Computing optical flow in the primate 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 show how gradient models, a well-known class of motion algorithms, can be implemented within the magnocellular pathway of the primate's visual system. Our cooperative algorithm computes optical flow in two steps. In the first stage, assumed to be located in primary visual cortex, local motion is measured while spatial integration occurs in the second stage, assumed to be located in the middle temporal area (MT). The final optical flow is extracted in this second stage using population coding, such that the velocity is represented by the vector sum of neurons coding for motion in different directions. Our theory, relating the single-cell to the perceptual level, accounts for a number of psychophysical and electrophysiological observations and illusions

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

Computing motion using analog VLSI vision chips: An experimental comparison among different approaches

We have designed, built and tested a number of analog CMOS VLSI circuits for computing 1-D motion from the time-varying intensity values provided by an array of on-chip phototransistors. We present experimental data for two such circuits and discuss their relative performance. One circuit approximates the correlation model while a second chip uses resistive grids to compute zero-crossings to be tracked over time by a separate digital processor. Both circuits integrate image acquisition with image processing functions and compute velocity in real time. For comparison, we also describe the performance of a simple motion algorithm using off-the-shelf digital components. We conclude that analog circuits implementing various correlation-like motion algorithms are more robust than our previous analog circuits implementing gradient-like motion algorithms

Optical Flow and Surface Interpolation in Resistive Networks: Algorithms and Analog VLSI Chips

To us, and to other biological organisms, vision seems effortless. We open our eyes and we "see" the world in all its color, brightness, and movement. Flies, frogs, cats, and humans can all equally well perceive a rapidly changing environment and act on it. Yet, we have great difficulties when trying to endow our machines with similar abilities. In this article, we 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. For instance, as detailed in this chapter, we can compute the optical flow by injecting currents into resistive networks and recording the resulting stationary voltage distribution at each node. These networks, which are implemented in subthreshold, analog, complementary metal oxide semiconductor (CMOS) very large scale integrated (VLSI) circuits, are very attractive for their technological potential

Modeling the development of cortical responses in primate dorsal (“where”) pathway to optic flow using hierarchical neural field models

Although there is a plethora of modeling literature dedicated to the object recognition processes of the ventral (“what”) pathway of primate visual systems, modeling studies on the motion-sensitive regions like the Medial superior temporal area (MST) of the dorsal (“where”) pathway are relatively scarce. Neurons in the MST area of the macaque monkey respond selectively to different types of optic flow sequences such as radial and rotational flows. We present three models that are designed to simulate the computation of optic flow performed by the MST neurons. Model-1 and model-2 each composed of three stages: Direction Selective Mosaic Network (DSMN), Cell Plane Network (CPNW) or the Hebbian Network (HBNW), and the Optic flow network (OF). The three stages roughly correspond to V1-MT-MST areas, respectively, in the primate motion pathway. Both these models are trained stage by stage using a biologically plausible variation of Hebbian rule. The simulation results show that, neurons in model-1 and model-2 (that are trained on translational, radial, and rotational sequences) develop responses that could account for MSTd cell properties found neurobiologically. On the other hand, model-3 consists of the Velocity Selective Mosaic Network (VSMN) followed by a convolutional neural network (CNN) which is trained on radial and rotational sequences using a supervised backpropagation algorithm. The quantitative comparison of response similarity matrices (RSMs), made out of convolution layer and last hidden layer responses, show that model-3 neuron responses are consistent with the idea of functional hierarchy in the macaque motion pathway. These results also suggest that the deep learning models could offer a computationally elegant and biologically plausible solution to simulate the development of cortical responses of the primate motion pathway