{"title": "Visual Development Aids the Acquisition of Motion Velocity Sensitivities", "book": "Advances in Neural Information Processing Systems", "page_first": 91, "page_last": 98, "abstract": "", "full_text": "Visual Development Aids the Acquisition of\n\nMotion Velocity Sensitivities\n\nRobert A. Jacobs\n\nMelissa Dominguez\n\nDepartment of Brain and Cognitive Sciences\n\nDepartment of Computer Science\n\nUniversity of Rochester\nRochester, NY 14627\n\nrobbie@bcs.rochester.edu\n\nUniversity of Rochester\nRochester, NY 14627\n\nmelissad@cs.rochester.edu\n\nAbstract\n\nWe consider the hypothesis that systems learning aspects of visual per-\nception may bene\ufb01t from the use of suitably designed developmental pro-\ngressions during training. Four models were trained to estimate motion\nvelocities in sequences of visual images. Three of the models were \u201cde-\nvelopmental models\u201d in the sense that the nature of their input changed\nduring the course of training. They received a relatively impoverished\nvisual input early in training, and the quality of this input improved as\ntraining progressed. One model used a coarse-to-multiscale develop-\nmental progression (i.e. it received coarse-scale motion features early\nin training and \ufb01ner-scale features were added to its input as training\nprogressed), another model used a \ufb01ne-to-multiscale progression, and\nthe third model used a random progression. The \ufb01nal model was non-\ndevelopmental in the sense that the nature of its input remained the same\nthroughout the training period. The simulation results show that the\ncoarse-to-multiscale model performed best. Hypotheses are offered to\naccount for this model\u2019s superior performance. We conclude that suit-\nably designed developmental sequences can be useful to systems learn-\ning to estimate motion velocities. The idea that visual development can\naid visual learning is a viable hypothesis in need of further study.\n\n1 Introduction\n\nWith relatively few exceptions, relationships between development and learning have\nlargely been ignored by the neural computation community. This is surprising because de-\nvelopment may be nature\u2019s way of biasing biological learning systems so that they achieve\nbetter performance. Development may also represent an effective means for engineers\nto bias machine learning systems. Learning systems are inherently faced with the bias-\nvariance dilemma [1]. Systems with little or no bias tend to interpolate in unpredictable\nways and, thus, have highly variable generalization performance. Systems with larger bias,\nin contrast, tend to show better generalization performance when exposed to those training\nsets that they can adequately learn. Development may be an effective means of adding\nsuitable bias to a system thereby enhancing the generalization performance of that system.\n\n\fIn previous work, we studied the effects of different types of developmental sequences on\nthe performances of systems trained to estimate the binocular disparities present in pairs\nof visual images [2]. Systems consisted of three components. The \ufb01rst component was a\npair of right-eye and left-eye images. For example, the images may have depicted a light\nor dark object against a gray background. The second component was a set of binocular\nenergy \ufb01lters. These \ufb01lters are widely used to model the binocular sensitivities of simple\nand complex cells in primary visual cortex of primates [3]. Based on local patches of the\nright-eye and left-eye images, each \ufb01lter acted as a disparity feature detector at a coarse,\nmedium, or \ufb01ne scale depending on whether the \ufb01lter was tuned to a low, medium, or high\nspatial frequency, respectively. The third component was an arti\ufb01cial neural network. The\noutputs of the binocular energy \ufb01lters were the inputs to this network. The network was\ntrained to estimate the disparity of the object which was de\ufb01ned as the amount that the\nobject was shifted between the right-eye and left-eye images.