Current Elastic SfT (Shape from Template) methods are based on ℓ2-norm minimization. None can accurately recover the spatial location of the acting forces since ℓ2-norm based minimization tends to find the best tradeoff among noisy data to fit an elastic model. In this work, we study shapes that are deformed with spatially sparse set of forces. We propose two formulations for a new class of SfT problems dubbed here SLE-SfT (Sparse Linear Elastic-SfT). The First ideal formulation uses an ℓ0-norm to minimize the cardinal of non-zero components of the deforming forces. The second relaxed formulation uses an ℓ1-norm to minimize the sum of absolute values of force components. These new formulations do not use Solid Boundary Constraints (SBC) which are usually needed to rigidly position the shape in the frame of the deformed image. We introduce the Projective Elastic Space Property (PESP) that jointly encodes the reprojection constraint and the elastic model. We prove that filling this property is necessary and sufficient for the relaxed formulation to: (i) retrieve the ground-truth 3D deformed shape, (ii) recover the right spatial domain of non-zero deforming forces. (iii) It also proves that we can rigidly place the deformed shape in the image frame without using SBC. Finally, we prove that when filling PESP, resolving the relaxed formulation provides the same ground-truth solution as the ideal formulation. Results with simulated and real data show substantial improvements in recovering the deformed shapes as well as the spatial location of the deforming forces.

This paper focusses on safe screening techniques for the LASSO problem. We derive a new sphere test, coined RFNE, exploiting the firmly non-expansiveness of projection operators. Our test generalizes some methods of the literature but, unlike the latter, exploits approximated primal-dual solutions of the LASSO problem while remaining safe and effective. Our simulation results show that the proposed RFNE test outperforms the best methodology of the state of the art, namely the GAP test derived by Fercoq et al.

We cast SfT (Shape-from-Template) as the search of a vector field (X, δX), composed of the pose X and the displacement δX that produces the deformation. We propose the first fully linear least-squares SfT method modeling elastic deformations. It relies on a set of Solid Boundary Constraints (SBC) to position the template at X in the deformed frame. The displacement is mapped by the stiffness matrix to minimize the amount of force responsible for the deformation. This linear minimization is subjected to the Reprojection Boundary Constraints (RBC) of the deformed shape X + δX on the deformed image. Compared to state-of-the-art methods, this new formulation allows us to obtain accurate results at a low computation cost.

We propose a new approach for template-based extensible surface reconstruction from a single view. We extend the method of isometric surface reconstruction and more recent work on conformal surface reconstruction. Our approach relies on the minimization of a proposed stretching energy formalized with respect to the Poisson ratio parameter of the surface. We derive a patch-based formulation of this stretching energy by assuming local linear elasticity. This formulation unifies geometrical and mechanical constraints in a single energy term. We prevent local scale ambiguities by imposing a set of fixed boundary 3D points. We experimentally prove the sufficiency of this set of boundary points and demonstrate the effectiveness of our approach on different developable and non-developable surfaces with a wide range of extensibility.

Image keypoints are broadly used in robotics for different purposes, ranging from recognition to 3D reconstruction, passing by SLAM and visual servoing. Robust keypoint matching across different views is problematic because of the relative motion between camera and scene that causes significant changes in feature appearance. The problem can be partially overcome by using state-of-the-art methods for keypoint detection and matching, that are resilient to common affine transformations such as changes in scale and rotation. Unfortunately, these approaches are not invariant to the radial distortion present in images acquired by cameras with wide field-of-view. This article proposes modifications to the Scale Invariant Feature Transform (SIFT), that improve the repeatability of detection and effectiveness of matching in the presence of distortion, while preserving the characteristics of invariance to scale and rotation. These modifications require an approximate modeling of the image distortion, and consist in using adaptative gaussian filtering for detection and implicit gradient correction for description. Extensive experiments, with both synthetic and real images, show that our method outperforms explicit distortion correction using image rectification.

Endoscopic camera for surgical navigation and 3D visualization requires precise and stable estimates of the calibration parameters. The estimation of the hand-eye transform between the camera frame and the opto-tracked body of the endoscope is an important issue of the calibration. This paper presents a new stable method for the hand-eye calibration problem. The most popular method estimates the transform directly in the special euclidean group SE(3) by computing separately the rotation and the translation. The second famous approach formulates the problem in the dual quaternion space and estimates jointly the rotation and the translation. In a first glance, the simultaneous estimation seems to be always advantageous. However, and according to the experiments, this is not the case for the rotation estimation that is affected by the noise in translation. Our approach takes advantage of the both methods and uses the dual quaternion to estimate separately the rotation and the translation. We show experimentally that our algorithm is more stable with minimal number and small amplitude of motions.