A degree is saturated bounding if it can compute a saturated model for any complete, decidable theory whose types are all computable. All high and PA degrees are saturated bounding (following from results of Jockusch and MacIntyre-Marker.) We show that for every n, no lown c.e. degree is saturated bounding, extending the previous known result that 0 is not saturated bounding, by Millar.

Bounding volumes are used in computer graphics to approximate the actual geometric shape of an object in a scene. The main intention is to reduce the costs associated with visibility or interference tests. The bounding volumes most commonly used have been axis-aligned bounding boxes and bounding spheres. In this paper, we propose the use of discrete orientation polytopes (k-dops) as bounding vo...

We present a novel, compact bounding volume hierarchy, TSS BVH, for ray tracing subdivision surfaces computed by the Catmull-Clark scheme. We use Tetrahedron Swept Sphere (TSS) as a bounding volume to tightly bound limit surfaces of such subdivision surfaces given a user tolerance. Geometric coordinates defining our TSS bounding volumes are implicitly computed from the subdivided mesh via a sim...

We present novel parallel algorithms for collision detection and separation distance computation for rigid and deformable models that exploit the computational capabilities of many-core GPUs. Our approach uses thread and data parallelism to perform fast hierarchy construction, updating, and traversal using tight-fitting bounding volumes such as oriented bounding boxes (OBB) and rectangular swep...

Tree-based multidimensional indexes are integral to efficient querying in multimedia and GIS applications. These indexes frequently use shapes in internal tree nodes to describe the data stored in a subtree below. We show that the standard Minimum Bounding Rectangle descriptor can lead to significant inefficiency during tree traversal, due to false positives. We also observe that there is often...

The tightness of the bounding volume is often difficult to adjust to suit different applications. In this paper, we present a technique to derive a tunable bounding volume for elliptic paraboloids, where the tightness can easily be controlled and altered at several levels. Our technique develops such a tunable bounding volume through the optimization process. Bounding volumes thus developed con...

Principle component analysis (PCA) is commonly used to compute a bounding box of a point set in Rd . The popularity of this heuristic lies in its speed, easy implementation and in the fact that usually, PCA bounding boxes quite well approximate the minimum-volume bounding boxes. In this paper we give a lower bound on the approximation factor of PCA bounding boxes of convex polytopes in arbitrar...

A new method of word segmentation for document images is presented. The method uses the bounding box regions to enclose the letters (characters) of the words and then the resulting letter spaces are progressively filled to merge the character bounding boxes to get the word bounding boxes. The method holds good for inclined and irregularly distributed words. The proposed method completely avoids...

Automatic discovery of foreground objects in video sequences is important in computer vision, with applications to object tracking, video segmentation and weakly supervised learning. This task is related to cosegmentation [4, 5] and weakly supervised localization [2, 6]. We propose an efficient method for the simultaneous discovery of foreground objects in video and their segmentation masks acr...