Robust Model Fitting Using Higher Than Minimal Subset Sampling.

Identifying the underlying model in a set of data contaminated by noise and outliers is a fundamental task in computer vision. The cost function associated with such tasks is often highly complex, hence in most cases only an approximate solution is obtained by evaluating the cost function on discrete locations in the parameter (hypothesis) space. To be successful at least one hypothesis has to be in the vicinity of the solution. Due to noise hypotheses generated by minimal subsets can be far from the underlying model, even when the samples are from the said structure. In this paper we investigate the feasibility of using higher than minimal subset sampling for hypothesis generation. Our empirical studies showed that increasing the sample size beyond minimal size ( p ), in particular up to p+2, will significantly increase the probability of generating a hypothesis closer to the true model when subsets are selected from inliers. On the other hand, the probability of selecting an all inlier sample rapidly decreases with the sample size, making direct extension of existing methods unfeasible. Hence, we propose a new computationally tractable method for robust model fitting that uses higher than minimal subsets. Here, one starts from an arbitrary hypothesis (which does not need to be in the vicinity of the solution) and moves until either a structure in data is found or the process is re-initialized. The method also has the ability to identify when the algorithm has reached a hypothesis with adequate accuracy and stops appropriately, thereby saving computational time. The experimental analysis carried out using synthetic and real data shows that the proposed method is both accurate and efficient compared to the state-of-the-art robust model fitting techniques.

Nonrigid registration of volumetric images using ranked order statistics.

Nonrigid image registration techniques using intensity based similarity measures are widely used in medical imaging applications. Due to high computational complexities of these techniques, particularly for volumetric images, finding appropriate registration methods to both reduce the computation burden and increase the registration accuracy has become an intensive area of research. In this paper, we propose a fast and accurate nonrigid registration method for intra-modality volumetric images. Our approach exploits the information provided by an order statistics based segmentation method, to find the important regions for registration and use an appropriate sampling scheme to target those areas and reduce the registration computation time. A unique advantage of the proposed method is its ability to identify the point of diminishing returns and stop the registration process. Our experiments on registration of end-inhale to end-exhale lung CT scan pairs, with expert annotated landmarks, show that the new method is both faster and more accurate than the state of the art sampling based techniques, particularly for registration of images with large deformations.

Quantification of smoothing requirement for 3D optic flow calculation of volumetric images.

Complexities of dynamic volumetric imaging challenge the available computer vision techniques on a number of different fronts. This paper examines the relationship between the estimation accuracy and required amount of smoothness for a general solution from a robust statistics perspective. We show that a (surprisingly) small amount of local smoothing is required to satisfy both the necessary and sufficient conditions for accurate optic flow estimation. This notion is called "just enough" smoothing, and its proper implementation has a profound effect on the preservation of local information in processing 3D dynamic scans. To demonstrate the effect of "just enough" smoothing, a robust 3D optic flow method with quantized local smoothing is presented, and the effect of local smoothing on the accuracy of motion estimation in dynamic lung CT images is examined using both synthetic and real image sequences with ground truth.