Computing motion using analog and binary resistive networks

The authors describe recent developments in the theory of early vision that led from the formulation of the motion problem as an ill-posed one to its solution by minimizing certain 'cost' functions. These cost or energy functions can be mapped onto simple analog and digital resistive networks. The optical flow is computed by injecting currents into resistive networks and recording the resulting stationary voltage distribution at each node. The authors believe that these networks, which they implemented in complementary metal-oxide-semiconductor (CMOS) very-large-scale integrated (VLSI) circuits, represent plausible candidates for biological vision systems

Analog hardware for detecting discontinuities in early vision

The detection of discontinuities in motion, intensity, color, and depth is a well-studied but difficult problem in computer vision [6]. We discuss the first hardware circuit that explicitly implements either analog or binary line processes in a deterministic fashion. Specifically, we show that the processes of smoothing (using a first-order or membrane type of stabilizer) and of segmentation can be implemented by a single, two-terminal nonlinear voltage-controlled resistor, the “resistive fuse”; and we derive its current-voltage relationship from a number of deterministic approximations to the underlying stochastic Markov random fields algorthms. The concept that the quadratic variation functionals of early vision can be solved via linear resistive networks minimizing power dissipation [37] can be extended to non-convex variational functionals with analog or binary line processes being solved by nonlinear resistive networks minimizing the electrical co-content. We have successfully designed, tested, and demonstrated an analog CMOS VLSI circuit that contains a 1D resistive network of fuses implementing piecewise smooth surface interpolation. We furthermore demonstrate the segmenting abilities of these analog and deterministic “line processes” by numerically simulating the nonlinear resistive network computing optical flow in the presence of motion discontinuities. Finally, we discuss various circuit implementations of the optical flow computation using these circuits

Computation of Smooth Optical Flow in a Feedback Connected Analog Network

In 1986, Tanner and Mead \cite{Tanner_Mead86} implemented an interesting constraint satisfaction circuit for global motion sensing in aVLSI. We report here a new and improved aVLSI implementation that provides smooth optical flow as well as global motion in a two dimensional visual field. The computation of optical flow is an ill-posed problem, which expresses itself as the aperture problem. However, the optical flow can be estimated by the use of regularization methods, in which additional constraints are introduced in terms of a global energy functional that must be minimized. We show how the algorithmic constraints of Horn and Schunck \cite{Horn_Schunck81} on computing smooth optical flow can be mapped onto the physical constraints of an equivalent electronic network

Computing motion in the primate's visual system

Computing motion on the basis of the time-varying image intensity is a difficult problem for both artificial and biological vision systems. We will show how one well-known gradient-based computer algorithm for estimating visual motion can be implemented within the primate's visual system. This relaxation algorithm computes the optical flow field by minimizing a variational functional of a form commonly encountered in early vision, and is performed in two steps. In the first stage, local motion is computed, while in the second stage spatial integration occurs. Neurons in the second stage represent the optical flow field via a population-coding scheme, such that the vector sum of all neurons at each location codes for the direction and magnitude of the velocity at that location. The resulting network maps onto the magnocellular pathway of the primate visual system, in particular onto cells in the primary visual cortex (V1) as well as onto cells in the middle temporal area (MT). Our algorithm mimics a number of psychophysical phenomena and illusions (perception of coherent plaids, motion capture, motion coherence) as well as electrophysiological recordings. Thus, a single unifying principle ‘the final optical flow should be as smooth as possible’ (except at isolated motion discontinuities) explains a large number of phenomena and links single-cell behavior with perception and computational theory