Estimation Of Visual Motion

The estimation of motion information from image sequences is one of the most important problems in computer vision. In computer vision, we are interested in determining the direction and the velocity of moving objects in the scene. The first step towards obtaining this information is the computation of the relative motion of the scene. the expression"relative"refers to the fact that we compute the motion relative to the possibly moving cameras and not to a static fixed point in the scene. Moreover, we restrict ourselves to image sequences that have been acquired by a single camera . Projective geometry tells us that in this case usually the depth of the scene can not be determined uniquely. What we compute is the projection of the actual motion onto a image plane. This 2-D displacement field that describes the apparent motion of the scene is the so-called optic ?ow.Although the optic ?ow is only the projection of the true motion of the scene, it proves to be useful for a variety of different tasks.For example, it allows to distinguish stationary from moving objects and to detect and avoid obstacles. This makes it particularly useful for tasks where vehicles have to be guided safely through an unknown environment. Moreover, the estimated motion allows to track objects on their way through the scene,In combination with approaches from machine learning, motion patterns can be trained in such a way that the obtained algorithms even allow for human-machine interfaces. Another field of application is the compression of video sequences. Finally, computing the optic ?ow is also directly related to other important correspondence problems in computer vision such as stereo reconstruction and image registration.We begin with a brief description of the computation of optical flow. This techniques was first presented by Horn and Schunch. This algorithm is based on that the brightness of a particular point in the pattern is constant,so that: v = dyrepresent the two components of optical flow,it is easy to see that we have This is what we called basic equations of optical flow. Optical flow has two components,we cannot determine the component of the movement in the direction of the iso-brightness contours. As a consequence,the flow cannot be computed locally without introducing additional constraints. Horn and Schunck combined the gradient constraint(basic equation) with a global smoothness term to constrain the estimated velocity,minimizing: Andε_b =E_xu+E_yv+E_t, To slove this energy functional we will use this equntions: (Euler-Lagrange equations)The minimizing functions of the convex energy functional are necessarily satisfying the Euler-Lagrange equations So we have xyyytWe have to approximate the equations above through a numerical method,we can have the iterative equations: One can compute optical flow using this iterative equations. There has been a lot of improved methods in the last two decades. But usually they come down to compute the minimizing functions. Therefore Euler-Lagrange equations from the calculus of variations and numericalmethods are used. Robustness of many algorithms that compute optical flow are very poor. So we want to improve the results through Landmarks. It works with two ways. One is to add constraint conditions to global energy functi- onal. ( x_i ,y_i)represent Landmarks,so we have to minimize a functional with constraint conditions. The other simple way is driectly modifing the iterative equations,adding a correction term to modifing the iterative equations: And are correction terms.