Conndence Measures for Image Motion Estimation 2. Introduction

1. Abstract Estimation of image motion, also known as the optic ow, from a sequence of images is known to be diicult. This is due to: the sensitivity of the image motion model to noise (the derivative property), the limited observability of the image motion from the luminance (the aperture problem), and, the non-validity of the optic ow constraint (the assumption of intensity conservation). In this paper we analyze measures that assign a conndence value to the estimated image motion: the sensitivity of the model to noise, the validity of the model and the estimated variance of the image motion. Experiments show that selection of image motion vectors based on these measures dramatically improve the estimates of the image motion while keeping as much image motion vectors as possible. We conclude that the proposed estimated variance of the image motion optimizes this trade-oo. The estimation of image motion ^ v(x;t) from a sequence of images I (x; t) is a well addressed 8] problem in computer vision. The assumption of conservation of image intensity results in the well known optic ow constraint 2]: rI(x; t) v(x;t) + I t (x; t) = 0 (1) Since the optic ow constraint (1) gives only one equation to the image motion vector at every point, an additional equation is needed to estimate the two components of the image motion vector. The method reported in 1] 7] uses a parametric model of the image motion to produce the image motion from the the optic ow constraint. The underlying assumption of the model is that the image motion is constant in a very small region S. Every op-tic ow constraint in region S eliminates one free parameter of the image motion vector. Since the vector has 2 free parameters, theoretically 2 such constraints are enough if the spatial derivatives are non coplanar. However, since the image (time) derivatives may be noisy, a Least Mean Square solution will generally be more robust. This can formally be translated in to minimizing the func