We present an algorithm to construct a bounding polyhedron for an affine Iterated Function System (IFS). Our algorithm expresses the IFS-bounding problem as a set of linear constraints on a linear objective function, which can then be solved via standard techniques for linear convex optimization. As such, our algorithm is guaranteed to find the optimum recursively instantiable bounding volume, ...

In virtual environment world, performing collision detection between various 3D objects requires sophisticated steps to be followed in order to properly visualize their effect. It is challenging due to the fact that multiple objects undergo various motion depending on the application’s genre. It is however an essential challenge to be resolved since it’s many use in the computer animation, simu...

Training object class detectors typically requires a large set of images in which objects are annotated by boundingboxes. However, manually drawing bounding-boxes is very time consuming. We propose a new scheme for training object detectors which only requires annotators to verify bounding-boxes produced automatically by the learning algorithm. Our scheme iterates between re-training the detect...

In this paper, we first give a characterization of a class of probability transition matrices having closed-form solutions for transient distributions and the steady-state distribution. We propose to apply stochastic comparison approach to construct bounding chains belonging to this class. Therefore bounding chains can be analyzed efficiently through closed-form solutions in order to provide bo...

R-trees can be used to store and query sets of point data in two or more dimensions. An easy way to construct and maintain R-trees for two-dimensional points, due to Kamel and Faloutsos, is to keep the points in the order in which they appear along the Hilbert curve. The R-tree will then store bounding boxes of points along contiguous sections of the curve, and the efficiency of the R-tree depe...

We present a scheme for exact collision detection between complex models undergoing rigid motion and deformation. The scheme relies on a hierarchical model representation using axis-aligned bounding boxes (AABBs). In recent work, AABB trees have been shown to be slower than oriented bounding box (OBB) trees. In this paper, we describe a way to speed up overlap tests between AABBs, such that for...

Few geospatial data representations are more basic than the bounding box; a rectangle surrounding a geographic feature or dataset. Bounding boxes are a key component of geospatial metadata and lie at the heart of many computational geometry algorithms as well as spatial indexing systems. Despite their ubiquity and common use, bounding boxes are more complicated than they first appear. The phras...