Pose synchronization, which seeks to estimate consistent absolute poses among a collection of objects from noisy relative poses estimated between pairs of objects in isolation, is a fundamental problem in many inverse applications. This paper studies an extreme setting where multiple relative pose estimates exist between each object pair, and the majority is incorrect. Popular methods that solve pose synchronization via recovering a low-rank matrix that encodes relative poses in block fail under this extreme setting. We introduce a three-step algorithm for pose synchronization under multiple relative pose inputs. The first step performs diffusion and clustering to compute the candidate poses of the input objects. We present a theoretical result to justify our diffusion formulation. The second step jointly optimizes the best pose for each object. The final step refines the output of the second step. Experimental results on benchmark datasets of structure-from-motion and scan-based geometry reconstruction show that our approach offers more accurate absolute poses than state-of-the-art pose synchronization techniques.

Automated assembly of 3D fractures is essential in orthopedics, archaeology, and our daily life. This paper presents Jigsaw, a novel framework for assembling physically broken 3D objects from multiple pieces. Our approach leverages hierarchical features of global and local geometry to match and align the fracture surfaces. Our framework consists of four components: (1) front-end point feature extractor with attention layers, (2) surface segmentation to separate fracture and original parts, (3) multi-parts matching to find correspondences among fracture surface points, and (4) robust global alignment to recover the global poses of the pieces. We show how to jointly learn segmentation and matching and seamlessly integrate feature matching and rigidity constraints. We evaluate Jigsaw on the Breaking Bad dataset and achieve superior performance compared to state-of-the-art methods. Our method also generalizes well to diverse fracture modes, objects, and unseen instances. To the best of our knowledge, this is the first learning-based method designed specifically for 3D fracture assembly over multiple pieces. Our code is available at https://jiaxin-lu.github.io/Jigsaw/.

Efficient 3D space sampling to represent an underlying 3D object/scene is essential for 3D vision, robotics, and beyond. A standard approach is to explicitly sample a dense collection of views and formulate it as a view selection problem, or, more generally, a set cover problem. In this paper, we introduce a novel approach that avoids dense view sampling. The key idea is to learn a view prediction network and a trainable aggregation module that takes the predicted views as input and outputs an approximation of their generic scores (e.g., surface coverage, viewing angle from surface normals). This methodology allows us to turn the set cover problem (or multi-view representation optimization) into a continuous optimization problem. We then explain how to effectively solve the induced optimization problem using continuation, i.e., aggregating a hierarchy of smoothed scoring modules. Experimental results show that our approach arrives at similar or better solutions with about 10 x speed up in running time, comparing with the standard methods.

In this paper, we introduce the problem of K-best transformation synchronization for the purpose of multiple scan matching. Given noisy pair-wise transformations computed between a subset of depth scan pairs, K-best transformation synchronization seeks to output multiple consistent relative transformations. This problem naturally arises in many geometry reconstruction applications, where the underlying object possesses self-symmetry. For approximately symmetric or even non-symmetric objects, K-best solutions offer an intermediate presentation for recovering the underlying single-best solution. We introduce a simple yet robust iterative algorithm for K-best transformation synchronization, which alternates between transformation propagation and transformation clustering. We present theoretical guarantees on the robust and exact recoveries of our algorithm. Experimental results demonstrate the advantage of our approach against state-of-the-art transformation synchronization techniques on both synthetic and real datasets.