Hutchinson, J., Koch, C., Luo, J. & C.A. Mead (1988) "Computing Motion using Analog and Binary Resistive Networks," IEEE Computers, Vol. 21, pp. 52-63, March.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....level of the physical world, on the interpretation of visual motion and results in increased robustness. In a different direction, various researchers have been looking at the real time computation of optical flow. Notable is the work on implementing optical flow equations using analog devices [45] which incorporates the idea of weak continuity for preserving motion discontinuities. Others have built hardware to perform real time correlation for optical flow, depth map generation, and tracking [46, 47] Computational models of optic flow and, in particular, the inclusion of the temporal ....

C. Koch, J. Luo, and C. Mead, Computing motion using analog and binary resistive networks, IEEE Computer, Mar. 1988, 52-63.

....level of the physical world, on the interpretation of visual motion and results in increased robustness. In a different direction, various researchers have been looking at the real time computation of optical flow. Notable is the work on implementing optical flow equations using analog devices [45] which incorporates the idea of weak continuity for preserving motion discontinuities. Others have built hardware to perform real time correlation for optical flow, depth map generation, and tracking [46, 47] Computational models of optic flow and, in particular, the inclusion of the temporal ....

C. Koch, J. Luo, and C. Mead, Computing motion using analog and binary resistive networks, 1EEE Computer, Mar. 1988, 52-63.

....unit. The test measurements of the implemented ASIC are presented in Section 4. We are concluding our paper with some remarks in Section 5. Previous contributions to systems for real time optical flow computation can be divided into two groups. The first group is more or less biology inspired [19, 10, 12, 1], where the approaches of Kramer and Ancona et al. are the most advanced ones. Kramer reported a sensor cell that measures the time of travel of edges between two fixed locations. The sensor cell is reported to be insensitive to stimulus contrast and selective to a high range of velocities. The ....

Hutchinson, J., Koch, C., Luo, J., and Mead, C. Computing motion using analog and binary resistive networks. IEEE Computer, 21(3):52--63, 1988.

....5, 27, 40, 45] on the cm2) Implementations on linear simd arrays, based on the same principle [13, 34, 33] have also been described, in order to design specialized architectures. Alternate approaches involve the development of highly specialized linear or non linear (electrical) analog networks [25, 32, 41], Hopfield neural networks [31, 38, 46] or Boltzmann machines [24] for mapping the underlying global optimization problems. Nevertheless, standard data parallelism does not exploit the large computing resources of the now available large massively parallel processor arrays when the image grid to ....

J. HUTCHINSON, C. KOCH, J. LUO, and C. MEAD. -- Computing motion using analog and binary resistive networks. -- Computer, Vol. 21: pages 52--63, March 1988. RR n2184 38 E. M'emin, F. Heitz and F. Charot

....MAGAZINE (JULY 1999) 19 among all separable constraints of the same order. It was also proposed to preserve boundaries in motion fields by nonstationary autoregressive modeling [27] or by a line process representing motion discontinuities (smoothness suspended across line elements switched on) [44], 57] Example of such adaptively smooth motion field and the associated line process is shown in Fig. 9. Note the improved motion discontinuities at object boundaries. However, since the line process model (discontinuity) is very local, a better object delineation is usually achieved by the ....

J. Hutchinson, C. Koch, J. Luo, and C. Mead, "Computing motion using analog and binary resistive networks," Computer, vol. 21, pp. 52--63, Mar. 1988.

....of a computational problem can be found, the resulting circuit is usually very simple, fast and dense compared to CPU based hardware. Particular problems solved by such networks include simulation of electromagnetic fields [1] linear image filtering [2] regularization for image processing [3], and D A conversion [4] Networks of resistors are especially attractive for CMOS integrated circuits, since it has been shown that a circuit obtained by replacing every resistor by a single MOS transistor has exactly the same branch currents as its resistive counterpart [5] In the following, a ....

J. Hutchinson, C. Koch, J. Luo, C. Mead, "Computing motion using analog and binary resistive networks", Computer, March 1988, pp. 52-63

....of the satellites on the percept of the ellipse suggests that motion information from the satellites is propagated across space thereby influencing the contour. But does the visual system propagate all motion constraints in the image indiscriminately Many authors (e.g. Terzopoulos, 1986; Hutchinson et al. 1988)) have pointed out that such global propagation would lead to estimates that are quite wrong. They have advocated an alternative approach whereby motion boundaries stop the propagation. In order to create a motion boundary between the ellipse and the dots, we placed the ellipse over a textured ....

