Shape Animation with Combined Captured and Simulated Dynamics

We present a novel volumetric animation generation framework to create new types of animations from raw 3D surface or point cloud sequence of captured real performances. The framework considers as input time incoherent 3D observations of a moving shape, and is thus particularly suitable for the output of performance capture platforms. In our system, a suitable virtual representation of the actor is built from real captures that allows seamless combination and simulation with virtual external forces and objects, in which the original captured actor can be reshaped, disassembled or reassembled from user-specified virtual physics. Instead of using the dominant surface-based geometric representation of the capture, which is less suitable for volumetric effects, our pipeline exploits Centroidal Voronoi tessellation decompositions as unified volumetric representation of the real captured actor, which we show can be used seamlessly as a building block for all processing stages, from capture and tracking to virtual physic simulation. The representation makes no human specific assumption and can be used to capture and re-simulate the actor with props or other moving scenery elements. We demonstrate the potential of this pipeline for virtual reanimation of a real captured event with various unprecedented volumetric visual effects, such as volumetric distortion, erosion, morphing, gravity pull, or collisions

Using Centroidal Voronoi Tessellations to Scale Up the Multi-dimensional Archive of Phenotypic Elites Algorithm

The recently introduced Multi-dimensional Archive of Phenotypic Elites (MAP-Elites) is an evolutionary algorithm capable of producing a large archive of diverse, high-performing solutions in a single run. It works by discretizing a continuous feature space into unique regions according to the desired discretization per dimension. While simple, this algorithm has a main drawback: it cannot scale to high-dimensional feature spaces since the number of regions increase exponentially with the number of dimensions. In this paper, we address this limitation by introducing a simple extension of MAP-Elites that has a constant, pre-defined number of regions irrespective of the dimensionality of the feature space. Our main insight is that methods from computational geometry could partition a high-dimensional space into well-spread geometric regions. In particular, our algorithm uses a centroidal Voronoi tessellation (CVT) to divide the feature space into a desired number of regions; it then places every generated individual in its closest region, replacing a less fit one if the region is already occupied. We demonstrate the effectiveness of the new "CVT-MAP-Elites" algorithm in high-dimensional feature spaces through comparisons against MAP-Elites in maze navigation and hexapod locomotion tasks

Probabilistic and parallel algorithms for centroidal Voronoi tessellations with application to meshless computing and numerical analysis on surfaces

Centroidal Voronoi tessellations (CVT) are Voronoi tessellations of a region such that the generating points of the tessellations are also the centroids of the corresponding Voronoi regions. Such tessellations are of use in very diverse applications, including data compression, clustering analysis, cell biology, territorial behavior of animals, optimal allocation of resources, and grid generation. A detailed review is given in chapter 1. In chapter 2, some probabilistic methods for determining centroidal Voronoi tessellations and their parallel implementation on distributed memory systems are presented. The results of computational experiments performed on a CRAY T3E-600 system are given for each algorithm. These demonstrate the superior sequential and parallel performance of a new algorithm we introduce. Then, new algorithms are presented in chapter 3 for the determination of point sets and associated support regions that can then be used in meshless computing methods. The algorithms are probabilistic in nature so that they are totally meshfree, i.e., they do not require, at any stage, the use of any coarse or fine boundary conforming or superimposed meshes. Computational examples are provided that show, for both uniform and non-uniform point distributions that the algorithms result in high-quality point sets and high-quality support regions. The extensions of centroidal Voronoi tessellations to general spaces and sets are also available. For example, tessellations of surfaces in a Euclidean space may be considered. In chapter 4, a precise definition of such constrained centroidal Voronoi tessellations (CCVT\u27s) is given and a number of their properties are derived, including their characterization as minimizers of a kind of energy. Deterministic and probabilistic algorithms for the construction of CCVT\u27s are presented and some analytical results for one of the algorithms are given. Some computational examples are provided which serve to illustrate the high quality of CCVT point sets. CCVT point sets are also applied to polynomial interpolation and numerical integration on the sphere. Finally, some conclusions are given in chapter 5

Decentralized Resource Allocation through Constrained Centroidal Voronoi Tessellations

The advancements in the fields of microelectronics facilitate incorporating team elements like coordination into engineering systems through advanced computing power. Such incorporation is useful since many engineering systems can be characterized as a collection of interacting subsystems each having access to local information, making local decisions, interacting with neighbors, and seeking to optimize local objectives that may well conflict with other subsystems, while also trying to optimize certain global objective. In this dissertation, we take advantage of such technological advancements to explore the problem of resource allocation through different aspects of the decentralized architecture like information structure in a team. Introduced in 1968 as a toy example in the field of team decision theory to demonstrate the significance of information structure within a team, the Witsenhausen counterexample remained unsolved until the analytical person-by-person optimal solution was developed within the past decade. We develop a numerical method to implement the optimal laws and show that our laws coincide with the optimal affine laws. For the region where the optimal laws are non-linear, we show that our laws result in the lowest costs when compared with previously reported costs. Recognizing that, in the framework of team decision theory, the difficulties arising from the non-classical information structure within a team currently limit its applicability in real-world applications, we move on to investigating Centroidal Voronoi Tessellations (CVTs) to solve the resource allocation problem. In one-dimensional spaces, a line communication network is sufficient to obtain CVTs in a decentralized manner, while being scalable to any number of agents in the team. We first solve the static resource allocation problem where the amount of resource is fixed. Using such static allocation solution as an initialization step, we solve the dynamic resource allocation problem in a truly decentralized manner. Furthermore, we allow for flexibility in agents\u27 embedding their local preferences through what we call a civility model. We end the dissertation by revisiting the application of Demand-response in smart grids and demonstrate the developed decentralized dynamic resource allocation method to solve the problem of power allocation in a group of building loads

On Volumetric Shape Reconstruction from Implicit Forms

International audienceIn this paper we report on the evaluation of volumetric shape reconstruction methods that consider as input implicit forms in 3D. Many visual applications build implicit representations of shapes that are converted into explicit shape representations using geometric tools such as the Marching Cubes algorithm. This is the case with image based reconstructions that produce point clouds from which implicit functions are computed, with for instance a Poisson reconstruction approach. While the Marching Cubes method is a versatile solution with proven efficiency, alternative solutions exist with different and complementary properties that are of interest for shape modeling. In this paper, we propose a novel strategy that builds on Centroidal Voronoi Tessellations (CVTs). These tessellations provide volumetric and surface representations with strong regularities in addition to provably more accurate approximations of the implicit forms considered. In order to compare the existing strategies, we present an extensive evaluation that analyzes various properties of the main strategies for implicit to explicit volumetric conversions: Marching cubes, Delaunay refinement and CVTs, including accuracy and shape quality of the resulting shape mesh

Adaptive meshing for finite element analysis of heterogeneous materials

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