontal slices arranged in a manner corresponding to the configuration of objects scanned on drawing 1, as described in commonly assigned patent application &#34;Method and Apparatus for Simplifying Run Length Data From Scanning of Images&#34; by John M. Roye, filed Feb. 19, 1987, now U.S. Pat. No. 4,821,336, issued Apr. 11, 1989 assigned to the present assignee, and incorporated herein by reference. An object classifier 3B determines from size and other geometric properties whether an object is small enough to be classified as a character, and if it is, feeds raw runlengths of the object into a runlength decoder 4A that converts the object runlengths back into the pixel image, i.e., to P(x,y) and computes certain parameters of the object. A border tracker 4D then operates upon P(x,y) to produce various input variables that are used in extracting features. A feature extraction system 5 produces intermediate computed variables and extracted features described in the above referenced Horowitz application. The extracted features are fed into the statistical character recognizer 6A, which is the subject of the present invention. The output of the statistical character recognizer 6A is fed through a rule based character context routine 6B, the output of which is fed from there into a file formatter 7, the output of which is loaded for editing into a work station 8. Work station 8 includes an IBM PC-AT computer, a keyboard, a high resolution graphics monitor, a high resolution plotter, a hard disc, and other suitable hardware. 
     Before describing the hierarchical parametric character recognition technique of the present invention, it would be helpful to refer to the example of FIG. 17 in order to more clearly understand the extracted features of characters upon which the character recognition system of the present invention operates. In the example of FIG. 17, numeral 32-0 represents a first minimum bounding rectangle of a character 32. A second minimum bounding rectangle 32-1 also can be drawn, rotated 15 degrees relative to the original x and y axes. Four further minimum bounding rectangles (not shown) each rotated 15 degrees clockwise (or counter clockwise) relative to the next also can be drawn. Each of the six minimum bounding rectangles may have a different center, a different height, and a different width. A variable clen(0) represents the height of the first minimum bounding rectangle 32-0, clen(7) is the width of that minimum bounding rectangle, clen(2) is the height of the first rotated minimum bounding rectangle 32-1, clen(8) is the width of rectangle 32-1, and so forth, so that a set of variables clen(0), . . . clen(11) represents the lengths of the two perpendicular sides of all six rotated minimum bounding rectangles of P(x,y), the function which represents all of the perimeter points of character 25. Similarly, another set of features cprd(0), cprd(5) can be extracted which are the areas of the six above minimum bounding rectangles. Other features that can be extracted including the height-to-width aspect ratios of each of the minimum bounding rectangles. The geometrical centers 26-0, 26-1, etc., of the six minimum bounding rectangles, the sum of the distances between the six minimum bounding rectangle center points, and numerous other geometric features and their statistical means and variances can be computed for the character 25. These, suitably normalized, and/or Fourier coefficients thereof are examples of the many features that can be used as extracted features which then are operated upon by the character recognition technique of the present invention to classify or recognize the character. 
     Referring now to FIG. 1, block 40A contains a parametric pattern recognition component or algorithm α k  which can be used in a training procedure that must be performed before any pattern recognition of a sample character can be achieved. k is an arbitrary index used to distinguish one particular pattern recognition component from another. Component α k  in FIG. 1 must be &#34;trained&#34; before it is capable of classifying unknown objects or samples s 1 , s 2 , s 3 , etc. 
     In order to train a component α k  to classify samples, that component must be trained by having it operate on a set of training samples S=[s 1 , s 2 , . . . s n  ]. L is a function giving the true label (i.e., classification) of each sample s in the set S. Block 41A in FIG. 1 means that the set S of training samples s 1 , s 2 , . . . s n  is provided as an input to component α k . Each training sample s i  is properly labeled as to which class it should be classified into. (For example, a handwritten B would be labeled as class 2, in the set [ω 1 , ω 2 , . . . ω 26  ] which represents the upper case alphabet [A, B, . . . Z].) 
     The output of α k  in FIG. 1 is indicated in block 42A, which contains a compact statistical representation R k  of the differences of extracted features from the training set S, including the mean and standard deviation for each feature extracted from the training set. L labels the correct class (i.e., A, B, M, Q, etc.) of each training sample s. 
     In a general sense, R k  may be anything that suitably describes the extracted features. For example, it can be a set of statistics or a statistical decision tree. At the end of the training procedure there is produced for each component α k  a data structure R k  which can be used by a recognition component α k  (which is now a &#34;trained&#34; version of the α k  component initially used in the training procedure) to recognize objects or samples scanned by the above mentioned scanner in FIG. 17. 
     The set Ω=[ω1, ω2, . . . ωm] is a set of m possible classes or types of characters, i.e., &#34;A&#34;, &#34;B&#34;, &#34;F&#34;, . . . &#34;Z&#34;. 
     In FIG. 2, which shows the recognition phase of parametric pattern recognition by a particular component α k  shown in block 40B, the above mentioned data structure R k  in block 42A is utilized to operate upon an unknown object s to be classified shown in block 41B. The result is a decision as to which ω of the set Ω the unknown objects should be assigned. Features are extracted, in accordance with the above referenced commonly assigned Horowitz application or other known feature extraction procedures as described in the Duda and Hart reference. The features extracted from the unknown character s are classified using R k  to enable the component α k  to render the decision. 
     By way of definition, the term &#34;component&#34; can be understood to encompass a &#34;trained&#34; component including the data structure R k  which results from the training process. 
     What has been described up to now is known in the prior art. In a feature extraction process, each object s i  is reduced to a vector V i  of real-valued features or measurements. The next step then is the computation of a mean vector ρ j  and a standard deviation vector σ j  for each of the m classes. Each vector has as many components as there are features extracted from the object s i . The training set S then is summarized by m mean vectors and m variance vectors. 
     In accordance with the present invention, a departure is made from the prior art technique of using a single pattern recognition component α k  to perform the entire classification for the entire universe of characters to be recognized. Instead, a &#34;hierarchy&#34; of components is utilized. 
     In FIG. 3, the extracted feature representation R1 is used by a component α 1  to operate upon an unknown character s as indicated in block 10. Associated with component α 1  is a delta-function δ 1 . In accordance with the present invention, the delta-function δ 1  may indicate that the unknown object s has been recognized or classified as an element ω of the set Ω or, if component α 1  is incapable of adequately classifying s, δ 1  may point to a lower member of the hierarchy shown in FIG. 3, i.e., to block 11, 12, or 13. Similarly, the component α j  of each of blocks 11, 12, or 13 has associated with it a delta-function δ j . Some of the components lower in the hierarchy result only in a decision that the unknown object s has been recognized, while for others the delta-function can point to a still lower component in the hierarchy. Each component α k  in the hierarchy below component α 1  utilizes a data structure or extracted feature representation R k  obtained during training of the hierarchy, as subsequently described. As indicated above, the trained components α 1 , α 2k , etc. can be considered to include the data structures R 1 , R 2 , etc., respectively. For example, in block 11, α 2  utilizes R 2  to operate on s to produce an output which is further operated on by δ 2  to produce a decision, which may be a classification or a reference to a lower component in the hierarchy. 
     Each delta-function tells us whether the decision of the corresponding component α i  is to be considered final, or whether additional components of the hierarchy need to be invoked for a final decision as to the proper classification of the unknown object s. This can be mathematically stated as: if δ i  (α i  (s))=ωεΩ, then ω is the final decision of the hierarchy as to the classification of s. If, on the other hand, δ i  (α i  (s))=α j  εA, wherein A is the set [α i , α 2 ,--α r  ] of possible components, then the decision is deferred and s is input to a lower component α j  in the hierarchy. Recognition of the unknown object s thus involves tracing through the hierarchy of pattern recognition components α i  until a decision ω i Ω is generated. 
     Generally, the recognition component α k  in FIG. 2 can be a Gaussian discriminant component of the type described in the Duda and Hart text or the Tou and Gonzalez text. Training of Gaussian discriminant components consists of merely extracting and saving parameters such as the mean and variance of suitable extracted features for each class or type of character to be recognized, as shown in the flow chart of FIG. 13, subsequently described. In this case, after training of a Gaussian discriminant component, recognition proceeds as indicated in the flow chart of FIG. 14. Posterior (after application of Bayes Rule) probabilities P(ω i  |s) are calculated for each class ω i  and a decision is made in favor of the class with the greatest P(ω i  |s). 
