During the last twenty years the problem of pattern recognition (specifically, image recognition) has been studied intensively by many investigators, yet it is far from being solved. The number of publications increases yearly, but all the experimental results-with the possible exception of some dealing with recognition of printed characters-report a probability of error significantly higher than that reported for the same images by humans. It is widely agreed that ideally the recognition problem could be thought of as a problem in testing statistical hypotheses. However, in most applications the immediate use of even the simplest statistical device runs head on into grave computational difficulties, which cannot be eliminated by recourse to general theory. We must accept the fact that it is impossible to build a universal machine which can learn an arbitrary classification of multidimensional signals. Therefore the solution of the recognition problem must be based on a priori postulates (concerning the sets of signals to be recognized) that will narrow the set of possible classifications, i.e., the set of decision functions. This notion can be taken as the methodological basis for the approach adopted in this book.
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ISBN-13
978-0-387-90440-5 (9780387904405)
DOI
10.1007/978-1-4612-6033-2
Schweitzer Klassifikation
I The Current State of the Recognition Problem.- 1.1 Basic Concepts and Terminology.- 1.2 Heuristic Paths.- 1.3 Methods Based on Assumptions on the Family of Decision Functions.- 1.4 Methods Based on Assumptions about the Properties of the Signals.- 1.5 Applications and Results.- 1.6 Conclusions.- II A Parametric Model of the Image-Generating Process.- 2.1 Difficulties in Image Recognition.- 2.2 A Parametric Model with Additive Noise.- 2.3 The General Parametric Model.- 2.4 Recognition and Learning Viewed as Problems of Optimal Decision with Respect to Parameter Values.- 2.5 Recognition in the Absence of Nuisance Parameters.- 2.6 Recognition with Nuisance Parameters.- 2.7 Optimization of the Decision Rule over a Prescribed Class.- 2.8 Learning and Self-Learning.- 2.9 Problems with Nonstatistical Criteria.- 2.10 Conclusions.- III The Parametric Learning Problem.- 3.1 Learning with a Sample of Mutually Dependent Signals in the Presence of a Nuisance Parameter.- 3.2 Learning with Independent Nuisance Parameters.- 3.3 Learning as the Minimization of the Conditional Risk.- 3.4 Conclusions.- IV On the Criteria for the Information Content of a System of Features.- 4.1 On the Choice of Primary and Secondary Features.- 4.2 Sufficient Statistics.- 4.3 A Measure of Insufficiency.- 4.4 Generalization of the Measure of Insufficiency to the Case of Probabilistic Transformations.- 4.5 Entropy as a Measure of Insufficiency.- 4.6 On the Kullback Divergence.- 4.7 Entropy and Error Probability.- 4.8 The Information Content of the Optimal Decision.- 4.9 Theorems on the Relation between the Conditional Entropy and the Error Probability.- 4.10 Conclusions.- V The Method of Admissible Transformations.- 5.1 Sets that are Closed under Transformations.- 5.2 Admissible Transformations and the Formalization of the Notion of "Similarity".- 5.3 Peculiarities of the Method of Admissible Transformations.- 5.4 Recognition by the Correlation Method.- 5.5 Experimental Results.- 5.6 Potential Applications of the Correlation Method.- 5.7 Conclusions.- VI Optimization of the Parameters of a Piecewise Linear Decision Rule.- 6.1 The Adequacy of a Piecewise Linear Rule and Formulation of the Optimization Problem.- 6.2 The Linear Decision Rule as a Special Case.- 6.3 The Optimization Problem and Its Solution.- 6.4 Solution of the Optimization Problem for a Piecewise Linear Rule.- 6.5 An Application to the Recognition of Alphanumeric Characters by a Character Reader.- 6.6 Conclusions.- VII The Reference-Sequence Method.- 7.1 Formal Statement of the Structural-Description Problem.- 7.2 Formal Syntactical Rules for Constructing Composite Images.- 7.3 Solution of the Problem of Maximum Similarity.- 7.4 Images on a Two-Dimensional Retina.- 7.5 Recognition of Lines with Restricted Change of Direction.- 7.6 Recognition of Handwritten Characters.- 7.7 Conclusions.- VIII The Recognition of Sequences of Images.- 8.1 Mathematical Model of a Typewritten Line, and Formulation of the Problem.- 8.2 Solution of the Problem.- 8.3 Solution of the Problem with a Correlation Criterion for the Similarity.- 8.4 Recognition of Sequences of Unbounded Length.- 8.5 Examples and Experiments.- 8.6 Scope of the Algorithm and Possible Generalizations.- 8.7 Conclusions.- IX The "?ARS" Character Reader.- 9.1 The Operational Algorithm for a Character Reader.- 9.2 The Technical Implementation of the Line Recognition Algorithm.- 9.3 The Choice of the Hardware for Finding and Scanning the Lines.- 9.4 Block Diagram of the ?ARS Reader.- 9.5 Tests of the Reader.- 9.6 Conclusions. On the Use of Character Readers.- References.- List of Basic Notations.
