PhasePack: A Phase Retrieval Library

Phase retrieval deals with the estimation of complex-valued signals solely from the magnitudes of linear measurements. While there has been a recent explosion in the development of phase retrieval algorithms, the lack of a common interface has made it difficult to compare new methods against the state-of-the-art. The purpose of PhasePack is to create a common software interface for a wide range of phase retrieval algorithms and to provide a common testbed using both synthetic data and empirical imaging datasets. PhasePack is able to benchmark a large number of recent phase retrieval methods against one another to generate comparisons using a range of different performance metrics. The software package handles single method testing as well as multiple method comparisons. The algorithm implementations in PhasePack differ slightly from their original descriptions in the literature in order to achieve faster speed and improved robustness. In particular, PhasePack uses adaptive stepsizes, line-search methods, and fast eigensolvers to speed up and automate convergence

Discontinuous Deformation Gradients in Plane Finite Elastostatics of Incompressible Materials. (I) General Considerations. (II) An Example

This investigation is concerned with the possibility of the change of type of the differential equations governing finite plane elastostatics for incompressible elastic materials, and the related is sue of the existence of equilibrium fields with discontinuous deformation gradients. Explicit necessary and sufficient conditions on the deformation invariants and the material for the ellipticity of the plane displacement equations of equilibrium are established. The issue of the existence, locally, of "elastostatic shocks" -- elastostatic fields with continuous displacements and discontinuous deformation gradients -- is then investigated. It is shown that an elastostatic shock exists only if the governing field equations suffer a loss of ellipticity at some deformation. Conversely, if the governing field equations have lost ellipticity at a given deformation at some point, an elastostatic shock can exist, locally, at that point. The results obtained are valid for an arbitrary homogeneous, isotropic, incompressible, elastic material. In order to illustrate the occurrence of elastostatic shocks in a physical problem, a specific displacement boundary value problem is studied. Here, a particular class of isotropic, incompressible, elastic materials which allow for a loss of ellipticity is considered. It is shown that no solution which is smooth in the classical sense exists to this problem for certain ranges of the applied loading. Next, we admit solutions involving elastostatic shocks into the discussion and find that the problem may then be solved completely. When this is done, however, there results a lack of uniqueness of solutions to the boundary value problem. In order to resolve this non-uniqueness, dissipativity and stability are investigated.</p

GANav: Group-wise Attention Network for Classifying Navigable Regions in Unstructured Outdoor Environments

We present a new learning-based method for identifying safe and navigable regions in off-road terrains and unstructured environments from RGB images. Our approach consists of classifying groups of terrain classes based on their navigability levels using coarse-grained semantic segmentation. We propose a bottleneck transformer-based deep neural network architecture that uses a novel group-wise attention mechanism to distinguish between navigability levels of different terrains.Our group-wise attention heads enable the network to explicitly focus on the different groups and improve the accuracy. In addition, we propose a dynamic weighted cross entropy loss function to handle the long-tailed nature of the dataset. We show through extensive evaluations on the RUGD and RELLIS-3D datasets that our learning algorithm improves the accuracy of visual perception in off-road terrains for navigation. We compare our approach with prior work on these datasets and achieve an improvement over the state-of-the-art mIoU by 6.74-39.1% on RUGD and 3.82-10.64% on RELLIS-3D