\n\nA non-developmental system was compared to three developmental systems. The net-\nwork of the non-developmental system received the outputs of all binocular energy \ufb01lters\nthroughout the entire training period. The networks of the developmental systems, in con-\ntrast, were trained in three stages. The network of the coarse-to-multiscale system received\nthe outputs of binocular energy \ufb01lters tuned to a low spatial frequency during the \ufb01rst train-\ning stage. It received the outputs of \ufb01lters tuned to low and medium spatial frequencies\nduring the second training stage, and it received the outputs of all \ufb01lters during the third\ntraining stage. The network of the \ufb01ne-to-multiscale system was trained in an analogous\nway, though its \ufb01lters were added in the opposite order. This network received the outputs\nof \ufb01lters tuned to a high frequency during the \ufb01rst training stage, and the outputs of medium\nand then low frequency \ufb01lters were added during subsequent stages. The network of the\nrandom developmental model was also trained in stages, though its inputs were chosen at\nrandom at each stage and, thus, were not organized by spatial frequency content.\n\nThe results show that the coarse-to-multiscale and \ufb01ne-to-multiscale systems consistently\noutperformed the non-developmental and random developmental systems. The fact that\nthey outperformed the non-developmental system is important because this demonstrates\nthat models that undergo a developmental maturation can acquire a more advanced percep-\ntual ability than one that does not. The fact that they outperformed the random develop-\nmental system is important because this demonstrates that not all developmental sequences\ncan be expected to provide performance bene\ufb01ts. To the contrary, only sequences whose\ncharacteristics are matched to the task should lead to superior performance. In conjunction\nwith other results not described here, these \ufb01ndings suggest that the most successful sys-\ntems at learning to detect binocular disparities are systems that are exposed to visual inputs\nat a single scale early in training, and for which the resolution of their inputs progresses in\nan orderly fashion from one scale to a neighboring scale during the course of training.\n\nAt a more general level, these results suggest that the idea that visual development aids\nvisual learning is a viable hypothesis in need of further study. This paper studies this hy-\npothesis in the context of visual motion velocity estimation. Our simulations show that\nthe tasks of disparity estimation and velocity estimation yield similar, though not identi-\ncal, patterns of results. Although a developmental approach to the velocity estimation task\nis shown to be bene\ufb01cial, it is not the case that all developmental progressions that lead\nto performance advantages on the disparity estimation task also lead to advantages on the\nvelocity estimation task. In particular, a coarse-to-multiscale developmental system outper-\nformed non-developmental and random developmental systems on the velocity estimation\ntask, but a \ufb01ne-to-multiscale system did not. We hypothesize that the performance advan-\ntage of the coarse-to-multiscale system relative to the \ufb01ne-to-multiscale system is due to\nthe fact that the coarse-to-multiscale system learned to make greater use of motion energy\n\ufb01lters tuned to a low spatial frequency. Analyses suggest that coarse-scale motion features\nare more informative for the velocity estimation task than \ufb01ne-scale features.\n\n\f2 Developmental and Non-developmental Systems\n\nThe structure of the developmental and non-developmental systems was as follows. The\ninput to each system was a sequence of 88 retinal images where each image was a one-\ndimensional array 40 pixels in length. As described below, this sequence depicted an object\nmoving at a constant velocity in front of a stationary background. The retinal array was\ntreated as if it were shaped like a circle in the sense that the leftmost and rightmost pixels\nwere regarded as neighbors. This wraparound of the left and right edges was done to\n\navoid edge artifacts in the spatial dimension. Although a one-dimensional retina is a sim-\npli\ufb01cation, its use is justi\ufb01ed by the need to keep the simulation times within reason. The\nsequence of retinal images was \ufb01ltered using motion energy \ufb01lters.\n\nBased on neurophysiological results, Adelson and Bergen [4] proposed motion energy \ufb01l-\nters as a way of modeling the motion sensitivities of simple and complex cells in primary\nvisual cortex. A sequence of one-dimensional images can be represented using a two-\ndimensional array where one dimension encodes space and the other dimension encodes\ntime. In this case, motion energy \ufb01lters are two-dimensional \ufb01lters which extract motion\ninformation in local patches of the spatiotemporal space.