Projective Manifold Gradient Layer for Deep Rotation Regression

Regressing rotations on SO(3) manifold using deep neural networks is an important yet unsolved problem. The gap between Euclidean network output space and the non-Euclidean SO(3) manifold imposes a severe challenge for neural network learning in both forward and backward passes. While several works have proposed different regression-friendly rotation representations, very few works have been devoted to improving the gradient backpropagating in the backward pass. In this paper, we propose a manifold-aware gradient that directly backpropagates into deep network weights. Leveraging the Riemannian gradient and a novel projective gradient, our proposed regularized projective manifold gradient (RPMG) helps networks achieve new state-of-the-art performance in a variety of rotation estimation tasks. The proposed gradient layer can also be applied to other smooth manifolds such as the unit sphere.

HuMoR: 3D Human Motion Model for Robust Pose Estimation

We introduce HuMoR: a 3D Human Motion Model for Robust Estimation of temporal pose and shape. Though substantial progress has been made in estimating 3D human motion and shape from dynamic observations, recovering plausible pose sequences in the presence of noise and occlusions remains a challenge. For this purpose, we propose an expressive generative model in the form of a conditional variational autoencoder, which learns a distribution of the change in pose at each step of a motion sequence. Furthermore, we introduce a flexible optimization-based approach that leverages HuMoR as a motion prior to robustly estimate plausible pose and shape from ambiguous observations. Through extensive evaluations, we demonstrate that our model generalizes to diverse motions and body shapes after training on a large motion capture dataset, and enables motion reconstruction from multiple input modalities including 3D keypoints and RGB(-D) videos.

Weakly Supervised Learning of Rigid 3D Scene Flow

We propose a data-driven scene flow estimation algorithm exploiting the observation that many 3D scenes can be explained by a collection of agents moving as rigid bodies. At the core of our method lies a deep architecture able to reason at the \textbf{object-level} by considering 3D scene flow in conjunction with other 3D tasks. This object level abstraction, enables us to relax the requirement for dense scene flow supervision with simpler binary background segmentation mask and ego-motion annotations. Our mild supervision requirements make our method well suited for recently released massive data collections for autonomous driving, which do not contain dense scene flow annotations. As output, our model provides low-level cues like pointwise flow and higher-level cues such as holistic scene understanding at the level of rigid objects. We further propose a test-time optimization refining the predicted rigid scene flow. We showcase the effectiveness and generalization capacity of our method on four different autonomous driving datasets. We release our source code and pre-trained models under \url{github.com/zgojcic/Rigid3DSceneFlow}.

Quantum Permutation Synchronization

We present QuantumSync, the first quantum algorithm for solving a synchronization problem in the context of computer vision. In particular, we focus on permutation synchronization which involves solving a non-convex optimization problem in discrete variables. We start by formulating synchronization into a quadratic unconstrained binary optimization problem (QUBO). While such formulation respects the binary nature of the problem, ensuring that the result is a set of permutations requires extra care. Hence, we: (i) show how to insert permutation constraints into a QUBO problem and (ii) solve the constrained QUBO problem on the current generation of the adiabatic quantum computers D-Wave. Thanks to the quantum annealing, we guarantee global optimality with high probability while sampling the energy landscape to yield confidence estimates. Our proof-of-concepts realization on the adiabatic D-Wave computer demonstrates that quantum machines offer a promising way to solve the prevalent yet difficult synchronization problems.

MultiBodySync: Multi-Body Segmentation and Motion Estimation via 3D Scan Synchronization

We present MultiBodySync, a novel, end-to-end trainable multi-body motion segmentation and rigid registration framework for multiple input 3D point clouds. The two non-trivial challenges posed by this multi-scan multibody setting that we investigate are: (i) guaranteeing correspondence and segmentation consistency across multiple input point clouds capturing different spatial arrangements of bodies or body parts; and (ii) obtaining robust motion-based rigid body segmentation applicable to novel object categories. We propose an approach to address these issues that incorporates spectral synchronization into an iterative deep declarative network, so as to simultaneously recover consistent correspondences as well as motion segmentation. At the same time, by explicitly disentangling the correspondence and motion segmentation estimation modules, we achieve strong generalizability across different object categories. Our extensive evaluations demonstrate that our method is effective on various datasets ranging from rigid parts in articulated objects to individually moving objects in a 3D scene, be it single-view or full point clouds.

Deep Bingham Networks: Dealing with Uncertainty and Ambiguity in Pose Estimation

In this work, we introduce Deep Bingham Networks (DBN), a generic framework that can naturally handle pose-related uncertainties and ambiguities arising in almost all real life applications concerning 3D data. While existing works strive to find a single solution to the pose estimation problem, we make peace with the ambiguities causing high uncertainty around which solutions to identify as the best. Instead, we report a family of poses which capture the nature of the solution space. DBN extends the state of the art direct pose regression networks by (i) a multi-hypotheses prediction head which can yield different distribution modes; and (ii) novel loss functions that benefit from Bingham distributions on rotations. This way, DBN can work both in unambiguous cases providing uncertainty information, and in ambiguous scenes where an uncertainty per mode is desired. On a technical front, our network regresses continuous Bingham mixture models and is applicable to both 2D data such as images and to 3D data such as point clouds. We proposed new training strategies so as to avoid mode or posterior collapse during training and to improve numerical stability. Our methods are thoroughly tested on two different applications exploiting two different modalities: (i) 6D camera relocalization from images; and (ii) object pose estimation from 3D point clouds, demonstrating decent advantages over the state of the art. For the former we contributed our own dataset composed of five indoor scenes where it is unavoidable to capture images corresponding to views that are hard to uniquely identify. For the latter we achieve the top results especially for symmetric objects of ModelNet dataset.

