Abstract
From a very young age, humans are able to recognize objects or living beings while they move and assume different postures. This ability to recognize object identities through flexible aspects could be based on invariant properties of shapes, such as for example the properties put forward by the formalism of the medial axis theory (also called skeleton theory). This formalism, which was originally designed to describe organic shapes such as bodies or plants, can indeed easily capture “natural” invariances, such as the shape of an animal’s body as it moves. Several behavioral or brain imaging studies have started to highlight the role of the medial axis parameters in human vision, including in categorization. However, all these studies used different characterizations of the medial axis properties, making it hard to compare their results. In particular, across studies the authors manipulated different aspects of the shapes and their medial axes and used different measures to quantify skeletal similarities. Our work had two aims. First, we created a formal mathematical space providing a full description of shapes in the language of the medial axis formalism, which can be used as a unifying framework for cognitive research. For this purpose, we defined three families of parameters: topological parameters describing the structure of the skeleton in the format of a non-measured graph; skeleton parameters specifying the details of the shape’s skeleton; and growth parameters describing how the shape can be grown from its skeleton. Second, we also implemented a Matlab toolbox generating shapes specified in the vocabulary of these medial-axis parameters, and selectively manipulating each skeleton and growth parameter in isolation. In conclusion, our work introduces both a unifying parametric language and a methodological tool paving the way for future systematic investigations of the role of the medial-axis parameters in human vision.