We present nonlinear formulations to Shape-from-Template (SfT) and Non-Rigid Structure-from-Motion (NRSfM) faithfully exploiting the isometric, conformal and equiareal deformation models. Existing work uses relaxations such as inextensibility or requires knowing the optic flow field around the correspondences, an impractical assumption. In contrast, the proposed formulations only require point correspondences and resolve all ambiguities using the notions of maximal depth and maximal isometry heuristics. We propose solution methods using Semi-Definite Programming (SDP) for all formulations. We show that straightforward SDP models conflict with the usual maximal depth heuristic and propose an adapted opposite-depth parameterisation demonstrating a lesser relaxation gap. Experimental results on many real-world benchmark datasets demonstrate superior accuracy over existing methods.

Non-Rigid Structure-from-Motion (NRSfM) reconstructs the time-varying 3D shape of a deforming object from 2D point correspondences in monocular images. Despite promising use-cases such as the grasping of deformable objects and visual navigation in a non-rigid environment, NRSfM has had limited applications in robotics due to a lack of accuracy. To remedy this, we propose a new method which boosts the accuracy of NRSfM using sparse surface normals. Surface normal information is available from many sources, including structured lighting, homography decomposition of infinitesimal planes and shape priors. However, these sources are not always available. We thus propose a widely available new source of surface normals: the specularities. Our first technical contribution is a method which detects specular highlights and reconstructs the surface normals from it. It assumes that the light source is approximately localised, which is widely applicable in robotics applications such as endoscopy. Our second technical contribution is an NRSfM method which exploits a sparse surface normal set. For that, we propose a novel convex formulation and a globally optimal solution method. Experiments on photo-realistic synthetic data and real household and medical data show that the proposed method outperforms existing NRSfM methods.1 2 3

Cameras on portable devices are manufactured with a rolling-shutter (RS) mechanism, where the image rows (aka. scanlines) are read out sequentially. The unknown camera motions during the imaging process cause the so-called RS effects which are solved by motion assumptions in the literature. In this work, we give a solution to the absolute pose problem free of motion assumptions. We categorically demonstrate that the only requirement is motion smoothness instead of stronger constraints on the camera motion. To this end, we propose a novel mathematical abstraction for RS cameras observing a planar scene, called the scanline-homography, a 3 × 2 matrix with 5 DOFs. We establish the relationship between a scanline-homography and the corresponding plane-homography, a 3 × 3 matrix with 6 DOFs assuming the camera is calibrated. We estimate the scanline-homographies of an RS frame using a smooth image warp powered by B-Splines, and recover the plane-homographies afterwards to obtain the scanline-poses based on motion smoothness. We back our claims with various experiments. Code and new datasets: https://bitbucket.org/clermontferrand/planarscanlinehomography/src/master/.

In this paper, we propose a framework for tracking the deformation of soft objects using a RGB-D camera by utilizing the physically-based model of the considered object. A coarse, 3D template of the object being tracked is the only prior information required by the proposed method. The proposed approach does not rely on the accurate knowledge of the material properties of the object being tracked. In this paper, we integrate computer vision based tracking methodology with physical model based deformation representation without requiring expensive numerical optimization for minimizing nonlinear error terms. The proposed approach enables deformation tracking by joint minimization of a geometric error and a direct photometric intensity error while utilizing co-rotational Finite Element Method (FEM) as the underlying deformation model. The proposed method has been validated both on synthetic data (with groundtruth) and real data.

In this paper, we propose a novel method to simultaneously track the deformation of soft objects and estimate their elasticity parameters. The tracking of the deformable object is performed by combining the visual information captured by a RGB-D sensor with interactive Finite Element Method simulations of the object. The visual information is more particularly used to distort the simulated object. In parallel, the elasticity parameter estimation minimizes the error between the tracked object and a simulated object deformed by the forces that are measured using a force sensor. Once the elasticity parameters are estimated, our tracking algorithm can be used to estimate the deformation forces applied to an object without the use of a force sensor. We validated our method on several soft objects with different shape complexities. Our evaluations show the ability of our method to estimate the elasticity parameters as well as its use to estimate the forces applied to a deformable object without any force sensor. These results open novel perspectives to better track and control deformable objects during robotic manipulations.

This paper presents a framework for accurately tracking objects of complex shapes with joint minimization of geometric and photometric parameters using a coarse 3D object model with the RGB-D cameras. Tracking with coarse 3D model is remarkably useful for industrial applications. A technique is proposed that uses a combination of point-to-plane distance minimization and photometric error minimization to track objects accurately. The concept of `keyframes' are used in this system of object tracking for minimizing drift. The proposed approach is validated on both simulated and real data. Experimental results show that our approach is more accurate than existing state-of-the-art approaches, especially when dealing with low-textured objects with multiple coplanar faces.

A method to accurately track deformable objects using a RGB-D camera with the help of a coarse object model is presented in this paper. The deformation model is based on corotational FEM formulation. The physical model of the object does not need to be exact, nor do we require the precise physical properties for accurately tracking the object. The position of the vertices of the surface mesh of the tracked object is deformed using a set of virtual forces. A point-to-plane distance based geometric error between the pointcloud and the mesh is minimized with respect to these virtual forces. The point of application of force is determined by analysis of the error obtained from rigid tracking, which is done in parallel with the non-rigid tracking. This architecture also enables the overall system to be realtime. The proposed approach is evaluated on a synthetic data with ground-truth for deformation at every frame, as well as on real data.