\n\nThe receptive \ufb01eld pro\ufb01le of a simple cell can be described mathematically as a Gabor\nfunction which is a sinusoid multiplied by a Gaussian envelope. A quadrature pair of such\nfunctions with even and odd phases tuned to leftward (-) and rightward (+) directions of\nmotion is given by\n\n\u0002\u0001\n\n\u0006\b\u0007\n\t\f\u000b\r\t\f\u000e\u0010\u000f\u0012\u0011\u0014\u0013\u0016\u0015\u0018\u0017\u001a\u0019\n\u0006\b\t\n\u0006\b\u0007\n\t\f\u000b\r\t\f\u000e\u0010\u000f\u0012\u0011\u0014\u0013\u0016\u0015\u0018\u0017\u001a\u0019\n\u0006\b\t\n\n\u000e\u001e\u001d\u0010\u001f\u0012 \u0018!#\"%$\n\u001d\u0010!.-0/1\"%$\n\u000e are the spatial and temporal variances of the Gaussian, and $\nand temporal frequencies of the sinusoids. The ratio $\n\nwhere\n\n\u0006\r\t\n\u0006\r\t\n\n&(')\u000e\n\u001c+*\n&(')\u000e\n\u001c+*\n\u000b and $\n\n(1)\n\n(2)\n\nand \u001c are the spatial and temporal distances to the center of the Gaussian, \t\n\n\u000b and\n\u000e are the spatial\n\u000b determines the orientation\n\n\u000e+2\n\nof a Gabor function in the spatiotemporal space which, in turn, determines the velocity\nsensitivity of the function.\n\nThe activity of a simple cell is given by the square of the convolution of the cell\u2019s receptive\n\ufb01eld pro\ufb01le with the spatiotemporal pattern. The activities of simple cells with even and\nodd phases are summed in order to form the activity of a complex cell. This activity is\nknown as a motion energy.\n\nIn our simulations, we used a subset of the possible receptive-\ufb01eld locations in the two-\n88 time frames) spatiotemporal space. This subset formed\n\ndimensional (40 pixels 3\na 20 3 4 uniform grid such that receptive \ufb01elds were centered on odd-numbered pixels\n\nand odd-numbered time frames. This grid was located in the center of the space with re-\nspect to the temporal dimension. An advantage of this choice of locations was that edge\nartifacts were avoided because all receptive-\ufb01elds fell entirely within the spatiotemporal\nspace.\n\nFifteen complex cells corresponding to three spatial frequencies and \ufb01ve temporal frequen-\ncies were centered at each receptive-\ufb01eld location. The spatial and temporal frequencies\nwere each separated by an octave. Temporal frequencies were chosen so that the set of\ncells at each spatial frequency had the same pattern of velocity tunings. Speci\ufb01cally, the\nsets tuned to low (0.0625 cycles/pixel), medium (0.125 cycles/pixel), and high (0.25 cy-\ncles/pixel) spatial frequencies had velocity tunings of 0.25, 0.5, 1.0, 2.0, and 4.0 pixels per\ntime frame. All cells were tuned to rightward motion because we restricted our data sets to\nonly include objects that were moving to the right. A cell\u2019s spatial and temporal standard\n\n\u0003\n\u0004\n\u0005\n\u001b\n\u001b\n\u000b\n\u0017\n\u001c\n\u001b\n\u001b\n\u000b\n\u0019\n\n\u0001\n,\n\u0004\n\u0005\n\u001b\n\u001b\n\u000b\n\u0017\n\u001c\n\u001b\n\u001b\n\u000e\n\u000b\n\u0019\n\u0019\n\u001b\n\t\n\u001b\n$\n\fdeviations were set to be inversely proportional to its spatial and temporal frequencies,\nrespectively. The outputs of the complex cells within each spatial frequency band were\nnormalized using a softmax nonlinearity. Consequently, complex cells tended to respond\nto relative contrast in the image sequence rather than absolute contrast [5] [6].\n\nThe normalized outputs of the complex cells were the inputs to an arti\ufb01cial neural network.\nThe network had 1200 input units (the complex cells had 80 receptive-\ufb01eld locations and\nthere were 15 cells at each location). The network\u2019s hidden layer contained 18 hidden\nunits which were organized into 3 groups of 6 units each. The connectivity of the hidden\nunits was set so that each group had a limited receptive \ufb01eld, and so that neighboring\ngroups had overlapping receptive \ufb01elds. A group of hidden units received inputs from\nthirty-two receptive \ufb01eld locations at the complex cell level, and the receptive \ufb01elds of\nneighboring groups overlapped by eight receptive-\ufb01eld locations. The hidden units used a\nlogistic activation function. The output layer consisted of a single linear unit; this unit\u2019s\noutput was an estimate of the object velocity depicted in the sequence of retinal images.\n\nThe weights of an arti\ufb01cial neural network were initialized to small random values, and\nwere adjusted during the course of training to minimize a sum of squared error cost function\nusing a conjugate gradient optimization procedure [7]. Weight sharing was implemented at\nthe hidden unit level so that corresponding units within each group of hidden units had the\nsame incoming and outgoing weight values, and so that a hidden unit had the same set of\nweight values from each receptive \ufb01eld location at the complex unit level. This provided\nthe network with a degree of translation invariance, and also dramatically decreased the\nnumber of modi\ufb01able weight values in the network. It therefore decreased the number of\ndata items needed to train the network, and the amount of time needed to train the network.