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

Deep metric learning to rank

We propose a novel deep metric learning method by revisiting the learning to rank approach. Our method, named FastAP, optimizes the rank-based Average Precision measure, using an approximation derived from distance quantization. FastAP has a low complexity compared to existing methods, and is tailored for stochastic gradient descent. To fully exploit the benefits of the ranking formulation, we also propose a new minibatch sampling scheme, as well as a simple heuristic to enable large-batch training. On three few-shot image retrieval datasets, FastAP consistently outperforms competing methods, which often involve complex optimization heuristics or costly model ensembles.Accepted manuscrip

Stability analysis of the five-dimensional energy demand-supply system

summary:In this paper, a five-dimensional energy demand-supply system has been considered. On the one hand, we analyze the stability for all of the equilibrium points of the system. For each of equilibrium point, by analyzing the characteristic equation, we show the conditions for the stability or instability using Routh-Hurwitz criterion. Then numerical simulations have been given to illustrate all of cases for the theoretical results. On the other hand, by introducing the phenomenon of time delay, we establish the five-dimensional energy demand-supply model with time delay. Then we analyze the stability of the equilibrium points for the delayed system by the stability switching theory. Especially, Hopf bifurcation has been considered by showing the explicit formulae using the central manifold theorem and Poincare normalization method. For each cases of the theorems including the Hopf bifurcation, numerical simulations have been given to illustrate the effectiveness of the main results

Observability Robustness under Sensor Failures: Complexities and algorithms

The problem of determining the minimal number of sensors whose removal destroys observability of a linear time invariant system is studied. This problem is closely related to the ability of unique state reconstruction of a system under adversarial sensor attacks, and the dual of it is the inverse to the recently studied minimal controllability problems. It is proven that this problem is NP-hard both for a numerically specific system, and for a generic system whose nonzero entries of its system matrices are unknown but can take values freely (also called structured system). Two polynomial time algorithms are provided to solve this problem, respectively, on a numerical system with bounded maximum geometric multiplicities, and on a structured system with bounded matching deficiencies, which are often met by practical engineering systems. The proposed algorithms can be easily extended to the case where each sensor has a non-negative cost. Numerical experiments show that the structured system based algorithm could be alternative when the exact values of system matrices are not accessible.Comment: 8 pages, 2 figures, add some materials, fix some type error