Motion segmentation from perspective images via rank minimization

In this thesis, we consider the problem of segmenting data points coming from rigid bodies under perspective projection. As we all know the perspective projection camera model is the most general camera model of computer imaging, but unfortunately it is also known to be non-linear. Thus making the problem at the hand harder.;To solve this most general form of segmentation problem, we assume that we are given point correspondence data in image sequences. The data set consist of the projected coordinates of the points in 3D. The main idea of the method is to group the points according to the complexity of their motion in 3D. This idea intuitively formalizes, the fact that points from the same object would share more modes of motion and hence leading to less complex models than points from different objects.;We approached to the problem at the hand from a systems theory perspective. Estimating model order complexity and projective depth of the points is reduced to minimizing the rank of a Hankel matrix, which is constructed using the correspondence data and the unknown depths. This leads to a simple non-iterative segmentation algorithm that optimizes the use of spatial and temporal information. Since the presented algorithm exploits both spatial and temporal constraints, it does not require the estimation of the fundamental matrix and it is less sensitive to the effect of noise and outliers than approaches that rely solely on factorizations of the measurements matrix. In addition, the method can also naturally handle degenerate cases, e.g. cases where the objects partially share motion modes.;We presented and demonstrated this novel motion segmentation algorithm, tested its performance on different kinds of cases as well as comparing it with some existing algorithms.