Transform Domain Motion Estimation

T h e coefficient-recursive algorithm described in this paper estimates the displacement of objects in a television scene. It is a generalization of a pel-recursive displacement estimation algorithm recently introduced by Netravali and Robbins. 12 Coefficient-recursive displacement estimation has potential application in hybrid transform-DPCM3,4 interframe image coders of the type discussed by Reader, 5 Roese, 6 and Jones.' T h e performance of a hybrid transform-DPCM interframe coder using coefficient recursive motion compensation is described in a companion paper. 8 Before defining the coefficient-recursive displacement estimation algorithm, it is useful to first describe pel-recursive displacement 1673 estimation. Let 7(x*, t) denote the intensity of a scene at the &th sample point X/, of a scan line, and let /(x*, t -- r) denote the intensity at the same spatial location in the previous frame. If the scene consists of an object that is undergoing pure translation, then, neglecting background, I(xk,t) = / ( x * - D , * - r ) , (1) where D is the displacement of the object in one frame interval T. Pelrecursive displacement estimation attempts to estimate D by minimizing the squared value of the displaced frame difference, DFD{xk, D) = I(xk, t) - 7(x* - D, t - r), recursively with k using a steepest descent algorithm of the form: D/H-I = D* - y2 e VD k [DFD(x k , D*)]2, (3a) (2)