Topo-Geometric Filtration Scheme for Geometric Active Contours and Level Sets: Application to Cerebrovascular Segmentation

One of the main problems of the existing methods for the segmentation of cerebral vasculature is the appearance in the segmentation result of wrong topological artefacts such as the kissing vessels. In this paper, a new approach for the detection and correction of such errors is presented. The proposed technique combines robust topological information given by Persistent Homology with complementary geometrical information of the vascular tree. The method was evaluated on 20 images depicting cerebral arteries. Detection and correction success rates were 81.80% and 68.77%, respectively

Charterparties: Law, Practice and Emerging Legal Issues

The bilateral filter is a nonlinear filter that smoothes a signal while preserving strong edges. It has demonstrated great effectiveness for a variety of problems in computer vision and computer graphics, and fast versions have been proposed. Unfortunately, little is known about the accuracy of such accelerations. In this paper, we propose a new signal-processing analysis of the bilateral filter which complements the recent studies that analyzed it as a PDE or as a robust statistical estimator. The key to our analysis is to express the filter in a higher-dimensional space where the signal intensity is added to the original domain dimensions. Importantly, this signal-processing perspective allows us to develop a novel bilateral filtering acceleration using downsampling in space and intensity. This affords a principled expression of accuracy in terms of bandwidth and sampling. The bilateral filter can be expressed as linear convolutions in this augmented space followed by two simple nonlinearities. This allows us to derive criteria for downsampling the key operations and achieving important acceleration of the bilateral filter. We show that, for the same running time, our method is more accurate than previous acceleration techniques. Typically, we are able to process a 2~megapixel image using our acceleration technique in less than a second, and have the result be visually similar to the exact computation that takes several tens of minutes. The acceleration is most effective with large spatial kernels. Furthermore, this approach extends naturally to color images and cross bilateral filtering