.... fixing the global smoothness assumption involves the use of discontinuities or line processes (Geman and Geman, 1984; Terzopoulos, 1986) Rather than assuming that the image motion can be well explained with a single smooth velocity field, these approaches to motion analysis (e.g. Horn, 1986; Hutchinson et al. 1988)) allow discontinuities to form in the velocity field. Thus in general the motion of two neighboring locations is assumed to be similar but if the local motions are highly dissimilar this assumption is abandoned and a boundary is posited between the two locations. To illustrate the ....

Hutchinson, J., Koch, C., Luo, J., and Mead, C. (1988). Computing motion using analog and binary resistive networks. IEEE Computer magazine, 21:52--64.

....inconsistent with Hildreth s model or any other model that assumes smoothness only along contours. Rather than restricting the smoothness assumption to contours, other approaches assume a smooth two dimensional velocity field with possible discontinuities. In these models, e.g. Terzopoulos, 1986; Hutchinson et al. 1988; Horn, 1986) nearby points are assumed to have similar velocities, but if the velocities are too dissimilar the assumption is abandoned and a discontinuity is assumed there instead. An advantage of these models over the standard smoothness models is that when the location of the discontinuity ....

....with Hildreth s model or any other model that assumes smoothness only along contours. An alternative approach to fixing the problems associated with global smoothness assumption was to assume piecewise smoothness, or smoothness with discontinuities. In these models, e.g. Terzopoulos, 1986; Hutchinson et al. 1988; Horn, 1986) nearby points are assumed to have similar velocities, but if the velocities are too dissimilar the assumption is abandoned and a discontinuity is assumed there instead. An advantage of these models over the standard smoothness models is that when the location of the discontinuity is ....

Hutchinson, J., Koch, C., Luo, J., and Mead, C. (1988). Computing motion using analog and binary resistive networks. IEEE Computer magazine, 21:52--64.

....of the Lie group algorithm. In addition, derivation of a dense optic ow eld such as that used in their experiments has been shown to be a di cult process in practice [36] This problem was addressed by Hutchinson, Koch, Luo and Mead, who obtained a dense optic ow eld using resistive networks [35]. The Lie group studies represent neural operations performed at a fairly high level in the visual hierarchy. As such, the techniques rely on point and edge grouping processes, rather than interior spectral properties of regions. However, there is evidence that both local and global region ....

....edge that are projected onto the neuron array. This behavior is accompanied by a trail of low ring rate neurons in the areas of the array that are disoccluded due to apparent motion of the objects. Analogous behavior was seen in motion analysis systems that replicated primate visual responses [17,35,46,55]. This e ect can be seen in Figure 16, where the salesman is moving a box with his right hand, while at the same time moving his left hand from the surface of the desk to clasp the box. The movement causes the neurons within the projected boundaries to re, with a di use trail of neuronal activity ....

Hutchinson, J., C. Koch, J. Luo, and C. Mead (1988). Computing motion using analog and binary resistive networks. IEEE Computer 21 (3), 52-64.

....Because there are limitations to the method (especially precision and flexibility) analog computers were generally abandoned in favor of digital computers. However, in the late 1980 s a novel interest in analog computation has emerged in the form of neural networks and analog VLSI (see [7] 8] [9] and many more) Some of the most promising results of these efforts are collected together in [16] and [17] For problems for which high precision is not mandatory, the simplicity, speed and natural parallelism of the analog formulation is very powerful. The formulation of robot path planning ....

....ffl for VLSI complexity ( wires are expensive, transistors are free ) we want low connectivity (e.g. hexagonal tessellation) Rectangular networks are somewhere in between and they map more naturally the way we are used to think about two dimensional space. On the other hand, as pointed out in [16, 9], they exhibit preferred directions in the form of the two axes which is especially annoying for path planning problems. In [9] the triangular network is considered nearly isotropic . This is somehow exaggerated because the problem of preferred directions is a direct consequence of the ....

