Compact real-time 2-D gradient-based analog VLSI motion sensor

In this work we present the first working focal plane analog VLSI sensor for the spatially resolved computation of the 2-D motion field based on temporal and spatial derivatives. Using an adaptive CMOS photoreceptor the temporal derivative and a function of the spatial derivative of the local light intensity are computed. By multiplying these values separately for both spatial dimensions a vector is obtained, which points in the direction of the normal optical flow and whose magnitude for a given stimulus is proportional to its velocity. The circuit consists of only 31 MOSFETs and three capacitors per pixel. We present measurement data from fully functional prototype 2-D pixel arrays for natural stimuli of varying velocity, orientation, contrast and spatial frequency. High direction selectivity even for very low contrast input is demonstrated. As application it is shown how the pixel-parallel architecture of the sensor can favourably be used for real-time computation of the focus of expansion and the axis of rotation. Because of its compactness, its robust operation and its uncritical handling the sensor might be favourably applied in industrial applications.