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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