{"title": "A Multiscale Adaptive Network Model of Motion Computation in Primates", "book": "Advances in Neural Information Processing Systems", "page_first": 349, "page_last": 355, "abstract": null, "full_text": "A Multiscale Adaptive Network Model of \n\nMotion Computation in Primates \n\nH. Taichi Wang \nScience Center, A18 \nRockwell International \n1049 Camino Dos Rios \nThousand Oaks, CA 91360 \n\nDimal Mathur \nScience Center, A 7 A \nRockwell International \n1049 Camino Dos Rios \nThousand Oaks, CA 91360 \n\nChristor Koch \nComputation & Neural Systems \nCaltech,216-76 \nPasadena, CA 91125 \n\nAbstract \n\nWe demonstrate a multiscale adaptive network model of motion \ncomputation in primate area MT. The model consists of two stages: (l) \nlocal velocities are measured across multiple spatio-temporal channels, \nand (2) the optical flow field is computed by a network of direction(cid:173)\nselective neurons at multiple spatial resolutions. This model embeds \nthe computational efficiency of Multigrid algorithms within a parallel \nnetwork as well as adaptively computes the most reliable estimate of \nthe flow field across different spatial scales. Our model neurons show \nthe same nonclassical receptive field properties as Allman's type I MT \nneurons. Since local velocities are measured across multiple channels, \nvarious channels often provide conflicting measurements to the \nnetwork. We have incorporated a veto scheme for conflict resolution. \nThis mechanism provides a novel explanation for the spatial frequency \ndependency of the psychophysical phenomenon called Motion Capture. \n\n1 MOTIVATION \nWe previously developed a two-stage model of motion computation in the visual system \nof primates (Le. magnocellular pathway from retina to V1 and MT; Wang, Mathur & \nKoch, 1989). This algorithm has these deficiencies: (1) the issue of optimal spatial scale \nfor velocity measurement, and (2) the issue optimal spatial scale for the smoothness of \nmotion field. To address these deficiencies, we have implemented a multi-scale motion \nnetwork based on multigrid algorithms. \nAll methods of estimating optical flow make a basic assumption about the scale of the \nvelocity relative to the spatial neighborhood and to the temporal discretization step of \ndelay. Thus, if the velocity of the pattern is much larger than the ratio of the spatial to \ntemporal sampling step, an incorrect velocity value will be obtained (Battiti, Amaldi & \nKoch, 1991). Battiti et al. proposed a coarse-to-fine strategy for adaptively detennining \n\n349 \n\n\f350 Wang, Mathur, and Koch \n\nthe optimal discretization grid by evaluating the local estimate of the relative error in the \nflow field due to discretization. The optimal spatial grid is the one minimizing this error. \nThis strategy both leads to a superior estimate of the optical flow field as well as \nachieving the speedups associated with multigrid methods. This is important. given the \nlarge number of iterations needed for relaxation-based algorithms and the remarkable speed \nwith which humans can reliably estimate velocity (on the order of 10 neuronal time \nconstants). \nOur previous model was based on the standard regularization approach. which involves \nsmoothing with weight A.. This parameter controls the smoothness of the computed \nmotion field. The scale over which the velocity field is smooth depends on the size of the \nobject The larger the object is. the larger the value of A. has to be. Since a real life vision \nsystem has to deal with objects of various sizes simultaneously. there does not exist an \n\"optimal\" smoothness parameter. Our network architecture allows us to circumvent this \nproblem by having the same smoothing weight A. at different resolution grids. \n\n2 NETWORK ARCHITECTURE \nThe overall architecture of the two-stage model is shown in Figure 1. In the rust stage. \nlocal velocities are measured at multiple spatial resolutions. At each spatial resolution p. \nthe local velocities are represented by a set of direction-selective neurons. u(ij.k.p). \nwhose preferred direction is in direction 8tc (the Component cells; Movshon. Adelson. \nGizzi & Newsome. 1985). In the second stage. the optical flow field is computed by a \nnetwork of direction-selective neurons (pattern cells) at multiple spatial resolutions. \nv(ij.k.p). In the following. we briefly summarize the network. \nWe have used a multiresolution population coding: \n\nNor Nru-l 1 \n\nV = L L n (: vf 81 \n\n, 1 \n\n1 \n\np: