Form, space and object

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“.