1. Introduction

    There are a large number of applications that use information of motion in image sequences, ranging from image compression( e.g. MPEG ) to computer vision applications( e.g. motion-based segmentation, structure from motion and etc ). This motion estimation problem is an ill-posed problem in the absence of any additional assumptions about the nature of the motion.
    In this final project, I propose a method for optical flow/motion estimation using feature matching. In this section, general assumptions and problems in motion estimation are explained. A brief survey of motion estimation algorithm is shown in section 2. The proposed algorithm, the simulation model and results are described in the subsequent sections.

    Since motion estimation is an ill-posed problem, some assumptions need to pooled to alleviate the problem. Common assumptions used in motion estimation algorithms are described here. The intensity conservation constraint assumes that the image brightness of a region remains constant while its location may change. This assumption underlies the common correlation and gradient-based approaches. This assumption can be violated if the luminace in the image is changed throughout time, or reflections, shadows are in the image. Note that this assumptions is more valid if the image is sampled at high rates with small time difference between frames.

    Another commonly used assumption is spatial coherence constraint. It assumes that the flow within a neighborhood changes gradually. This further assumes that there are only a single motion within a confined range. However, optical flow is not totally continuous but is only piecewise smooth since depth boundaries in the scene may give rise to discontinuities in the flow. This assumption is commonly violated when there are multiple objects moving at different depth. If this assumption is falsely imposed, then motion estimation error can occur and object boundaries. Note that this assumption cannot be alleviated even when the image is sampled at high rates.
 

    Occlusion refers to covering/uncovering of a surface due to 3-D rotation and traslation of an object which occupies only part of the field of view. To illustrate this point, let's assume that an object is in front of a background. Depending on the location of the object, some parts of the background hidden behind the object. If these hidden regions are to be uncovered in the next frame, then it is not possible to find a correspondence for these pixels between the two frames. Since optical flow/motion estimation involves finding correspondence between pixels, the estimator can produce erroneous results for these regions.

    Another problem is the aperture problem. Estimation of optical flow involes the pooling of constraints over some spatial neighborhood. Since the image is prone to noise, the region must be sufficiently large enough to robustly and accurately estimate the solution. For example, in gradient-based approches, estimating the x, y and t gradient of each point in the image is essential and fairly large region is requred to calculate this robustly. This problem also  happens in correspondence problem when you want to match two corresponding pixels. To declare that the two pixels in the different frame correspond to each other, not only the pixel value itself but also the neighboring region of the pixels have to be looked at. However, for larger region of integration, it is more likely to contain multiple motions with competing constraint. That is, the region must be small to avoid violating assumptions such as single motion for the region. Therefore, deciding how large of a region we should choose remains to be a very hard problem.