Three dimensional object recognition from two-dimensional image is implemented in this work with the use of 512 different poses of the object (which is represented by an airplane or a cube or a satellite). The object is rotated in the three directions (x,y,z) by an angle of 2/8 rad. (45). Centroidal sample representation was used to represent the data extracted from the object. Also four or f...

This paper provides implementation details of the algorithm proposed in Schvartzman and Otaduy [2014] to simulate brittle fracture. We cast brittle fracture as the computation of a high-dimensional centroidal Voronoi diagram (CVD), where the distribution of fracture fragments is guided by the deformation field of the fractured object. We accelerate the fracture animation process with example-ba...

We present an object recognition system that identifies objects by their silhouette from single views of a greyscale camera. The centroidal profile describing the object boundary is matched with boundaries from a model base using a dynamic programming technique. Objects are modelled by a multi-view representation which can either be learned from a set of images or generated from a geometric mod...

Isosceles trapezoids are dissected into three similar triangles and rearranged to form two additional isosceles trapezoids. Moreover, triangle centers, one from each similar triangle, form the vertices of a centric triangle which has special properties. For example, the centroidal triangles are congruent to each other and have an area one-ninth of the area of the trapezoids; whereas, the circum...

We present a simple, biologically motivated model for the creation of phyllotactical patterns in capitula and their computer simulation. An in-depth investigation of Ridley's contact pressure model is performed and a refinement of contact pressure between primordia on the basis of local centroidal Voronoi relaxation is presented. Using this method in combination with Hofmeisters rule for placin...

This paper proposes a new method for isotropic remeshing of triangulated surface meshes. Given a triangulated surface mesh to be resampled and a user-specified density function defined over it, we first distribute the desired number of samples by generalizing error diffusion, commonly used in image halftoning, to work directly on mesh triangles and feature edges. We then use the resulting sampl...

This paper introduces Lp-Centroidal Voronoi Tessellation (LpCVT), a generalization of CVT that minimizes a higher-order moment of the coordinates on the Voronoi cells. This generalization allows for aligning the axes of the Voronoi cells with a predefined background tensor field (anisotropy). Lp-CVT is computed by a quasi-Newton optimization framework, based on closed-form derivations of the ob...

Centroidal Voronoi tessellations (CVT’s) are special Voronoi tessellations for which the generators of the tessellation are also the centers of mass (or means) of the Voronoi cells or clusters. CVT’s have been found to be useful in many disparate and diverse settings. In this paper, CVT-based algorithms are developed for image compression, image segmenation, and multichannel image restoration a...