Defining the Pose of any 3D Rigid Object and an Associated Distance

The pose of a rigid object is usually regarded as a rigid transformation, described by a translation and a rotation. However, equating the pose space with the space of rigid transformations is in general abusive, as it does not account for objects with proper symmetries -- which are common among man-made objects.In this article, we define pose as a distinguishable static state of an object, and equate a pose with a set of rigid transformations. Based solely on geometric considerations, we propose a frame-invariant metric on the space of possible poses, valid for any physical rigid object, and requiring no arbitrary tuning. This distance can be evaluated efficiently using a representation of poses within an Euclidean space of at most 12 dimensions depending on the object's symmetries. This makes it possible to efficiently perform neighborhood queries such as radius searches or k-nearest neighbor searches within a large set of poses using off-the-shelf methods. Pose averaging considering this metric can similarly be performed easily, using a projection function from the Euclidean space onto the pose space. The practical value of those theoretical developments is illustrated with an application of pose estimation of instances of a 3D rigid object given an input depth map, via a Mean Shift procedure

Image collection pop-up: 3D reconstruction and clustering of rigid and non-rigid categories

© 20xx IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.This paper introduces an approach to simultaneously estimate 3D shape, camera pose, and object and type of deformation clustering, from partial 2D annotations in a multi-instance collection of images. Furthermore, we can indistinctly process rigid and non-rigid categories. This advances existing work, which only addresses the problem for one single object or, if multiple objects are considered, they are assumed to be clustered a priori. To handle this broader version of the problem, we model object deformation using a formulation based on multiple unions of subspaces, able to span from small rigid motion to complex deformations. The parameters of this model are learned via Augmented Lagrange Multipliers, in a completely unsupervised manner that does not require any training data at all. Extensive validation is provided in a wide variety of synthetic and real scenarios, including rigid and non-rigid categories with small and large deformations. In all cases our approach outperforms state-of-the-art in terms of 3D reconstruction accuracy, while also providing clustering results that allow segmenting the images into object instances and their associated type of deformation (or action the object is performing).Postprint (author's final draft

Articulation-aware Canonical Surface Mapping

We tackle the tasks of: 1) predicting a Canonical Surface Mapping (CSM) that indicates the mapping from 2D pixels to corresponding points on a canonical template shape, and 2) inferring the articulation and pose of the template corresponding to the input image. While previous approaches rely on keypoint supervision for learning, we present an approach that can learn without such annotations. Our key insight is that these tasks are geometrically related, and we can obtain supervisory signal via enforcing consistency among the predictions. We present results across a diverse set of animal object categories, showing that our method can learn articulation and CSM prediction from image collections using only foreground mask labels for training. We empirically show that allowing articulation helps learn more accurate CSM prediction, and that enforcing the consistency with predicted CSM is similarly critical for learning meaningful articulation.Comment: To appear at CVPR 2020, project page https://nileshkulkarni.github.io/acsm

Capturing Hands in Action using Discriminative Salient Points and Physics Simulation

Hand motion capture is a popular research field, recently gaining more attention due to the ubiquity of RGB-D sensors. However, even most recent approaches focus on the case of a single isolated hand. In this work, we focus on hands that interact with other hands or objects and present a framework that successfully captures motion in such interaction scenarios for both rigid and articulated objects. Our framework combines a generative model with discriminatively trained salient points to achieve a low tracking error and with collision detection and physics simulation to achieve physically plausible estimates even in case of occlusions and missing visual data. Since all components are unified in a single objective function which is almost everywhere differentiable, it can be optimized with standard optimization techniques. Our approach works for monocular RGB-D sequences as well as setups with multiple synchronized RGB cameras. For a qualitative and quantitative evaluation, we captured 29 sequences with a large variety of interactions and up to 150 degrees of freedom.Comment: Accepted for publication by the International Journal of Computer Vision (IJCV) on 16.02.2016 (submitted on 17.10.14). A combination into a single framework of an ECCV'12 multicamera-RGB and a monocular-RGBD GCPR'14 hand tracking paper with several extensions, additional experiments and detail

Extrinisic Calibration of a Camera-Arm System Through Rotation Identification

Determining extrinsic calibration parameters is a necessity in any robotic system composed of actuators and cameras. Once a system is outside the lab environment, parameters must be determined without relying on outside artifacts such as calibration targets. We propose a method that relies on structured motion of an observed arm to recover extrinsic calibration parameters. Our method combines known arm kinematics with observations of conics in the image plane to calculate maximum-likelihood estimates for calibration extrinsics. This method is validated in simulation and tested against a real-world model, yielding results consistent with ruler-based estimates. Our method shows promise for estimating the pose of a camera relative to an articulated arm's end effector without requiring tedious measurements or external artifacts. Index Terms: robotics, hand-eye problem, self-calibration, structure from motio

Real-time content-aware texturing for deformable surfaces

Animation of models often introduces distortions to their parameterisation, as these are typically optimised for a single frame. The net effect is that under deformation, the mapped features, i.e. UV texture maps, bump maps or displacement maps, may appear to stretch or scale in an undesirable way. Ideally, what we would like is for the appearance of such features to remain feasible given any underlying deformation. In this paper we introduce a real-time technique that reduces such distortions based on a distortion control (rigidity) map. In two versions of our proposed technique, the parameter space is warped in either an axis or a non-axis aligned manner based on the minimisation of a non-linear distortion metric. This in turn is solved using a highly optimised hybrid CPU-GPU strategy. The result is real-time dynamic content-aware texturing that reduces distortions in a controlled way. The technique can be applied to reduce distortions in a variety of scenarios, including reusing a low geometric complexity animated sequence with a multitude of detail maps, dynamic procedurally defined features mapped on deformable geometry and animation authoring previews on texture-mapped models. © 2013 ACM

A Combinatorial Solution to Non-Rigid 3D Shape-to-Image Matching

We propose a combinatorial solution for the problem of non-rigidly matching a 3D shape to 3D image data. To this end, we model the shape as a triangular mesh and allow each triangle of this mesh to be rigidly transformed to achieve a suitable matching to the image. By penalising the distance and the relative rotation between neighbouring triangles our matching compromises between image and shape information. In this paper, we resolve two major challenges: Firstly, we address the resulting large and NP-hard combinatorial problem with a suitable graph-theoretic approach. Secondly, we propose an efficient discretisation of the unbounded 6-dimensional Lie group SE(3). To our knowledge this is the first combinatorial formulation for non-rigid 3D shape-to-image matching. In contrast to existing local (gradient descent) optimisation methods, we obtain solutions that do not require a good initialisation and that are within a bound of the optimal solution. We evaluate the proposed method on the two problems of non-rigid 3D shape-to-shape and non-rigid 3D shape-to-image registration and demonstrate that it provides promising results.Comment: 10 pages, 7 figure