Penalty approaches can be used to efficiently resolve collisions of dynamically simulated rigid and deformable objects. These approaches compute penalty forces based on the penetration depth of intersecting objects and there exist many algorithms for estimating the exact penetration depth. However, in discrete-time simulations, this information can cause non-plausible collision responses in cas...

We propose notions of simplicial band depth for multivariate functional data that extend the univariate functional band depth. The proposed simplicial band depths provide simple and natural criteria to measure the centrality of a trajectory within a sample of curves. Based on these depths, a sample of multivariate curves can be ordered from the center outward and order statistics can be defined...

We introduce ProveProp , a procedure for proving safety properties. ProveProp is based on a technique called Partial Quantifier Elimination (PQE). In contrast to complete quantifier elimination, in PQE, only a part of the formula is taken out of the scope of quantifiers. So PQE can be dramatically more efficient than complete quantifier elimination. The appeal of ProveProp is twofold. First, it...

This paper presents a general refinement procedure that enhances any given depth map obtained by passive or active sensing. Given a depth map, either estimated by triangulation methods or directly provided by the sensing system, and its corresponding 2-D image, we correct the depth values by separately treating regions with undesired effects such as empty holes, texture copying or edge blurring...

Data depth functions are a generalization of one-dimensional order statistics and medians to real spaces of dimension greater than one; in particular, a data depth function quantifies the centrality of a point with respect to a data set or a probability distribution. One of the most commonly studied data depth functions is halfspace depth. It is of interest to computational geometers because it...

Best-first search (BFS) expands the fewest nodes among all admissible algorithms using the same cost function, but typically requires exponential space. Depth-first search needs space only linear in the maximumsearch depth, but expands more nodes than BFS. Using a random tree, we analytically show that the expected number of nodes expanded by depth-first branch-and-bound (DFBnB) is no more than...

Complex Gabor filters with phases in quadrature are often used to model evenand odd-symmetric simple cells in the primary visual cortex. In stereo vision, the phase difference between the responses of the left and right views can be used to construct a disparity or depth map. Various constraints can be applied in order to construct smooth maps, but this leads to very imprecise depth transitions...

This paper presents an e cient technique for unsupervised content-based segmentation in stereoscopic video sequences by appropriately combined di erent content descriptors in a hierarchical framework. Three main modules are involved in the proposed scheme; extraction of reliable depth information, image partition into color and depth regions and a constrained fusion algorithm of color segments ...

This paper describes a method of extracting depth information about a scene from a single, static viewpoint. The. approach uses aperture variation to obtain a sequence of images differing only in depth of field, thus avoiding the 'correspondence problem associated with stereo and optical flow techniques. These images contain the necessary coded depth information. By using one image (that with t...

This paper reviews the recent progresses of the depth map generation for dynamic scene and its corresponding computational models. This paper mainly covers the homogeneous ambiguity models in depth sensing, resolution models in depth processing, and consistency models in depth optimization. We also summarize the future work in the depth map generation.