     Alternately, a decision tree recognition technique, subsequently described, can be utilized to implement the recognition component α k  in FIG. 2. 
     Use of the above hierarchical technique of parametric pattern recognition results in better classification decisions than the prior art, wherein a single level component α k  frequently is incapable of providing a strong decision and frequently requires a &#34;no decision&#34; outcome. The output of δ i   according to the present invention is either a class, indicating a correct decision or classification of the unknown object s, or δ i  is a pointer to another component lower in the hierarchy, which then operates on an appropriate extracted feature representation R k  in a more &#34;refined&#34; attempt to classify the present character. R k  will be different for different components at different levels in the hierarchy. The hierarchical parametric pattern recognition component technique allows different use of both decision tree components and Gaussian discriminant components at different levels of the hierarchy to obtain a previously unachieved level of accuracy at a reasonable cost. 
     It should be noted that a prior technique developed by Wald, known as the &#34;sequential probability ratio test&#34;, determines the confidence of the decision of a component operating on certain extracted features, and if the confidence level is below a certain value, more features are extracted from the unknown object and compared to features obtained during a global training process. The present invention distinguishes over Wald&#39;s techniques by utilizing separately trained recognition components in a sequential manner. 
     In the described embodiment of the invention, a parametric character recognition component α i  can be of two different types, the first type being a decision tree having a structure generally as indicated in FIG. 4. This type of decision tree is based on ideas presented in the two references &#34;An Analysis of a Decision Tree Based on Entropy Reduction and its Application to Large Character Set Recognition&#34;, by Wang and Suen, &#34;IEEE Transactions on Pattern Analysis and Machine Intelligence&#34;, vol. 6 no. 4, July, 1984, pp 406-417 and &#34;Chinese Character Classification by Globally Trained Tree Classifier and Fourier Descriptors of Condensed Patterns&#34;, by Tang, Suen &amp; Wang, First International Conference on Computers and Applicators, Beijing, China, 1984, and &#34;Isoetrp--An Interactive Clustering Algorithym With New Objectives&#34;, Pattern Recognition, by C. Y. Suen, vol. 17, no. 2, pp 211-219, 1984, all three of which are incorporated herein by reference. The other type of parametric character pattern recognition component is a simple Gaussian discriminant component, which uses Bayes&#39; decision rule, as described in Chapter 2 of the Duda and Hart reference, incorporated herein by reference. 
     Referring to FIG. 5, the main program HRECOGNIZE for recognizing an unknown character s is entered at label 50, wherein the unknown object s is provided as an input. The program goes to block 51, and sets the component index i to 1, and goes to block 52. In block 52, the program calls either the TREERECOGNIZE subroutine of FIG. 8, or the GAUSSRECOGNIZE subroutine of FIG. 10, depending upon whether α i  is a decision tree component or a Gaussian discriminant component. These two subroutines will be described subsequently, after the training procedure is described. Once the α i  (s) component has operated upon the unknown objects by extracting the features required and going through the appropriate decision tree classifying procedure or the application of the Bayes rule computations, the HRECOGNIZE program goes to decision block 53 and determines if a deltafunction δ i  associated with the present component α i  indicates that the unknown character s has been recognized, or if δ i  instead designates the index of a component lower in the hierarchy of FIG. 3. If χ, the value of δ i , has a value that is within the set of possible classes, i.e., within the set Ω=[A, B, . . . Z], decision block 53 produces an affirmative decision, and reports that the class of the unknown characters is the present value of χ in block 54 and exits at label 56. 
     However, if decision block 53 determines that s has not been adequately classified, the program goes to block 55 and sets i to the value of χ, which indicates the next component to be tried in the hierarchy of FIG. 3. The program then returns to block 52 and calls the appropriate TREERECOGNIZE or GAUSSRECOGNIZE subroutine, and computes a new corresponding value of δ i . This procedure continues until an end point ωεΩ (FIG. 3) of the parametric recognition component hierarchy, is reached, at which point the appropriate decision is reported in block 54 and the HRECOGNIZE program is exited by label 56, and recognition of the unknown character s has been accomplished. 
