MOTION PARAMETER-ESTIMATION FROM GLOBAL FLOW FIELD DATA

We present two methods for the determination of the parameters of moti on of a sensor, given the vector flow field induced by an imaging syst em governed by a perspective transformation of a rigid scene. We assum e that the flow field V = (u(x, y), v(x, y)) is given. Both algorithms are new, and both integrate global data to determine motion parameter s. The first algorithm (the flow circulation algorithm) determines the rotational parameters. It uses the curl of the flow field (curl (V)), which under many conditions is approximately a linear function of the form g(x, y) = ax + by + c. The coefficients of the linear function, a, b, and c, which may be determined by simple regression, are proport ional to the desired rotational parameters of motion. Circulation valu es may be used in place of curl values, resulting in less noise. The s econd algorithm (the FOE search algorithm) determines the translationa l parameters of the motion independently of the first algorithm. This algorithm extends a recent method of Heeger and Jepson, giving a metho d for searching for the image focus of expansion. For every location ( x0, y0) in the image plane, we compute a function u . (-y + y0) + v . (x - x0). When (x0, y0) is located at the focus of expansion, this fun ction will be a quadratic polynomial (of a special form). We suggest s everal methods for determining when the function has the appropriate f orm; one method involves filtering the function by a collection of cir cular-surround zero-mean receptive fields. The other methods project t he function onto a linear space of quadratic polynomials and measures the distance between the two functions. The error function for the fir st two methods is a quadratic polynomial of the candidate position, yi elding a very ra id search strategy.