Local orientation analysis in images and image sequences using steerable filters

In this thesis, we address the issue of local orientation analysis using steerable filters. From the standpoint of the sampling theory, current orientation steerable filters sample the spectrum of the orientation space with Dirac functions. According to the well known uncertainty principle, we cannot simultaneously localize a signal both in the spatial domain and in the spectral domain exactly. This kind of uncertainty has a lower bound which can be achieved only using filters with Gaussian shape. With respect to this criterion, current steerable filters are not optimal because Dirac functions localize spectral components of the signal so exactly that the spatial counterparts of these Dirac functions almost lose their localization ability totally. As a result, we have to combine a large number of basis filters in order to achieve high resolution in orientation, which increase the computational complexity. Our contribution is that we use angular Gaussian filters in constructing steerable filters to achieve the lower bound in the uncertainty principle. Theoretical analysis and experimental results show that this new steerable filter achieves higher orientation resolution with lower computation complexity. These advantages benefit many applications ranging from 2D/3D junction characterization, volume image processing, facial analysis to symmetry detection, and specially multiple motion analysis. We analyze occlusion and transparency in detail both in the spatial domain and in the spectral domain and propose a unified multiple motion model in the spectral domain. Using the fact that multiple motions are equivalent to multiple planes in the derivative space or in the frequency space, we apply our 3D steerable filter for multiple motion estimation. We compare our approach with current motion algorithms like the 3D Hough transform, expectation maximization algorithm, and early 3D steerable filter approaches. In occlusion analysis we introduce amulti-window strategy to detect and to eliminate outliers. This improves the quality of input data and therefore provides more exact results in motion estimation. We further apply the “shift-and-subtract” technique to localize occlusion boundaries and to track their movement in occlusion sequences. This technique can also be used to distinguish occlusion from transparency and to decompose transparency scenes into multi-layers.