Three types of HST: square tiling (e.g., Quadtree and Spatial Pyramid), rectangular tiling (HST-RECT), triangular tiling (HST-TRI) Representation Given a set of scene configurations (scene label maps), we present a learning-by-parsing (EM-like) method to learn the HST representation including the branching probability at Or-nodes and the tiling dictionary. E-Step: fix HST and infer parse tree b...

Conway’s Game of Life rules can be applied to Cellular Automata (CAs) running on aperiodic grids, namely Penrose tilings. Here we investigate the result of running such CAs from random initial conditions. This requires development of a Penrose tiling algorithm suitable for CA experiments, in particular, a tiling that can be lazily expanded as CA activity reaches an edge. We describe such an alg...

Finding an efficient optimal partial tiling algorithm is still an open problem. We have worked on a special case, the tiling of Manhattan polyominoes with dominoes, for which we give an algorithm linear in the number of columns. Some techniques are borrowed from traditional graph optimisation problems. For our purpose, a polyomino is the (non necessarily connected) union of unit squares (for wh...

Unimodular transformations, tiling, and software prefetching are loop optimizations known to be effective in increasing parallelism, reducing cache miss rates, and eliminating processor stall time. Although these optimizations individually are quite effective, there is the expectation that even better improvements can be obtained by combining them together. In this paper we show that indeed thi...

We consider a weighted square-and-domino tiling model obtained by assigning real number weights to the cells and boundaries of an n-board. An important special case apparently arises when these weights form periodic sequences. When the weights of an nm-tiling form sequences having period m, it is shown that such a tiling may be regarded as a meta-tiling of length n whose weights have period 1 e...

Computing aggregates over selected categories of multidimensional discrete data (MDD) cubes is the core operation of many on-line analytical processing (OLAP) systems. In order to support efficient computations of these aggregates in a multidimensional OLAP (MOLAP) system, a careful design of the database storage architecture must be undertaken. In particular, tiling (i.e., subdivision of an MD...

It is well known that two regular tetrahedra can be combined with a single regular octahedron to tile (complete fill) three-dimensional Euclidean space . This structure was called the "octet truss" by Buckminster Fuller. It was believed that such a tiling, which is the Delaunay tessellation of the face-centered cubic (fcc) lattice, and its closely related stacking variants, are the only tessell...

This paper is concerned with the stability of the set of trajectories of a patchy vector field, in the presence of impulsive perturbations. Patchy vector fields are discontinuous, piecewise smooth vector fields that were introduced in Ancona and Bressan (1999) to study feedback stabilization problems. For patchy vector fields in the plane, with polygonal patches in generic position, we show tha...

Polygonal meshes are used in many application scenarios. Often the generated meshes are too complex not allowing proper interaction, visualization or transmission through a network. To tackle this problem, simplification methods can be used to generate less complex versions of those meshes. For this purpose many methods have been proposed in the literature and it is of paramount importance that...

complexity of the scene which can be formed by several partially occluded objects (e.g. the bin-picking task). We describe the use of geometric reasoning and proI n t h e l i t e r a t u r * J t i s P° s s i b l e t o find <&* a TMmbe o f jective geometry to infer 3-D information about cirm e t h o d s f o r e l h P t i c a l 8 b u t t h e P r o b l e m o f d e a l i n 8 cles which project elli...