| Preface | p. xi |
| Thinking, Visual Thinking and Shape Understanding | p. 1 |
| Introduction | p. 1 |
| Shape and Form | p. 4 |
| Understanding | p. 9 |
| Cognition | p. 13 |
| Visual Perception | p. 14 |
| Visual Intelligence | p. 16 |
| Knowledge | p. 17 |
| Learning | p. 22 |
| Reasoning | p. 24 |
| Recognition | p. 26 |
| Thinking | p. 26 |
| Shape Understanding System | p. 34 |
| Shape Classes | p. 47 |
| Possible Classes of Shape | p. 47 |
| General Classes: A Priori Classes | p. 48 |
| Convex Classes | p. 50 |
| Convex Polygon Class and Its Subclasses | p. 50 |
| Convex Curve-Polygon Class and Its Subclasses | p. 52 |
| Convex Curve Class and Its Subclasses | p. 54 |
| Concave Classes | p. 57 |
| Levels of Iterations | p. 58 |
| Concave Polygon Class | p. 61 |
| Concave Curve-Polygon Class | p. 64 |
| Thin Classes | p. 66 |
| Cyclic Class | p. 72 |
| Complex Cyclic Class | p. 74 |
| Cyclic Thin Class: The G-Class | p. 75 |
| Convex Cyclic Thin G-Class | p. 77 |
| Concave Cyclic Thin G-Class | p. 78 |
| Colored Classes | p. 79 |
| The a Posteriori Classes | p. 80 |
| The Star Class | p. 81 |
| The Spade Class | p. 84 |
| The Letter Class | p. 89 |
| String Form: Type of the Class | p. 93 |
| Generalization | p. 96 |
| Digital Objects, Image Transformations, and Reasoning Process | p. 101 |
| Digital Image Representation | p. 101 |
| Processing Methods: Image Transformations | p. 102 |
| Image Transformation and the Visibility Measure | p. 103 |
| Reasoning Process | p. 105 |
| Convex Object: Reasoning Process | p. 107 |
| Concave Polygon Object: Reasoning Process | p. 121 |
| Thin Object: Reasoning Processes | p. 125 |
| Cyclic Object: Reasoning Process | p. 132 |
| Categories | p. 135 |
| Introduction | p. 135 |
| Category of Visual Objects | p. 139 |
| Perceptual Categories | p. 141 |
| Structural Categories | p. 143 |
| Element Category | p. 143 |
| Pattern Category | p. 146 |
| Picture Category | p. 149 |
| Category of Animation | p. 153 |
| Ontological Categories | p. 153 |
| Interpretation of the Visual Object | p. 154 |
| Dependence Among Ontological Categories | p. 157 |
| Figure Category | p. 163 |
| Polygon Category | p. 164 |
| Category of Curves | p. 166 |
| Category of Curve-Polygon Figures | p. 168 |
| Category of Mathematical Objects | p. 168 |
| Category of 2D Mathematical Objects | p. 168 |
| Category of 3D Figures | p. 175 |
| Category of Mathematical Coordinate Systems | p. 175 |
| Category of Statistical Objects | p. 177 |
| Category of Visual Physical Models | p. 180 |
| Category of Signs | p. 182 |
| Category of Visual Symbols | p. 183 |
| Category of Mathematical Symbols | p. 184 |
| Category of Musical Symbols | p. 186 |
| Category of Engineering Symbols | p. 187 |
| Category of Symbolic Signs | p. 190 |
| Category of Letters | p. 193 |
| Category of Real-World Objects | p. 196 |
| Categories of Macro- and Micro-Objects | p. 204 |
| Category of Earthy-World Objects | p. 205 |
| Category of Non-Living Objects | p. 206 |
| Category of Living Objects | p. 213 |
| Category of Animals | p. 214 |
| Category of Plants | p. 217 |
| Category of Imaginary Objects | p. 223 |
| Category of Real-World Processes | p. 224 |
| Category of Visual Tests | p. 228 |
| Categorical Learning | p. 234 |
| Visual Thinking: Understanding | p. 241 |
| Understanding in the Context of Shape Understanding System | p. 241 |
| Thinking and Visual Thinking | p. 245 |
| Visual Thinking as a Problem Solving Process | p. 247 |
| Problem Solving | p. 251 |
| Problems Given in the Form of the Symbolic Representations | p. 255 |
| Problem Given in the Form of Both Symbolic and Visual Representations | p. 258 |
| Problem Given in the Form of the Visual Representation | p. 260 |
| Performing Task Given by the User | p. 260 |
| Visual Thinking as a Problem Solving | p. 267 |
| Perception: Problem Solving | p. 267 |
| Naming and Recognition of the Different Categories of Objects | p. 278 |
| Figure Naming: Assigning the Name to the Figure | p. 280 |
| Naming of the Figure Without Name | p. 281 |
| Naming of the Figure with Name | p. 282 |
| Naming of the Sign | p. 284 |
| Naming of Mathematical Symbols | p. 285 |
| Naming of Symbolic Signs | p. 287 |
| Letter Naming | p. 292 |
| Naming of the Different Fonts of the Letter | p. 292 |
| Similarities of Different Letters | p. 298 |
| Naming and Recognition of Real-World Objects | p. 304 |
| Naming of the Mathematical Object | p. 326 |
| Identification of Statistical Visual Objects | p. 329 |
| Data Analysis | p. 330 |
| Category of Physical and Engineering Models | p. 334 |
| Visual Resemblance: Visual Analogy | p. 336 |
| Spatial Problems | p. 342 |
| Problem Solving - Categorical Knowledge | p. 348 |
| Visual Diagnosis | p. 350 |
| Assembling Tools | p. 355 |
| Moving Object Outside | p. 371 |
| Obstacle Detection and Motion Planning | p. 372 |
| Visual Intelligence Tests | p. 375 |
| Visual Discrimination Test | p. 376 |
| Visual Sequential Memory Test | p. 378 |
| Visual Form Constancy Test | p. 379 |
| Matrix Test | p. 380 |
| Category of Spatial Tests | p. 394 |
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