Variational Autoencoders for Deforming 3D Mesh Models

3D geometric contents are becoming increasingly popular. In this paper, we study the problem of analyzing deforming 3D meshes using deep neural networks. Deforming 3D meshes are flexible to represent 3D animation sequences as well as collections of objects of the same category, allowing diverse shapes with large-scale non-linear deformations. We propose a novel framework which we call mesh variational autoencoders (mesh VAE), to explore the probabilistic latent space of 3D surfaces. The framework is easy to train, and requires very few training examples. We also propose an extended model which allows flexibly adjusting the significance of different latent variables by altering the prior distribution. Extensive experiments demonstrate that our general framework is able to learn a reasonable representation for a collection of deformable shapes, and produce competitive results for a variety of applications, including shape generation, shape interpolation, shape space embedding and shape exploration, outperforming state-of-the-art methods.Comment: CVPR 201

Comparisons of elastic and creep deformation linearly dependent upon stress

The theory of linear elasticity provides a complete description of reversible deformation under small stresses for both isotropic and anisotropic solids. At elevated temperatures, creep deformation sometimes occurs at a rate that is linearly dependent upon stress. When this form of creep arises from vacancy movement, there is possibility of anisotropic behaviour through the orientational dependence of average grain dimensions. This indicates that the elasticity theory may be utilised to provide comparable descriptions of such creep deformation, with creep strain built up of equal increments of strain occurring in equal intervals of time. The extent of this analogy is explored with the conclusion that its usefulness is substantial when grains are small in relation to geometrical features of the component but it is no longer applicable when the grains approach the size of these features and where there is a high gradient of stress

Synthetic 3D Pap smear nucleus generation

Gómez Aguilar, S. (2010). Synthetic 3D Pap smear nucleus generation. http://hdl.handle.net/10251/10215.Archivo delegad

Subjectively interpreted shape dimensions as privileged and orthogonal axes in mental shape space

The shape of an object is fundamental in object recognition but it is still an open issue to what extent shape differences are perceived analytically (i.e., by the dimensional structure of the shapes) or holistically (i.e., by the overall similarity of the shapes). The dimensional structure of a stimulus is available in a primary stage of processing for separable dimensions, although it can also be derived cognitively from a perceived stimulus consisting of integral dimensions. Contrary to most experimental paradigms, the present study asked participants explicitly to analyze shapes according to two dimensions. The dimensions of interest were aspect ratio and medial axis curvature, and a new procedure was used to measure the participants' interpretation of both dimensions (Part I, Experiment 1). The subjectively interpreted shape dimensions showed specific characteristics supporting the conclusion that they also constitute perceptual dimensions with objective behavioral characteristics (Part II): (1) the dimensions did not correlate in overall similarity measures (Experiment 2), (2) they were more separable in a speeded categorization task (Experiment 3), and (3) they were invariant across different complex 2-D shapes (Experiment 4). The implications of these findings for shape-based object processing are discussed

Quantum Mechanics for the Swimming of Micro-Organism in Two Dimensions

In two dimensional fluid, there are only two classes of swimming ways of micro-organisms, {\it i.e.}, ciliated and flagellated motions. Towards understanding of this fact, we analyze the swimming problem by using $w_{1+\infty}$ and/or $W_{1+\infty}$ algebras. In the study of the relationship between these two algebras, there appear the wave functions expressing the shape of micro-organisms. In order to construct the well-defined quantum mechanics based on $W_{1+\infty}$ algebra and the wave functions, essentially only two different kinds of the definitions are allowed on the hermitian conjugate and the inner products of the wave functions. These two definitions are related with the shapes of ciliates and flagellates. The formulation proposed in this paper using $W_{1+\infty}$ algebra and the wave functions is the quantum mechanics of the fluid dynamics where the stream function plays the role of the Hamiltonian. We also consider the area-preserving algebras which arise in the swimming problem of micro-organisms in the two dimensional fluid. These algebras are larger than the usual $w_{1+\infty}$ and $W_{1+\infty}$ algebras. We give a free field representation of this extended $W_{1+\infty}$ algebra.Comment: OCHA-PP-48, NDA-FP-16, Latex file, 15p