     Before describing the TREERECOGNIZE and GAUSSRECOGNIZE subroutines called by HRECOGNIZE, it will be helpful to first understand the procedure for &#34;training&#34; the parametric pattern recognition components α i . This is accomplished in the HTRAIN subroutine of FIG. 6. 
     Referring to FIG. 6, the program HTRAIN(i,T) operates on a training set T[t1, t2 . . .] of training samples to build a component hierarchy similar to the one shown in FIG. 3. The HTRAIN program goes from block 60 to block 61 and, beginning with an initial value of i=1, makes a determination whether this component should be a decision tree component or a Gaussian discriminant component. (Presently, α 1  is a decision tree component, and lower levels of χ are Gaussian discriminant components, as this has produced good results up to now.) If the component α i  is to be a decision tree component, the TREETRAIN subroutine of FIG. 7 is called; otherwise, the GAUSSTRAIN subroutine of FIG. 13 is called. The HTRAIN program then goes to block 62 and sets an initial value of a class counter k equal to 1. The program then goes from block 62 to decision block 63 and determines if k is greater than m, the number of classes ω in Ω. If it is, it means that all of the classes have been trained and all of the components α i  in the hierarchy have been trained and linked together to produce a parametric pattern recognition hierarchy similar to the one shown in FIG. 3. The program in this case exits via label 64. If k is less than or program in this case exits via label 64. If k is less than or equal to m, the program goes to block 65 The loop controlled by decision block 63 thus requires HTRAIN to train a sufficient number of components α i  to classify all of the elements t of the training set T. 
     If the determination of decision block 63 is negative, the program goes to block 65. In block 65 the program generates a subset θ k  of the training set T, which the component α i  (t) &#34;thinks&#34; belongs in the present class ω k . In mathematical notation, the expression within the brackets means that θ k  is equal to the set of elements t in the training set T such that component α i , when presented with a sample t, decides that t is in the class ω k . 
     After producing the subset θ k  the program goes from block 65 to decision block 66 and determines whether it is true that for all of the t&#39;s in the set θ k  they are in fact labeled by the function L(t) as being in the class ω k . If this determination is true, it means that the present delta-function α i  should be set equal to ω k  ; this is what is done in block 67. The program then goes to block 71, increments the class counter k, and returns to the beginning of decision block 63. 
     However, if the determination of decision block 66 is false, it means that there are some elements t in the training set T that had been identified as not falling within the present class ω k , so more processing is required to properly classify those elements. The program in this event goes from decision block 66 to block 68 and sets α i  (ω k ) to the index of a component lower in the hierarchy, i.e., to i+1. The program then goes to block 69 and accordingly increments i to equal i+1. The program then goes to block 70 and recursively repeats the entire procedure shown in FIG. 6 until an affirmative decision is obtained in decision block 66 and α i  (ω k ) is set to δ i  k, thereby classifying the present value of t. 
     Thus, the HTRAIN program generates all of the delta-functions δ i  associated with the various levels of α i  that are required to classify all members of the training set T. 
     θ k  is actually the set of elements t within the training set T that have been provisionally assigned to class ω k . If they all are definitely in the class ω k , as determined by referring to their labels L(t), then δ i  is set equal to ω k . Otherwise, if further decisions must be made before final classification of members of θ k , δ i  is set to i+1, which is the index of a lower component in the hierarchy. Index i is incremented in block 69. (There should be a limit (not shown) on the number of components or depth of the hierarchy to prevent potentially infinite computation in training which might run if the extracted features are inadequate to allow perfect classification.) 
     Referring next to FIG. 7, the flow chart of the TREETRAIN routine called in block 61 of HTRAIN is entered at label 80. In block 81 the TREETRAIN subroutine uses features extracted from all elements of the training set T and computes the mean μ and the variance σ 2  each of the classes k in the training set T for some set of features for that class. HTRAIN then calls the TREE EDIT subroutine of FIG. 8 in block 82, which is an interactive subroutine that enables the user to build a decision tree similar to the one shown in FIG. 4. TREETRAIN then is exited via label 83. 
