caa a22 4500 463245334 CHVBK 20180405153324.0 cr unu---uuuuu 170326e20070601xx s 000 0 eng 10.1007/s00422-007-0145-5 doi (NATIONALLICENCE)springer-10.1007/s00422-007-0145-5 Affine differential geometry analysis of human arm movements [Elektronische Daten] [Tamar Flash, Amir Handzel] Humans interact with their environment through sensory information and motor actions. These interactions may be understood via the underlying geometry of both perception and action. While the motor space is typically considered by default to be Euclidean, persistent behavioral observations point to a different underlying geometric structure. These observed regularities include the "two-thirds power law” which connects path curvature with velocity, and "local isochrony” which prescribes the relation between movement time and its extent. Starting with these empirical observations, we have developed a mathematical framework based on differential geometry, Lie group theory and Cartan's moving frame method for the analysis of human hand trajectories. We also use this method to identify possible motion primitives, i.e., elementary building blocks from which more complicated movements are constructed. We show that a natural geometric description of continuous repetitive hand trajectories is not Euclidean but equi-affine. Specifically, equi-affine velocity is piecewise constant along movement segments, and movement execution time for a given segment is proportional to its equi-affine arc-length. Using this mathematical framework, we then analyze experimentally recorded drawing movements. To examine movement segmentation and classification, the two fundamental equi-affine differential invariants—equi-affine arc-length and curvature are calculated for the recorded movements. We also discuss the possible role of conic sections, i.e., curves with constant equi-affine curvature, as motor primitives and focus in more detail on parabolas, the equi-affine geodesics. Finally, we explore possible schemes for the internal neural coding of motor commands by showing that the equi-affine framework is compatible with the common model of population coding of the hand velocity vector when combined with a simple assumption on its dynamics. We then discuss several alternative explanations for the role that the equi-affine metric may play in internal representations of motion perception and production. Springer-Verlag, 2007 Flash Tamar Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, 76100, Rehovot, Israel aut Handzel Amir Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, 76100, Rehovot, Israel aut Biological Cybernetics Springer-Verlag 96/6(2007-06-01), 577-601 0340-1200 96:6<577 2007 96 422 https://doi.org/10.1007/s00422-007-0145-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00422-007-0145-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Flash Tamar Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, 76100, Rehovot, Israel aut NATIONALLICENCE 700 1- Handzel Amir Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, 76100, Rehovot, Israel aut NATIONALLICENCE 773 0- Biological Cybernetics Springer-Verlag 96/6(2007-06-01), 577-601 0340-1200 96:6<577 2007 96 422 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer