Relative coordinates are crucial for Ulam's "trick to the train of thought"

Abstract

Spatial signal processing algorithms often use pre-given coordinate systems to label pixel positions. These processing algorithms are thus burdened by an external reference grid, making the acquisition of relative, intrinsic features difficult. This is in contrast to animal vision and cognition: animals recognize features without an external coordinate system. We show that a coordinate system-independent algorithm for visual signal processing is not only important for animal vision, but also fundamental for concept formation. In this paper we start with a visual object deformation transfer experiment. We then formulate an algorithm that achieves deformation-invariance with relative coordinates. The paper concludes with implications for general concept formation.