     In the TREE EDIT program, the person doing the editing is able to make modifications to a existing decision tree or to create an entirely new decision tree. TREE EDIT has the ability to supply feedback to the user to guide the tree building process, including providing pairwise feature correlations, the Fisher Merit measure of the features under consideration, and cluster overlap information. The Fisher Merit measure is known to those skilled in the art, as indicated in the reference Fisher, R. A., &#34;The Statistical Utilization of Multiple Measurements&#34;, Ann. Eugen., 8, 376-386 (1938). 
     It should be appreciated that a thorough understanding of the above Suen reference is necessary to appreciate how the feedback information is utilized. The basic idea, however, is that each node of the decision tree represents a cluster of character classes. The node at the root of the decision tree corresponds to the cluster containing all possible classes. In FIG. 4, node 20 is the root node. Child nodes such as 21, 22, 23, etc., represent subclusters of the universal cluster. Those subclusters are then further subdivided by their own child nodes, until each cluster contains only a single class ω k . 
     Still referring to FIG. 8, the program TREE EDIT called from block 82 of FIG. 7 is entered at label 90 and goes to decision block 91. Decision block 91 determines if a decision tree already exists, or whether it is necessary to call the EXPAND(i) subroutine of FIG. 9 to allow the user to interactively build a new tree structure. If the determination of block 91 is negative, the program goes to block 92 and calls the EXPAND(i) routine. In block 92, the program sets the index i of the EXPAND(i) subroutine to 1 and prompts the user, as subsequently described, to build a decision tree, starting with a root node i=1. 
     The program goes from an affirmative determination of block 91 or from block 92 into block 93, once a decision tree exists, and prompts the user to enter a code. The code can be an &#34;e&#34;, &#34;R&#34;, &#34;Q&#34;, or a &#34;W&#34;. The TREE EDIT subroutine then goes to block 94, reads the code entered by the user, and decision block 95 determines if the code is an &#34;e&#34;. If it is, the program goes to block 96 and prompts the user for a node number n. The number &#34;n&#34; represents the first node that the user wants to edit. The program goes from block 96 to block 97, calls the EXPAND(i) subroutine of FIG. 9 with i=n. The user then makes the desired modifications to the decision tree. The subroutine then returns to block 93. 
     If the determination of block 95 is negative, the subroutine goes to block 98 and determines if the user entered code is &#34;R&#34;. If this determination is affirmative, the subroutine causes the computer to display the tree structure in block 99 on a monitor, and returns to block 93. If a code &#34;Q&#34; is entered, this means that the user is finished editing the decision tree, and returns via label 101. If a code &#34;W&#34; is entered, this means that the decision tree is to be written to a suitable file, as indicated in block 103, and the program returns to block 93. 
     Finally, if a code not recognized in decision blocks 95, 98, 100, or 102 is entered by the user, the TREE EDIT subroutine causes the computer to print an &#34;invalid code&#34; message and returns via block 93. 
     Referring now to FIG. 9, the EXPAND(i) subroutine is entered via label 110, and first goes to block 111 and calls up the subroutine INTERACT(i) of FIG. 10. It would be helpful to the understanding of the TREE EDIT subroutine to describe the INTERACT(i) program of FIG. 10 next. Note that the EXPAND(i) subroutine deals with building the whole decision tree. The EXPAND(i) subroutine, as it is building the whole decision tree, calls the INTERACT(i) subroutine for each node. 
     Referring to FIG. 10, the INTERACT(i) subroutine is entered via label 130, goes to block 131, and allocates a predetermined amount of storage for the maximum number of child nodes. INTERACT(i) then enters the CLUSTER subroutine of FIG. 10A in block 132. Referring now to FIG. 10A, the CLUSTER subroutine enters block 132A and performs an isodata clustering procedure on the set of classes represented in training set T. For each class, such as A, B, and C in FIG. 15, isodata clustering generates information indicative of whether grouping of these classes allows them to be properly clustered. i.e., M and N are clusters in FIG. 15. The CLUSTER subroutine then goes to block 132B, and computes the amount of cluster overlap. In FIG. 16, the shaded area indicates cluster overlap. In block 132B of FIG. 10A the feature cluster overlaps are computed in order to determine whether the clusters presently selected do in fact effectively partition the data. Then, in block 132C, this information is displayed to the user, who then can determine precisely what the tentative clusters are and how much they overlap. The clustering is performed by conventional statistical computations. See, for example, the reference Tou and Gonzalez, Ch. 3, incorporated herein by reference. In the example shown in FIG. 15, probability distributions A, B, and C form one isodata cluster, and probability distributions X, Y, and Z, which also are relatively close together, form another isodata cluster. The determination of overlap is based on the Bhatacharyya estimate of Bayes error. See the reference Statistical Pattern Recognition, Chi-hau Chen, 1973 Spartan Books, Hayden Book Co. ISBN 0-87671-177-8, incorporated herein by reference. Statistical estimators of how much overlap there is between the clusters allow the user to determine how well the data is partitioned and whether to accept the two clusters A, B, C, and X, Y, Z. The CLUSTER subroutine then returns to calling subroutine via label 132D. 