CaSPR: Learning Canonical Spatiotemporal Point Cloud Representations

We propose CaSPR, a method to learn object-centric canonical spatiotemporal point cloud representations of dynamically moving or evolving objects. Our goal is to enable information aggregation over time and the interrogation of object state at any spatiotemporal neighborhood in the past, observed or not. Different from previous work, CaSPR learns representations that support spacetime continuity, are robust to variable and irregularly spacetime-sampled point clouds, and generalize to unseen object instances. Our approach divides the problem into two subtasks. First, we explicitly encode time by mapping an input point cloud sequence to a spatiotemporally-canonicalized object space. We then leverage this canonicalization to learn a spatiotemporal latent representation using neural ordinary differential equations and a generative model of dynamically evolving shapes using continuous normalizing flows. We demonstrate the effectiveness of our method on several applications including shape reconstruction, camera pose estimation, continuous spatiotemporal sequence reconstruction, and correspondence estimation from irregularly or intermittently sampled observations.

6D Camera Relocalization in Ambiguous Scenes via Continuous Multimodal Inference

We present a multimodal camera relocalization framework that captures ambiguities and uncertainties with continuous mixture models defined on the manifold of camera poses. In highly ambiguous environments, which can easily arise due to symmetries and repetitive structures in the scene, computing one plausible solution (what most state-of-the-art methods currently regress) may not be sufficient. Instead we predict multiple camera pose hypotheses as well as the respective uncertainty for each prediction. Towards this aim, we use Bingham distributions, to model the orientation of the camera pose, and a multivariate Gaussian to model the position, with an end-to-end deep neural network. By incorporating a Winner-Takes-All training scheme, we finally obtain a mixture model that is well suited for explaining ambiguities in the scene, yet does not suffer from mode collapse, a common problem with mixture density networks. We introduce a new dataset specifically designed to foster camera localization research in ambiguous environments and exhaustively evaluate our method on synthetic as well as real data on both ambiguous scenes and on non-ambiguous benchmark datasets. We plan to release our code and dataset under $\href{https://multimodal3dvision.github.io}{multimodal3dvision.github.io}$.

Deformation-Aware 3D Model Embedding and Retrieval

We introduce a new problem of $\textit{retrieving}$ 3D models that are not just similar but are deformable to a given query shape. We then present a novel deep $\textit{deformation-aware}$ embedding to solve this retrieval task. 3D model retrieval is a fundamental operation for recovering a clean and complete 3D model from a noisy and partial 3D scan. However, given a finite collection of 3D shapes, even the closest model to a query may not be a satisfactory reconstruction. This motivates us to apply 3D model deformation techniques to adapt the retrieved model so as to better fit the query. Yet, certain restrictions are enforced in most 3D deformation techniques to preserve important features of the original model that prevent a perfect fitting of the deformed model to the query. This gap between the deformed model and the query induces $\textit{asymmetric}$ relationships among the models, which cannot be dealt with typical metric learning techniques. Thus, to retrieve the best models for fitting, we propose a novel deep embedding approach that learns the asymmetric relationships by leveraging location-dependent egocentric distance fields. We also propose two strategies for training the embedding network. We demonstrate that both of these approaches outperform other baselines in both synthetic evaluations and real 3D object reconstruction.

Synchronizing Probability Measures on Rotations via Optimal Transport

We introduce a new paradigm, $\textit{measure synchronization}$, for synchronizing graphs with measure-valued edges. We formulate this problem as maximization of the cycle-consistency in the space of probability measures over relative rotations. In particular, we aim at estimating marginal distributions of absolute orientations by synchronizing the $\textit{conditional}$ ones, which are defined on the Riemannian manifold of quaternions. Such graph optimization on distributions-on-manifolds enables a natural treatment of multimodal hypotheses, ambiguities and uncertainties arising in many computer vision applications such as SLAM, SfM, and object pose estimation. We first formally define the problem as a generalization of the classical rotation graph synchronization, where in our case the vertices denote probability measures over rotations. We then measure the quality of the synchronization by using Sinkhorn divergences, which reduces to other popular metrics such as Wasserstein distance or the maximum mean discrepancy as limit cases. We propose a nonparametric Riemannian particle optimization approach to solve the problem. Even though the problem is non-convex, by drawing a connection to the recently proposed sparse optimization methods, we show that the proposed algorithm converges to the global optimum in a special case of the problem under certain conditions. Our qualitative and quantitative experiments show the validity of our approach and we bring in new perspectives to the study of synchronization.