Moment calculations by digital filters

We present a simple recursive algorithm for computing moments of two-dimensional integer arrays. It uses only additions and can be implemented for high-speed and real-time computation at video rates. We describe Complementary Metal-Oxide Semiconductor (CMOS), Very Large-Scale Integrated (VLSI) implementation of the algorithm in a single chip that can calculate the 16 moments μi, j (i, j = 0, 1, 2, 3) (i.e., up to the sixth-order moment) on 512 × 512 array of 8-bit integers in real time (at video rate). Such a chip can have potential applications in image processing, graphics, and robotics. The basic building block of the system is a single-pole digital filter that is implemented by recursive addition. The complexities involved in designing the chip, as well as its area, are significantly reduced by taking advantage of the fact that the column samples of the data array can be processed at a much slower rate than the row samples. An estimate of the chip area obtained from the layout design of the individual cells is given.