Relative coordinates are crucial for Ulam's "trick to the train of thought"
This addresses a fundamental issue in visual processing and concept formation, with potential implications for improving algorithms in computer vision and AI, though it appears incremental in method.
The paper tackles the problem of spatial signal processing algorithms being dependent on external coordinate systems, which hinders the acquisition of intrinsic features, and shows that a coordinate-independent algorithm achieves deformation-invariance for visual signals.
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.