In order to recognize an object, the visual system has to solve two basic problems: The first one is how to recognize an object after spatial transformations, i.e. regardless of its orientation, size and position. The second problem refers to the question how we perceive and categorize different objects as members of the same category.
A central hypothesis in this book is that both problems have a similar structure, and can be conceptualized within an integrative transformational account, based on concepts from geometry: Recognition after spatial transformations, on one hand, relies on Euclidean transformation processes that are conceptualized as frame transformations (or coordinate transformations). Categorization up to the basic level, on the other hand, can be accounted for by non-Euclidean topological (i.e. potentially space-curving) transformations. Thus, an integrative theory of recognition and categorization is suggested, based on a process-based interpretation of Felix Klein's Erlanger Program.

Markus Graf
Form, Space and Object. Geometrical Transformations in Object Recognition and Categorization
ISBN 10: 3-932089-91-X
ISBN 13: 978-3-932089-91-6
285 S. 25 EUR. 2002 (Diss.)

0. Two basic problems of object recognition ........ 15

1. Transformation processes in object recognition ........ 21
1.1 How can objects be recognized after spatial transformations?
1.2 Systematic relation between the amount of spatial transformation and recognition performance
1.3 Evidence for analog transformations in mental imagery and in object recognition
1.4 Congruency effects in object recognition and the adjustment of reference frames
1.5 The transformational model of recognition (TMR)
1.6 The relation between object recognition and mental rotation
1.7 Do the existing recognition models explain the data?
1.8 Are the arguments against transformational models of recognition convincing?
1.9 Conclusions, unresolved issues and outlook

2. Transformation processes in object categorization ........ 75
2.1 Accumulation of evidence against the traditional view of categorization
2.2 Evidence for image-based representations up to the basic level of categorization
2.3 A transformational model of basic level categorization: basic ideas
2.4 An integrative account through a process-based interpretation of the transformations of Klein's Erlanger Program
2.5 Evidence for analog nonrigid transformation processes in the visual system
2.6 A transformational account of shape similarity
2.7 A new view on typicality in basic level categorization
2.8 Scope of the transformational model and possible constraints for deforming transformation processes
2.9 Summary of the research questions

3. The experiments ........ 115
3.1 Experiment 1: A speeded categorization task on the basis of a sequential matching paradigm
3.1.1 Introduction
3.1.2 Methods Subjects Stimuli Procedure Design
3.1.3 Results and discussion Systematic relationship between the amount of topological transformation and categorization performance Sequential additivity
3.2 Experiment 2: Similarity and typicality ratings
3.2.1 Introduction Similarity Typicality
3.2.2 Methods Subjects Stimuli Procedure Design
3.2.3 Results and discussion Similarity ratings Typicality ratings

4. General discussion ........ 173
4.1 Summary of the findings from Experiment 1 and 2
4.2 Alternative models of recognition and categorization
4.2.1 Invariant property models
4.2.2 Traditional feature models
4.2.3 Structural description models
4.2.4 Image-based models Alignment models Interpolation models Image feature models Other image-based models
4.2.5 Summary of the discussion of the alternative models
4.3 TMRC and the part structure of object representations
4.4 An image-based conception of category representations
4.5 Concluding remarks

5. References ........ 209
Appendix A. Stimuli for Experiment 1
Appendix B. Stimuli and graded structures: Experiment 2
Appendix C. Objects with similar spatial configuration of parts
Appendix D. Tables
Appendix E. German summary / Deutsche Zusammenfassung