\n\nModels were trained and tested using separate sets of training and test data items. Each\nset contained 250 randomly generated items. Training was terminated after 100 iterations\nthrough the training set. The results reported below are based on the data items from the\ntest set.\n\nThree developmental systems and one non-developmental system were simulated. The\ncoarse-to-multiscale system, or model C2M, was trained using a coarse-to-multiscale de-\nvelopmental sequence which was implemented as follows. The training period was divided\ninto three stages. During the \ufb01rst stage, the neural network portion of the model only re-\nceived the outputs of complex cells tuned to the low spatial frequency (the outputs of other\ncomplex cells were set to zero). During the second stage, the network received the outputs\nof complex cells tuned to low and medium spatial frequencies; it received the outputs of all\ncomplex cells during the third stage. The training of the \ufb01ne-to-multiscale system, or model\nF2M, was identical to that of model C2M except that its training used a \ufb01ne-to-multiscale\ndevelopmental sequence. During the \ufb01rst stage of training, its network received the outputs\nof complex cells tuned to the high spatial frequency. This network received the outputs\nof complex cells tuned to high and medium spatial frequencies during the second stage,\nand received the outputs of all complex cells during the third stage. The training of the\nrandom developmental system, or model RD, also used a developmental sequence, though\nthis sequence was generated randomly and, thus, was not based on the spatial frequency\ntunings of the complex cells. The collection of complex cells was randomly partitioned\ninto three equal-sized subsets with the constraint that each subset included one-third of the\ncells at each receptive-\ufb01eld location. During the \ufb01rst stage of training, the neural network\nportion of the model only received the outputs of the complex cells in the \ufb01rst subset. It\nreceived the outputs of the cells in the \ufb01rst and second subsets during the second stage of\ntraining, and received the outputs of all complex cells during the third stage. In contrast,\nthe training period of the non-developmental system, or model ND, was not divided into\nseparate stages; its neural network received the outputs of all complex cells throughout the\nentire training period.\n\n\fSolid object data item\n\nNoisy object data item\n\nFigure 1: Ten frames of an image sequence from the solid object data set (top) and ten\nframes of an image sequence from the noisy object data set (bottom).\n\n3 Data Sets and Simulation Results\n\nThe performances of the four models were evaluated on two data sets. In all cases the\nimages were gray scale with luminance values between 0 and 1, and motion velocities were\nrightward with magnitudes between 0 and 4 pixels per time frame. Fifteen simulations of\neach model on each data set were conducted.\n\nIn the solid object data set, images consisted of a moving light or dark object in front of a\nstationary gray background. The object\u2019s gray-scale values were randomly chosen to either\nbe in the range from 0.0 to 0.1 or from 0.9 and 1.0, whereas the gray-scale value of the\nbackground was always 0.5. The size of the object was randomly chosen to be an integer\nbetween 6 and 12 pixels, its initial location was a randomly chosen pixel on the retina, and\nits velocity was randomly chosen to be a real value between 0 and 4 pixels per time frame.\nGiven a sequence of images, the task of a model was to estimate the object\u2019s velocity. The\ntop portion of Figure 1 gives an example of ten frames of an image sequence from the solid\nobject data set.\n\nThe bar graph in Figure 2 illustrates the results. The horizontal axis gives the model, and\nthe vertical axis gives the root mean squared error (RMSE) on the data items from the test\nset at the end of training (the error bars give the standard error of the mean). The labels for\nthe developmental models C2M, F2M, and RD include a number. Recall that the training of\nthese models was divided into three training stages (or developmental stages). The number\nin the label gives the length of developmental stages 1 and 2 (the length of developmental\nstage 3 can be calculated using the fact that the entire training period lasted 100 iterations).