When we physically interact with our environment using our hands, we touch objects and force them to move: contact and motion are defining properties of manipulation. In this paper, we present an active, bottom-up method for the detection of actor-object contacts and the extraction of moved objects and their motions in RGBD videos of manipulation actions. At the core of our approach lies non-rigid registration: we continuously warp a point cloud model of the observed scene to the current video frame, generating a set of dense 3D point trajectories. Under loose assumptions, we employ simple point cloud segmentation techniques to extract the actor and subsequently detect actor-environment contacts based on the estimated trajectories. For each such interaction, using the detected contact as an attention mechanism, we obtain an initial motion segment for the manipulated object by clustering trajectories in the contact area vicinity and then we jointly refine the object segment and estimate its 6DOF pose in all observed frames. Because of its generality and the fundamental, yet highly informative, nature of its outputs, our approach is applicable to a wide range of perception and planning tasks. We qualitatively evaluate our method on a number of input sequences and present a comprehensive robot imitation learning example, in which we demonstrate the crucial role of our outputs in developing action representations plans from observation.
The non-rigid alignment of 3D point sets can be viewed as a generalization of scene flow, in the sense that the estimated motion field is supported by a 3D point cloud: the goal is to estimate point-wise transformations (usually rigid) that best align the point set to the target geometry under certain global prior constraints (e.g., as-rigid-as-possible' @cite_48 ). The warp field estimation is performed either by iterating between correspondence estimation and motion optimization @cite_45 @cite_36 @cite_30 @cite_40 , or in a correspondence-free fashion, by aligning volumetric SDFs (Signed Distance Fields) @cite_28 . For this work, and due to lack of publicly available solutions, we have implemented a non-rigid registration algorithm similar to @cite_30 and @cite_40 (Section ) and released it as part of our cilantro @cite_26 library.
@cite_30 @cite_26 @cite_36 @cite_48 @cite_28 @cite_40 @cite_45
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In this paper, we cast the problem of point cloud matching as a shape matching problem by transforming each of the given point clouds into a shape representation called the Schrodinger distance transform (SDT) representation. This is achieved by solving a static Schrodinger equation instead of the corresponding static Hamilton-Jacobi equation in this setting. The SDT representation is an analytic expression and following the theoretical physics literature, can be normalized to have unit 2 norm -- making it a square-root density, which is identified with a point on a unit Hilbert sphere, whose intrinsic geometry is fully known. The Fisher-Rao metric, a natural metric for the space of densities leads to analytic expressions for the geodesic distance between points on this sphere. In this paper, we use the well known Riemannian framework never before used for point cloud matching, and present a novel matching algorithm. We pose point set matching under rigid and non-rigid transformations in this framework and solve for the transformations using standard nonlinear optimization techniques. Finally, to evaluate the performance of our algorithm -- dubbed SDTM -- we present several synthetic and real data examples along with extensive comparisons to state-of-the-art techniques. The experiments show that our algorithm outperforms state-of the-art point set registration algorithms on many quantitative metrics. We introduce a geometry-driven approach for real-time 3D reconstruction of deforming surfaces from a single RGB-D stream without any templates or shape priors. To this end, we tackle the problem of non-rigid registration by level set evolution without explicit correspondence search. Given a pair of signed distance fields (SDFs) representing the shapes of interest, we estimate a dense deformation field that aligns them. It is defined as a displacement vector field of the same resolution as the SDFs and is determined iteratively via variational minimization. To ensure it generates plausible shapes, we propose a novel regularizer that imposes local rigidity by requiring the deformation to be a smooth and approximately Killing vector field, i.e. generating nearly isometric motions. Moreover, we enforce that the level set property of unity gradient magnitude is preserved over iterations. As a result, KillingFusion reliably reconstructs objects that are undergoing topological changes and fast inter-frame motion. In addition to incrementally building a model from scratch, our system can also deform complete surfaces. We demonstrate these capabilities on several public datasets and introduce our own sequences that permit both qualitative and quantitative comparison to related approaches. This paper presents a novel solution for flow-based tracking and 3D reconstruction of deforming objects in monocular image sequences. A non-rigid 3D object undergoing rotation and deformation can be effectively approximated using a linear combination of 3D basis shapes. This puts a bound on the rank of the tracking matrix. The rank constraint is used to achieve robust and precise low-level optical flow estimation without prior knowledge of the 3D shape of the object. The bound on the rank is also exploited to handle occlusion at the tracking level leading to the possibility of recovering the complete trajectories of occluded disoccluded points. Following the same low-rank principle, the resulting flow matrix can be factored to get the 3D pose, configuration coefficients, and 3D basis shapes. The flow matrix is factored in an iterative manner, looping between solving for pose, configuration, and basis shapes. The flow-based tracking is applied to several video sequences and provides the input to the 3D non-rigid reconstruction task. Additional results on synthetic data and comparisons to ground truth complete the experiments. We introduce Coherent Point Drift (CPD), a novel probabilistic method for non-rigid registration of point sets. The registration is treated as a Maximum Likelihood (ML) estimation problem with motion coherence constraint over the velocity field such that one point set moves coherently to align with the second set. We formulate the motion coherence constraint and derive a solution of regularized ML estimation through the variational approach, which leads to an elegant kernel form. We also derive the EM algorithm for the penalized ML optimization with deterministic annealing. The CPD method simultaneously finds both the non-rigid transformation and the correspondence between two point sets without making any prior assumption of the transformation model except that of motion coherence. This method can estimate complex non-linear non-rigid transformations, and is shown to be accurate on 2D and 3D examples and robust in the presence of outliers and missing points.