Statistical analysis of visual data segmentation

A simplified theoretical framework for the prediction of feasibility of segmentation of a two-dimensional linear equation system is presented in this thesis. A statistical definition of a separable motion (structure) is offered and a relatively straightforward criterion for predicting the separability of two different motions in this framework is derived. The applicability of the proposed criterion for prediction of the existence of multiple motions in practice is examined using both synthetic and real image sequences. The prescribed separability criterion is useful in designing computer vision applications as it is solely based on the amount of relative motion and the scale of measurement noise.

Measurement of local differences in the 3D motions of dynamic body organs (captured by volumetric scanners) is of increasing interest in biomedical imaging applications. Estimation methods of 3D optical flow in these images have been studied in recent years. The theoretical limits of 3D optical flow-based motion estimation and segmentation are, however, yet to be analysed. In this thesis, a novel criterion is proposed to statistically predict the separability of local 3D motions. %Simulation results demonstrate how the proposed approach works in principle to predict separability of two motions in terms of the amount of relative motion and the scale of noise.

This thesis investigated the theoretical feasibility of line detection in Hough domain in presence of multiple nearby lines. The limits of separability and detectability in terms of line distances and the quality of given data is identified. This thesis also investigated the effect of discretization on the success of line detection and analyzed the optimality of an appropriate discretization regime. Experiments showed that the results can be used in practice. These models and analyses address two important questions of lines separability and detectability but the range of potential applications is much broader than these questions.