\nFor example, the label \u2018C2M-5\u2019 corresponds to a version of model C2M in which the\n\n\fRMSE\n\n0.55\n\n0.50\n\n0.45\n\n0.40\n\nsolid object data set\n\nND\n\nRD-20 C2M-5 C2M-10 C2M-20 C2M-30 F2M-5 F2M-10 F2M-20 F2M-30\n\nFigure 2: The root mean squared errors (RMSE) on the test set data items for model ND,\nthe best performing version of model RD, and different versions of models C2M and F2M\nafter training on the solid object data set (the error bars give the standard error of the mean).\n\n \n\n\ufb01rst stage was 5 iterations, the second stage was 5 iterations, and the third stage was 90\niterations. In regard to model RD, we simulated four versions of this model (RD-5, RD-\n10, RD-20, and RD-30). For the sake of brevity, only the version that performed best is\nincluded in the graph.\n\nModel C2M signi\ufb01cantly outperformed all other models. The version of this model which\nperformed best was version C2M-20 which had an 11.5% smaller generalization error than\n0.02). In addition, C2M-20 had a 9.6% smaller error than the best\nmodel ND (t = 2.50, p\n0.01), and a 7.2% smaller error than the best version\nversion of model F2M (t = 3.57, p\nof model RD (t = 2.30, p\n0.05).\n\nThe images in the second data set, referred to as the noisy object data set, were meant to\nresemble random-dot kinematograms frequently used in behavioral experiments. Images\ncontained a noisy object which was moving to the right and a noisy background which\nwas stationary. The gray-scale values of the object pixels and the background pixels were\nset to random numbers between 0 and 1. The size of the object was randomly chosen to\nbe an integer between 6 and 12 pixels, its initial location was a randomly chosen pixel on\nthe retina, and its velocity was randomly chosen to be an integer between 0 and 4 pixels\nper time frame. As before, the task was to map an image sequence to an estimate of an\nobject velocity. The bottom portion of Figure 1 gives an example of ten frames of an image\nsequence from the noisy object data set.\n\nThe results are shown in Figure 3. Model C2M, once again, outperformed the other models.\nRelative to model ND, all versions of model C2M showed superior performance (ND vs.\nC2M-5: t = 2.69, p\n0.01; ND vs. C2M-20: t\n= 3.03, p\n0.001). The version of model C2M\nwhich performed best was version C2M-30. On average, this version had an 8.9% smaller\ngeneralization error than model ND, a 6.1% smaller error than the best version of model\nF2M, and a 4.3% smaller error than the best version of model RD.\n\n0.02; ND vs. C2M-10: t = 2.78, p\n\n0.01; ND vs. C2M-30: t = 4.14, p\n\n\n\n\n\n\n\n\n\fRMSE\n\n0.80\n\n0.75\n\n0.70\n\n0.65\n\nnoisy object data set\n\nND\n\nRD-20 C2M-5 C2M-10 C2M-20 C2M-30 F2M-5 F2M-10 F2M-20 F2M-30\n\nFigure 3: The root mean squared errors (RMSE) on the test set data items for model ND,\nthe best performing version of model RD, and different versions of models C2M and F2M\nafter training on the noisy object data set (the error bars give the standard error of the mean).\n\n \n\nWhy did model C2M show the best performance? Simulation results described in Jacobs\nand Dominguez [8] suggest that coarse-scale motion features are more informative for the\nvelocity estimation task than \ufb01ne-scale features. For example, networks that received only\nthe outputs of complex cells tuned to a low spatial frequency consistently outperformed\nnetworks that received only the outputs of mid frequency complex cells or only the outputs\nof high frequency complex cells. We speculate that coarse-scale motion features are more\ninformative for a number of reasons. First, complex cells tuned to the lowest spatial fre-\nquency have the largest receptive \ufb01elds. As discussed by Weiss and Adelson [9], motion\nsignals tend to be less ambiguous when the stimulus is viewed for a long duration and more\nambiguous when the stimulus is viewed for a short duration. This type of reasoning also\napplies to the activities of complex cells with receptive \ufb01elds in the spatiotemporal domain.\nThat is, there is comparatively less ambiguity in the activities of complex cells with larger\nreceptive \ufb01elds than in the activities of cells with smaller receptive \ufb01elds. Because cells\ntuned to a low spatial frequency tend to have larger receptive \ufb01elds than cells tuned to a\nhigh spatial frequency, low frequency tuned cells tend to be more reliable for the purposes\nof motion velocity estimation. Second, model C2M may have bene\ufb01ted from the fact that\ncomplex cells with large, overlapping receptive \ufb01elds provide a high resolution coarse-code\nof the spatiotemporal space [10]-[12]. This code could provide model C2M with accurate\ninformation as to the location of the moving object at