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J. Hutchinson, C. Koch, J. Luo, C. Mead, "Computing motion using analog and binary resistive networks", IEEE Computer, March 1988, pp.52-63.

....need to deal with mixed distributions. All of these methods follow the basic structure of Geman and Geman (1984) or Blake and Zisserman (1987) The most common approach utilizes a Markov random field (MRF) formulation with explicit line processes (Murray and Buxton, 1987; Gamble and Poggio 1987; Hutchinson et al. 1988; Koch et al. 1989; Konrad and Dubois, 1992; Heitz and Bouthemy, 1993) Interacting region and line processes are involved. The region processes combine information over local neighborhoods to reduce ambiguity and improve reliability of individual flow estimates. The line processes estimate ....

J. Hutchinson, C Koch, J. Luo, and C Mead. Computing motion using analog and binary resistive networks. Computer, 21:52--63, March 1988.

....this requires a much shorter settling time constant for the network than the brightness changes in the image. 3 A Physical Analog Model 3. 1 Continuous space Standard regularization problems can be mapped onto electronic networks consisting of conductances and capacitors [5] Hutchinson et al. [6] showed how resistive networks can be used to compute optical flow and Poggio et al. 7] introduced electronic network solutions for second order derivative optic flow computation. However, these proposed network architectures all require complicated and sometimes negative conductances although ....

J. Hutchinson, C. Koch, J. Luo, and C. Mead. Computing motion using analog and binary resistive networks. Computer, 21:52--64, March 1988.

....in images. 3.2 Nonconvex Log Prior Distributions Non Gaussian MRF s are interesting because they can potentially model both the edges and smooth regions of images. Initial approaches often used an additional unobserved random field called a line process which determines the location of edges[2, 26]. More recently, many approaches have focused on MRF s with simpler Gibbs distributions of the general form log g(x) X s,r #C b sr #(# x s x r ) constant (3) where # is a scaling parameter, and # is a monotone increasing, but not convex function[7, 8, 5, 6, 9, 12, 13, 27] A typical ....

J. Hutchinson, C. Koch, J. Luo and C. Mead, "Computing Motion Using Analog and Binary Resistive Networks," Computer, vol. 21, pp. 53-63, March 1988.

....motion fields are usually smooth functions of spatial position x, except at motion boundaries. Thus, we model trajectories c p t by continuous valued vector MRFs C p t [46] 35] and also we model occlusions o t and motion discontinuities l t by multi level and binary MRFs O t [13] and L t [28], 37] respectively. We ensure the smoothness of c p t and o t , and continuity of l t by appropriate choice of Gibbs distribution parameters. Motion trajectory model As stated before, in order to uniquely characterize a MRF it is sufficient to specify parameters of its Gibbs distribution. ....

....to (3.27) the probability of having a particular trajectory at location (x; t) depends on the occlusion and motion discontinuity fields as well as on the observations. The dependence on local discontinuities is expressed through the multiplicative term 1 Gamma l( x i ; x j ; t) in (3. 29) [28], 37] For a line element on (l( x i ; x j ; t) 1) no contribution (penalty) is added to the energy U c . Since the potential V c is non negative, such a contribution would lower the probability of c( x i ; t) Thus, a jump in trajectory parameters is not penalized if a motion ....

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J. Hutchinson, C. Koch, J. Luo, and C. Mead, "Computing motion using analog and binary resistive networks," Computer, vol. 21, pp. 52--63, Mar. 1988.

.... in analog computers( 8] Because there are limitations to the method (especially precision and flexibility) analog computers were abandoned in favor of digital computers, but in the late 1980 s a novel interest in analog computation has emerged in the form of neural networks and analog VLSI ([5, 6, 7] and many more) The most promising results of these efforts can be collected together in [3, 4] For problems for which high precision is not mandatory, the simplicity, speed and natural parallelism of the analog formulation is very powerful. The formulation of robot path planning using Laplace s ....

....solutions that could use the intrinsic nonlinearity of floating point numbers to compensate for the shallow nonlinear regions of the solution to Laplace s equation. Another very interesting approach would be to consider a two dimensional cartesian space and instead of memory to use a retina mesh ( [7, 3]) This would enable a constant parallel update of the environment and would eliminate the initial cumbersome loading of the memory with information about obstacles, source and target. Such a device could control the movement of an autonomous mobile in a two dimensional space. The environment ....

