Jinpeng Huang, Gangshan Jing, Kai Zhao, Yongduan Song
原文摘要
Angle rigidity theory provides a theoretical basis for characterizing the geometric shape of graphs embedded in the plane under angle constraints, and establishing global convergence of angle-based network localization algorithms. The related references, however, are largely restricted to graphs generated by triangulation or bilateration ordering, which are sufficient but not necessary for angle rigidity. This paper addresses this challenge by focusing on establishing the equivalence between angle constraints and bearing constraints. The conditions for cycle compatible frameworks (with possibly non-generic configurations) to be angle fixable are provided. Moreover, it is shown for the first time that Laman graphs equivalently characterize minimally globally angle rigid graphs, implying that a Laman graph is the simplest graph that allows a generic embedding in the plane to be uniquely determined by subtended angles. As an application, a distributed algorithm for angle-based sensor network localization is proposed, which guarantees global convergence under a much milder network topology condition than those in the literature.
Generating an articulated object from a single image requires recovering both its appearance and the mechanism governing its parts. A compact encoding of joint attributes does not by itself ensure that reconstruction preserves the resulting motion. We present MoRE, Motion-Regularized Encoding for articulated 3D generation. MoRE represents coordinate-aligned joint lines with axis classification and two axis-orthogonal Plücker moment coefficients, removing the arbitrary choice of an origin along the axis. During representation learning, decoded joint hypotheses are used to move corresponding three-dimensional anchors, and their motions are compared with those of annotated joints. A differentiable expectation over joint types and axis directions couples attribute reconstruction to the motion it induces. An image-conditioned flow learns the resulting functional latents, while a multi-state-adapted Gaussian model supplies appearance. At inference, recovered part assignments and joints articulate a single set of rest-pose Gaussians without regenerating the object for each state. Experiments on PartNet-Mobility and ACD show stronger part-box agreement, articulated-state geometry and visual similarity than the compared baselines, while joint prediction reduces axis, origin and range errors relative to ArtiLatent. Controlled ablations support the joint-line encoding and show that motion supervision reduces anchor-motion error. Code and pretrained checkpoints will be released in the future.