     In block 135 of FIG. 10, the INTERACT(i) subroutine prompts the user to enter a command. (The command can be any of the commands defined in the PARSECMD(y) subroutine of FIG. 11, described next.) In block 136 the INTERACT(i) subroutine reads the command y entered by the user, and in decision block 137 determines if that command was a &#34;X&#34; If it was, it means that the INTERACT(i) procedure is over for the present child node. In this case, the program releases part of the storage previously allocated in block 131, as indicated in block 138, and returns to block 112 of FIG. 9. If the command is not a &#34;X&#34; the program goes to the PARSECMD(y) in block 140, and then returns to block 135. 
     At this point, it will be helpful to describe the PARSECMD(y) subroutine of FIG. 11, which is entered via label 150. In decision block 151 the PARSECMD(y) subroutine determines if the user entered command is an &#34;A&#34;, and if it is, goes to block 152 and adds a feature from the features previously extracted from T, if the user thinks the displayed clusters are not well enough separated. The subroutine then calls the CLUSTER subroutine of FIG. 10A, and returns to INTERACT(i) via label 168. If the command y is a &#34;C&#34;, the subroutine goes to block 154 and combines two clusters. The user is prompted to specify two clusters, on the basis of judging the overlap and Mahalanobis distance between the clusters. The program then calls the CLUSTER subroutine, as indicated in block 154A, and returns. If the command is a &#34;D&#34;, the subroutine deletes a cluster, as indicated in block 56. After calling CLUSTER in block 156A, PARSECMD(y) returns via label 168. If the user command is &#34;E&#34;, PARSECMD(y) enters block 158 and changes an error tolerance, calls CLUSTER in block 158A, and returns. (Error tolerance is a threshold that specifies when the classes with two clusters overlap.) In block 159, an affirmative determination that the user command is a &#34;O&#34; causes PARSECMD(y) to enter block 160 and reseed the current node. (The isodata clustering algorithym requires inputs called &#34;seeds&#34;, which are initial cluster centers in the feature space. These serve as starting points for aggregating the classes into clusters. The clustering can yield different results depending on how seed points are selected.) 
     The subroutine then calls CLUSTER in block 160A, and returns. If the user command is determined in block 161 to be &#34;M&#34;, the subroutine goes to block 162 and displays the Fisher Feature Merit Measure. The Fisher Merit indicates how well a particular feature separates the classes under consideration. The subroutine then returns via label 168. If the user command is an &#34;S&#34;, the subroutine goes to block 164 and splits a cluster. (i.e., an existing cluster center is replaced by a pair of points in the feature space to test if the present cluster ought to be split into two clusters.) 
     After calling CLUSTER in block 164A the subroutine returns via label 168. If decision block 165 determines that the user command is a &#34;Z&#34;, the subroutine goes to block 160 and displays a routine of the pairwise correlations between pairs of features. The subroutine then returns via label 168. Finally, if none of the above indicated user commands were entered, the subroutine prints an &#34;unrecognized command&#34; message in block 167 and returns via label 168. 
     Returning to FIG. 9, after block 111, the EXPAND(i) subroutine goes from block 111 to block 112 and sets n equal to the number of children of the present node i in the decision tree being constructed. The value of n is determined by the isodata clustering procedure of FIG. 10A. 