J. Hutchinson, C. Koch, J. Luo, C. Mead, "Computing motion using analog and binary resistive networks", IEEE Computer, March 1988, pp.5263.

.... the availability of massively parallel architectures [Hillis, 1985] and the appearance of fast RISC microprocessors [Hennessy and Patterson, 1990] Eventually, many of the low level processing algorithms used in our research could be implemented using analog processing [Koch et al. 1986; Hutchinson et al. 1988] One of the focuses of our research is the use of fine grained parallel algorithms [Poggio et al. 1985; Little et al. 1989] However, unlike much of the current research in low level vision which embeds the computation in a 2 D plane of processors our 3 D models will require more complex ....

J. Hutchinson, C. Koch, J. Luo, and C. Mead. Computing motion using analog and binary resistive networks. Computer, 21(3):52--63, March 1988.

....example, Besag [4] found that progressively increasing improved the performance of ICM in certain cases. Also, a number of studies have found that varying the parameters of the Gibbs distribution during ICM or SA can improve results when modeling continuously valued fields with discontinuities [10, 12]. However, in the case of continuous valued fields, the parameters were progressively reduced from initially large values. In any case, the schedule needed for changing these parameters introduces additional free parameters which generally are image dependent. Therefore, our approach is to fix the ....

J. Hutchinson, C. Koch, J. Luo and C. Mead, "Computing Motion Using Analog and Binary Resistive Networks," Computer, vol. 21, pp. 53-63, March 1988.

....calculated with a higher precision. Additional gain is due to the analog nature of computations; no digital operations are needed and thus calculations are very rapid (the speed is limited only by propagation constraints of the electrical signals) This is similar to the resistive nets proposed in [6]. Such a continuous Hopfield network is described by the following equations; du i (t) dt = Gamma E(v) v i ; v i (t) f(u i (t) 1) where t is time, u i and v i are the internal state and the output of neuron i, and E is an energy function that is minimized by the network. The ....

J. Hutchinson, C. Koch, J. Luo, and C. Mead, "Computing motion using analog and binary resistive networks," Computer, vol. 21, pp. 52--63, Mar. 1988.

....be considered when computing the line samples l t . In general, a 3D scene giving rise to a motion discontinuity will also contribute to an intensity edge. Only under specific circumstances will a motion discontinuity not correspond to an edge of intensity. Hence, similarly to Hutchison et al. [18], we assume that an introduction of a line element should coincide with an intensity edge. We use the following potential function for one element cliques: V l 1 (l t ; g t Gamma ; c l ) 8 : ff (r v g t Gamma ) 2 l h ( x i ; x j ; t) for horizontal c l = fx i ; x j g ff (r h g ....

....l ( b l t jg t Gamma ) is a stabilizing functional and 1= g is a regularization parameter. Hence, the Bayesian formulation comprises, as a specific case, the regularization method which has been frequently used in computer vision [2] The objective function in (17) is similar to that used in [18], which is derived from the original formulation of Horn and Schunck [17] with the additional non stochastic motion discontinuity model. We pursue the stochastic approach by using two coupled MRFs and a random displaced pixel difference instead of the motion constraint equation. Also, the line ....

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J. Hutchinson, C. Koch, J. Luo, and C. Mead, "Computing motion using analog and binary resistive networks," Computer, vol. 21, pp. 52--63, Mar. 1988.

....C l 3 . It is assumed that, in general, the introduction of a motion discontinuity should coincide with an intensity edge. This is enforced by the potential function V l 1 which uses single element cliques to associate a high penalty whenever a motion discontinuity does not match an intensity edge [21]. V l 1 can therefore be formulated as follows: V l 1 (l i ; e i ) 10 Delta (1:1 Gamma e i ) Delta l i ; 4.10) with l i and e i denoting the values of the line element and the intensity edge, respectively, at position x i . Hence, the introduction of a motion discontinuity (l i = 1) is ....

J. Hutchinson, C. Koch, J. Luo, and C. Mead, "Computing Motion Using Analog and Binary Resistive Networks," Computer, vol. 21, pp. 52--63, March 1988.

