Continuous Viewpoint Planning in Conjunction with Dynamic Exploration for Active Object Recognition

Active object recognition (AOR) aims at collecting additional information to improve recognition performance by purposefully adjusting the viewpoint of an agent. How to determine the next best viewpoint of the agent, i.e., viewpoint planning (VP), is a research focus. Most existing VP methods perform viewpoint exploration in the discrete viewpoint space, which have to sample viewpoint space and may bring in significant quantization error. To address this challenge, a continuous VP approach for AOR based on reinforcement learning is proposed. Specifically, we use two separate neural networks to model the VP policy as a parameterized Gaussian distribution and resort the proximal policy optimization framework to learn the policy. Furthermore, an adaptive entropy regularization based dynamic exploration scheme is presented to automatically adjust the viewpoint exploration ability in the learning process. To the end, experimental results on the public dataset GERMS well demonstrate the superiority of our proposed VP method.     

Least Wasserstein distance between disjoint shapes with perimeter regularization

We prove the existence of global minimizers to the double minimization problem where $P(E)$ denotes the perimeter of the set E, $W_p$ is the p-Wasserstein distance between Borel probability measures, and $\lambda >0$ is arbitrary. The result holds in all space dimensions, for all $p\in [1,\infty )$, and for all positive λ. This answers a question of Buttazzo, Carlier, and Laborde.     

An inverse problem of identifying the time-dependent potential in a fourth-order pseudo-parabolic equation from additional condition

The aim of this work is to identify numerically, for the first time, the time-dependent potential coefficient in a fourth-order pseudo-parabolic equation with nonlocal initial data, nonlocal boundary conditions, and the boundary data as overdetermination condition. This problem emerges significantly in the modeling of various phenomena in physics and engineering. From literature we already know that this inverse problem has a unique solution. However, the problem is still ill-posed by being unstable to noise in the input data. For the numerical realization, we apply the quintic B-spline (QB-spline) collocation method for discretizing the pseudo-parabolic problem and the Tikhonov regularization for finding a stable and accurate solution. The resulting nonlinear minimization problem is solved using the MATLAB subroutine lsqnonlin. Moreover, the von Neumann stability analysis is also discussed.