     The EXPAND(i) subroutine then goes from block 112 to block 113, sets k=1, goes to decision block 114 and determines if k exceeds n, and if it does, returns via label 115 to the calling routine. A negative determination by block 114 causes the EXPAND(i) subroutine to go to block 116 and determine if the present child node k is a &#34;terminal&#34; node that represents a decision. If this determination is negative, the subroutine goes to block 117, and recursively repeats the EXPAND(i) subroutine of FIG. 9 with i=k. Either an affirmative determination from decision block 116 that the present node k is terminal or completion of recursive execution of EXPAND(k) in block 117, causes k to be incremented, as indicated in block 118. The subroutine then returns to decision block 114. This procedure is repeated until either a new decision tree is completely constructed in block 92 of FIG. 8 or until editing of an existing tree is completed in block 97 of FIG. 8. 
     Thus, the EXPAND(i) subroutine recursively goes down the decision tree being constructed or edited, calling the INTERACT(i) subroutine at each node, allocating storage for the maximum number of child nodes that each node can have, and performs the cluster procedure on all of the classes at each node to separate the classes or partition them into different sets. For example, at the root node 20 in FIG. 4 the entire set of classes is partitioned into three clusters: a cluster 22 which contains a single class, namely the class &#34;B&#34;, containing characters which have two holes in them; cluster 21 which consists of this class of characters each of which has only a single hole in it; and cluster 23 which consists of the classes of characters which have no holes. The child node 21 then is determined to have two child nodes, one being node 24 the characters of which have the characteristic that the hole is not in the upper portion of the character, and node 25 the characters of which have the characteristic that the single hole is in the upper portion of each character. The procedure is continued in order to expand each child node into a further cluster until finally the child node contains only a single character. 
     After the HTRAIN program of FIG. 6 has been executed by constructing a hierarchy of parametric pattern recognition components α i  appropriate to the hand drawn characters s to be recognized, the HRECOGNIZE program of FIG. 5, which calls the TREERECOGNIZE program of FIG. 12 and the GAUSSRECOGNIZE program of FIG. 14, can be executed to recognize an unknown character s. 
     The procedure for the Gaussian discriminant method is indicated in the flow chart of FIG. 13, wherein the subroutine GAUSSTRAIN called by block 61 of HTRAIN (FIG. 6) if a Gaussian discriminant component is desired. GAUSTRAIN is entered at label 200, goes to block 201, and sets an index i with an initial value of 1 and sets m to the number of classes in the set Ω. GAUSSTRAIN then goes to decision block 202 and determines if i is greater than m, and if it is, produces a list of all of the means μ i , the variances σ i   2 , and the prior probabilities P i  in block 203, and exits via label 204. If i is not less than m, the subroutine goes to block 205, and applies the standard statistical formulas to compute μ i , σ i   2 , and P i . (See for example, Duda and Hart.) Thus, GAUSSTRAIN simply loops through all of the classes, and computes the mean, variance, and prior probability for the extracted features for each class ω i . The use of the prior probabilities P i  is important because this may indicate that the sample characters in the training set corresponding to the present class have a very lopsided distribution: for example, there may be ninety A&#39;s and two H&#39;s in it. The prior probability then informs the classifier that the present character is more likely to be an A. 
     Referring to FIG. 12, if the HRECOGNIZE program calls TREERECOGNIZE from block 52, the TREERECOGNIZE subroutine is entered via label 180, and first loads the decision tree computed by TREE EDIT in block 181. The TREERECOGNIZE subroutine then goes to block 182 and reads the unknown character s. 
     The subroutine goes from block 182 to block 183 and sets an initial value of i=1, the root node of the decision tree. The subroutine then goes to decision block 184 and determines if the node of the present index i is a terminal node, i.e., if it is a node that has no child nodes depending therefrom. If this is the case, it means that the TREERECOGNIZE subroutine has passed entirely through the decision tree. The subroutine therefore goes to block 185 and reports the decision or class ω k  which the unknown character s is recognized to be. For example, if the present value of i corresponds to terminal node E in FIG. 4, the decision reported in block 185 is that the character s is a &#34;E&#34;. The TREERECOGNIZE subroutine then is exited via label 186. 