....cliques to a high value whenever a motion discontinuity does not match an intensity edge. This can be done in two ways. We can detect intensity edges first, and then set the potential to a large value whenever motion discontinuity is attempted at locations where no intensity edge is present [22, 19]. The other approach is to make the potential inversely proportional to a norm of the local image gradient [24] In order to model continuity of motion boundaries, a sufficiently large neighborhood system N l should be used. Example of such a neighborhood system can be found in [26] cross shaped ....

J. Hutchinson, C. Koch, J. Luo, and C. Mead, "Computing motion using analog and binary resistive networks," Computer, vol. 21, pp. 52--63, Mar. 1988.

....constraints of the same order. As another extension, boundaries present in motion fields have been preserved by nonstationary autoregressive modelling in [27] Explicit estimation of a line process representing motion discontinuities and suspending smoothing across those lines has been proposed in [45] and [56] Example of such adaptively smooth motion field and the associated line process is shown in Fig. 9. Note the improved motion discontinuities at object boundaries. However, since the line process model (discontinuity) is very local, a better object delineation is usually achieved by the ....

J. Hutchinson, C. Koch, J. Luo, and C. Mead, "Computing motion using analog and binary resistive networks," Computer, vol. 21, pp. 52--63, Mar. 1988.

....system can either be fully implemented in hardware or virtually implemented in software[25] A full implementation provides a dedicated processor for each cell, and a dedicated information channel for each interconnect. Modest sized fully implemented analog systems have been realized on VLSI chips[31]. Electro optical implementations are also being explored[48] Once built, fully implemented systems are difficult to reconfigure. However, they are attractive for certain special purpose applications such as sensory processing, vision and pattern classification[25] Virtual implementations ....

J. Hutchinson, C. Koch, J. Luo, and C. Mead. Computing motion using analog and binary resistive networks. IEEE Computer, 21(3):52--63, 1988.

....cliques [11] It is assumed that, in general, the introduction of a motion discontinuity coincides with an intensity edge. This is enforced by the potential function V l which uses single element cliques to associate a high penalty whenever a motion discontinuity does not match an intensity edge [15]. Therefore, V l can be formulated as follows: V l (l; e) 10 Delta (1:1 Gamma e) Delta l: Hence, the introduction of a motion discontinuity (l = 1) is penalized by 11 in the absence of an intensity edge (e = 0) and by 1 if such edge is present (e = 1) This latter value assures a penalty ....

J. Hutchinson, C. Koch, J. Luo, and C. Mead, "Computing motion using analog and binary resistive networks," Computer, vol. 21, pp. 52--63, Mar. 1988.

....based on the regularisation theory [2] or on the Markov random field theory [3] often require some heavy computational efforts without ensuring perfect results and sufficient noise immunity. However these last two approaches come down to a problem of minimisation of an energy function [4] 5] [6] and might be solved with the use of analog resistive networks [2] 6] in order to reduce the computational effort. Even though analog neural networks are used to analyse the visual motion, their relations with some biological data are often very far in spite of a great interest in the biological ....

....theory [3] often require some heavy computational efforts without ensuring perfect results and sufficient noise immunity. However these last two approaches come down to a problem of minimisation of an energy function [4] 5] 6] and might be solved with the use of analog resistive networks [2] [6] in order to reduce the computational effort. Even though analog neural networks are used to analyse the visual motion, their relations with some biological data are often very far in spite of a great interest in the biological mechanisms involved in this process [7] In the present paper, we ....

J. Hutchinson, C. Koch, J. Luo, C. Mead, Computing Motion Using Analog and Binary Resistive Networks, IEEE Computer, 52-63 (1988)

....image function S can be computed: S(x i ; t) n if x i 2 n , where (x i ; t) is a spatio temporal position in the image sequence. Central to the algorithm developed below is the observation that in an image sequence motion boundaries almost always coincide with intensity boundaries [2]. An exception to this rule would be, for example, the situation when a region is split into two parts moving in different directions. We consider, however, such scenarios unlikely and neglect them. Assume that the displacement of each point x = x; y] T in an image region can be described by ....

J. Hutchinson, C. Koch, J. Luo, and C. Mead, "Computing motion using analog and binary resistive networks, " Computer, vol. 21, pp. 52--63, Mar. 1988.