each moment in time. For example,\nthe activities of the population of these cells may have coded with high accuracy the fact\n. If so, the\nthat the moving object was at location\nmodel\u2019s neural network could have easily learned to accurately estimate the object velocity\n\nat time \u001c\u0002\u0001 and at location\n\nat time \u001c\u0005\u0004\n\nby calculating \"\n\n* . Model C2M would have an advantage over other mod-\n\nels because it received this high resolution coarse-code throughout training. In contrast,\nmodel F2M, for example, received early in training only the outputs of complex cells with\nsmaller, less-overlapping receptive \ufb01elds. The activities of a population of these cells form\na lower resolution coarse-code of the spatiotemporal space.\n\n\n\u0003\n\u0003\n\u0017\n\n*\n2\n\"\n\u001c\n\u0004\n\u0017\n\u001c\n\u0001\n\fAs described above, in earlier work we found that the most successful systems at learning\na binocular disparity estimation task were those that: (1) received inputs at a single fre-\nquency scale early in training, and (2) for which the resolution of their inputs progressed in\nan orderly fashion from one scale to a neighboring scale during the course of training [2].\nCondition (1) allowed a system to combine and compare input features at an early training\nstage without the need to compensate for the fact that these features could be at different\nspatial scales. If condition (2) was satis\ufb01ed, when a system received inputs at a new spatial\nscale, it was close to a scale with which the system was already familiar. Although not\ndescribed here (see Jacobs and Dominguez [8]), we tested the importance on the motion\nvelocity estimation task for the resolution of a system\u2019s inputs to progress in an orderly\nfashion from one scale to a neighboring scale. The results suggest that this factor is moder-\nately important, but not highly important, for a developmental system learning to estimate\nmotion velocities. Overall, it is more important for a system to receive the outputs of the\nlow spatial frequency complex cells as early in training as possible.\n\nBased on the entire set of simulations, we conclude that suitably designed developmental\nsequences can be useful to systems learning to estimate motion velocities. The idea that\nvisual development can aid visual learning is a viable hypothesis in need of further study.\n\nAcknowledgments\n\nThis work was supported by NIH research grant RO1-EY13149.\n\nReferences\n\n[1] Geman, S., Bienenstock, E., and Doursat, R. (1995) Neural networks and the bias/variance\n\ndilemma. Neural Computation, 4, 1-58.\n\n[2] Dominguez, M. and Jacobs, R.A. (2003) Developmental constraints aid the acquisition of binoc-\n\nular disparity sensitivities. Neural Computation, in press.\n\n[3] Ohzawa, I., DeAngelis, G.C., and Freeman, R.D. (1990) Stereoscopic depth discrimination in\n\nthe visual cortex: Neurons ideally suited as disparity detectors. Science, 249, 1037-1041.\n\n[4] Adelson, E.H. and Bergen, J.R. (1985) Spatiotemporal energy models for the perception of\n\nmotion. Journal of the Optical Society of America A, 2, 284-299.\n\n[5] Heeger, D.J. (1992) Normalization of cell responses in cat striate cortex. Visual Neuroscience,\n\n9, 181-197.\n\n[6] Nowlan, S.J. and Sejnowski, T.J. (1994) Filter selection model for motion segmentation and\n\nvelocity integration. Journal of the Optical Society of America A, 11, 3177-3200.\n\n[7] Press, W.H., Teukolsky, S.A., Vetterling, W.T., and Flannery, B.P. (1992) Numerical Recipes in\n\nC: The Art of Scienti\ufb01c Computing. Cambridge, UK: Cambridge University Press.\n\n[8] Jacobs, R.A. and Dominguez, M. (2003) Visual development and the acquisition of motion\n\nvelocity sensitivities. Neural Computation, in press.\n\n[9] Weiss, Y. and Adelson, E.H. (1998) Slow and smooth: A Bayesian theory for the combination\nof local motion signals in human vision. Center for Biological and Computational Learning\nPaper Number 158, Massachusetts Institute of Technology, Cambridge, MA.\n\n[10] Milner, P.M. (1974) A model for visual shape recognition. Psychological Review, 81, 521-535.\n[11] Hinton, G.E. (1981) Shape representation in parallel systems. In A. Drina (Ed.), Proceedings of\n\nthe Seventh International Joint Conference on Arti\ufb01cial Intelligence.\n\n[12] Ballard, D.H. (1986) Cortical connections and parallel processing: Structure and function. Be-\n\nhavioral and Brain Sciences, 9, 67-120.\n\n\f", "award": [], "sourceid": 2225, "authors": [{"given_name": "Robert", "family_name": "Jacobs", "institution": null}, {"given_name": "Melissa", "family_name": "Dominguez", "institution": null}]}