Photometric stereo (PS) techniques nowadays remain constrained to an ideal laboratory setup where modeling and calibration of lighting is amenable. To eliminate such restrictions, we propose an efficient principled variational approach to uncalibrated PS under general illumination. To this end, the Lambertian reflectance model is approximated through a spherical harmonic expansion, which preserves the spatial invariance of the lighting. The joint recovery of shape, reflectance and illumination is then formulated as a single variational problem. There the shape estimation is carried out directly in terms of the underlying perspective depth map, thus implicitly ensuring integrability and bypassing the need for a subsequent normal integration. To tackle the resulting nonconvex problem numerically, we undertake a two-phase procedure to initialize a balloon-like perspective depth map, followed by a "lagged" block coordinate descent scheme. The experiments validate efficiency and robustness of this approach. Across a variety of evaluations, we are able to reduce the mean angular error consistently by a factor of 2-3 compared to the state-of-the-art. * Authors contributed equally. 1 https://github.com/zhenzhangye/general_ups
Abstract-Dealing with the unknown future behavior of other traffic participants is one of the main challenges when generating safe trajectories for autonomous vehicles. When the ego vehicle (i.e., the vehicle to be controlled) follows a given trajectory, an emergency maneuver should be kept available for all times in order to avoid collisions. However, generating an emergency maneuver for each time step is computationally expensive and often not required. In this paper, we propose an algorithm for determining the maximum time horizon under which the ego vehicle can safely follow a given trajectory. First, an upper and a lower bound of this time horizon are computed. Then, binary search is used to find the maximum time horizon for which safety is still guaranteed. Our algorithm reduces the frequency of generating emergency maneuvers while still guaranteeing collision-free trajectories. The approach is tested on real traffic data, and it is shown that our algorithm indeed reduces the frequency of generating emergency maneuvers compared to previous work.
Graph matching aims to establish correspondences between vertices of graphs such that both the node and edge attributes agree. Various learning-based methods were recently proposed for finding correspondences between image key points based on deep graph matching formulations. While these approaches mainly focus on learning node and edge attributes, they completely ignore the 3D geometry of the underlying 3D objects depicted in the 2D images. We fill this gap by proposing a trainable framework that takes advantage of graph neural networks for learning a deformable 3D geometry model from inhomogeneous image collections, i.e. a set of images that depict different instances of objects from the same category. Experimentally we demonstrate that our method outperforms recent learning-based approaches for graph matching considering both accuracy and cycle-consistency error, while we in addition obtain the underlying 3D geometry of the objects depicted in the 2D images.
Structured convex optimization on weighted graphs finds numerous applications in machine learning and computer vision. In this work, we propose a novel adaptive preconditioning strategy for proximal algorithms on this problem class. Our preconditioner is driven by a sharp analysis of the local linear convergence rate depending on the "active set" at the current iterate. We show that nested-forest decomposition of the inactive edges yields a guaranteed local linear convergence rate. Further, we propose a practical greedy heuristic which realizes such nested decompositions and show in several numerical experiments that our reconditioning strategy, when applied to proximal gradient or primal-dual hybrid gradient algorithm, achieves competitive performances. Our results suggest that local convergence analysis can serve as a guideline for selecting variable metrics in proximal algorithms.
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