....level of distortion may be permitted around the boundary due to the spatial masking of the HVS. Below, we propose an approach to region based representation of motion. It is based on the observation that only under specific circumstances motion boundaries will not coincide with intensity edges [10]. Thus, we study three blocks from Fig. 1 that are pertinent to the region based representation of motion: ffl intensity based (intra frame) segmentation, ffl inter frame segmentation and motion estimation, ffl coding of segmentation maps. To compute the intensity based segmentation we ....

....motion representation and estimation developed below are based on two underlying assumptions. First, we assume that in an image sequence motion boundaries almost always coincide with intensity boundaries. This observation is not new and has been exploited before in the computation of motion [10, 13]. Secondly, we assume that the displacement of each point x = x; y] T in an image region can be described by the following affine transformation [6] d(x; OE) a 1 a 2 # b 11 b 12 b 21 b 22 # x Gamma x g y Gamma y g # where x g ; y g are the coordinates of the center of ....

J. Hutchinson, C. Koch, J. Luo, and C. Mead, "Computing motion using analog and binary resistive networks," Computer, vol. 21, pp. 52--63, Mar. 1988.

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J. Hutchinson, C. Koch, J. Luo and C. Mead, "Computing motion using analog and binary resistive networks," IEEE Computers, Vol. 21, pp. 52-63, 1988.

.... sensing array into a resistive network to smooth out random noise and circuit offsets, we can use motion discontinuity signals to diminish or eliminate locally the amount of smoothing across object boundaries by increasing the local resistance or by opening switches at their respective locations [14, 10]. With such an architecture it would be possible to implement smoothing and segmentation simultaneously. Unlike a resistive fuse network [8, 17] where discontinuities tend to persist, so that for a given input stimulus multiple stable states may exist depending on the history of the stimulus, ....

J. Hutchinson, C. Koch, J. Luo, and C. Mead. Computing motion using analog and binary resistive networks. IEEE Computers, 21:52--63, 1988.

.... of neighboring velocity sensing elements to smooth out random noise and circuit offsets, we can use the motion discontinuity signals to diminish or eliminate the amount of smoothing across object boundaries by increasing the local resistance or by opening switches at their locations respectively [10, 8]. With such a feedback architecture it would be possible to implement smoothing and segmentation simultaneously. Due to the analog nature of the discontinuity signals, they could be used to vary the local resistance of the network in such a way that the smoothing gradually decreases with ....

J. Hutchinson, C. Koch, J. Luo, and C. Mead. Computing motion using analog and binary resistive networks. IEEE Computers, 21:52--63, 1988.

....of optical flow fields extracted from typical vehicle navigation scenes [3] The two features that we shall discuss are heading direction and time to contact. Among other features that can be estimated are also motion discontinuities, to help segregate objects (e.g. cars) from the background [37, 38, 39]. In order to analyze the computational properties of the optical flow and to determine the most suitable architectures for analog VLSI implementations, we performed software simulations on sequences of images obtained from a commercially available camera with a 64 Theta 64 pixel silicon retina ....

J. Hutchinson, C. Koch, J. Luo and C. Mead, "Computing motion using analog and binary resistive networks," IEEE Computer, vol. 21, pp. 52-64, 1988.

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Hutchinson, J., Koch, C., Luo, J. & C.A. Mead (1988) "Computing Motion using Analog and Binary Resistive Networks," IEEE Computers, Vol. 21, pp. 52-63, March.

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J. Hutchinson, C. Koch, J. Luo, and C. Mead, "Computing motion using analog and binary resistive networks," Computer, vol. 21, pp. 52--64, March 1988.

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J. Hutchinson, C. Koch, J. Luo, and C. Mead. Computing motion using analog and binary resistive networks. Computer, 21:52--64, March 1988.

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J. Hutchinson, C. Koch, J. Luo, and C. Mead. "Computing motion using analog and binary resistive networks." Computer, Vol. 21, pp. 52--63, 1988.

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J. Hutchinson, C. Koch, J. Luo, and C. Mead, "Computing motion using analog and binary resistive networks," IEEE Computer Magazine, pp. 52--63, March 1988.

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J. Hutchinson, C. Koch, J. Luo, and C. Mead, "Computing motion using analog and binary resistive networks, " Computer, vol. 21, pp. 52--63, Mar. 1988.

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