     If the current node i (as TREERECOGNIZE traverses the decision tree) is not terminal, the subroutine goes to block 187 and extracts the features of the present character s needed at node i of the decision tree, in order to meaningfully compare it with corresponding features of various clusters of the present node. For example, in FIG. 4, if the present node is node 21, features are extracted from the current value of the unknown character s that enable it to be meaningfully compared with the children of cluster 21. The TREERECOGNIZE subroutine then goes to block 188 and finds which of the child clusters of the present node has the least Mahalanobis distance from its cluster center to the position of the unknown character s in the present feature space. For example, in FIG. 16, reference numeral 230 indicates the position of the unknown character s in the feature space, 231A designates the cluster center of a first child cluster having a probability distribution 231, and 232A designates that cluster center of a second child cluster having a probability distribution 232. The Mahalanobis distance can be visualized as the distance 233 from position 230 to the center of child cluster 232. Since that distance 233 is shorter than the corresponding distance to the center 231A of the first child cluster 231, cluster 232 would be the one chosen in block 188. This technique is described in standard references, such as the above mentioned Duda and Hart reference. The center of each child cluster is its mean μ. The Mahalanobis distance is a quantity analogous to the Euclidian distance between the position of the unknown characters and the mean of a particular child cluster, modified by the covariance matrix values of the child cluster under consideration. 
     Next, TREERECOGNIZE goes to block 189 and assigns to index i the index of the node associated with the cluster C having the least Mahalanobis distance to the position of the unknown character s. If that node is a terminal node, an affirmative decision is obtained in decision block 184, and the character represented by the node i is reported as the decision of the tree. 
     The GAUSSRECOGNIZE subroutine of FIG. 14, when called by block 52 of HRECOGNIZE (FIG. 5), is entered via label 210 and goes to block 211 and reads the unknown character s. The subroutine then goes to block 212 and extracts the needed features from s, goes to block 213, and sets an initial value of C to a large negative number, sets m to the number of classes in Ω, and sets the index i to an initial value of 1. The subroutine then goes to decision block 214, which reports the decision of GAUSSRECOGNIZE, if i exceeds m, in block 215 and exits via label 216. If GAUSSRECOGNIZE has not operated on all of the m classes, a negative determination is obtained from block 214, and the subroutine goes to block 217 and reads the values of μ i , σ i   2  and R i  from the extracted feature representation R k  that corresponds to the present value of i. Then, using a conventional Bayes rule technique in block 218, the subroutine computes the posterior probability P(ω i  |s) that tells how likely it is that s is truly a member of class ω i , in accordance with standard techniques, as disclosed in the Duda and Hart reference. The subroutine then goes to block 219 and determines whether P(ω i  |s) exceeds C, and if it does, it goes to block 220 and sets C equal to the present value of P(ω i  |s), which is the probability that ω i  is the classification of s. In block 220 the subroutine also sets a decision parameter d to ω i , the highest probability class encountered so far by GAUSSRECOGNIZE. The subroutine increments i in block 220A and then returns to decision block 214. If the determination of block 219 is negative, the subroutine increments i and then goes to decision block 214. Thus, the highest probability decision is the one reported in block 215. 
     The above described technique is an adaptive compromise between the computational tractability of prior parametric methods and the power of prior non-parametric methods. At the root of the hierarchy of parametric pattern recognition components, the original training set T is summarized by the usual set of parameters. If these parameters are adequate for perfect classification of all training samples, then recognition is complete. It usually happens, however, that there are certain class distinctions (for example, a &#34;q&#34; versus a &#34;9&#34;) that are not handled adequately by the initial parameterization. The training technique described above identifies these problem areas and takes additional passes through the same training data, concentrating only on those unknown samples that are misclassified by the original classifier (i.e., the root component α 1 ). This process is continued recursively until classification is accomplished. The benefit is that the time and computational resources during the training process are spent where most needed, on the problem areas. The &#34;easy&#34; distinctions are made quickly, on the first parameterization. If all distinctions are &#34;easy&#34; the process is equivalent to simple parametric pattern recognition. If the distinctions are not &#34;easy&#34;, the process is much more accurate than simple parametric pattern recognition, but not nearly as expensive and computationally tractable as the traditional non-parametric methods. 
     Appendix A attached hereto is a printout containing the program of FIGS. 5-11, written in the language C. 
     While the invention has been described with reference to a particular embodiment thereof, those skilled in the art will be able to make various modifications to the described embodiment of the invention without departing from the true spirit and scope thereof. ##SPC1##