Latent variable models provide valuable compact representations for learning and inference in many computer vision tasks. However, most existing models cannot directly encode prior knowledge about the specific problem at hand. In this paper, we introduce a constrained latent variable model whose generated output inherently accounts for such knowledge. To this end, we propose an approach that explicitly imposes equality and inequality constraints on the model's output during learning, thus avoiding the computational burden of having to account for these constraints at inference. Our learning mechanism can exploit non-linear kernels, while only involving sequential closed-form updates of the model parameters. We demonstrate the effectiveness of our constrained latent variable model on the problem of non-rigid 3D reconstruction from monocular images, and show that it yields qualitative and quantitative improvements over several baselines.

Most recent approaches to monocular nonrigid 3D shape recovery rely on exploiting point correspondences and work best when the whole surface is well textured. The alternative is to rely on either contours or shading information, which has only been demonstrated in very restrictive settings. Here, we propose a novel approach to monocular deformable shape recovery that can operate under complex lighting and handle partially textured surfaces. At the heart of our algorithm are a learned mapping from intensity patterns to the shape of local surface patches and a principled approach to piecing together the resulting local shape estimates. We validate our approach quantitatively and qualitatively using both synthetic and real data.

It has been shown that the 3D shape of a deformable surface in an image can be recovered by establishing correspondences between that image and a reference one in which the shape is known. These matches can then be used to set-up a convex optimization problem in terms of the shape parameters, which is easily solved. However, in many cases, the correspondences are hard to establish reliably. In this paper, we show that we can solve simultaneously for both 3D shape and correspondences, thereby using 3D shape constraints to guide the image matching and increasing robustness, for example when the textures are repetitive. This involves solving a mixed integer quadratic problem. While optimizing this problem is NP-hard in general, we show that its solution can nevertheless be approximated effectively by a branch-and-bound algorithm.

It has recently been shown that deformable 3D surfaces could be recovered from single video streams. However, existing techniques either require a reference view in which the shape of the surface is known a priori, which often may not be available, or require tracking points over long sequences, which is hard to do. In this paper, we overcome these limitations. To this end, we establish correspondences between pairs of frames in which the shape is different and unknown. We then estimate homographies between corresponding local planar patches in both images. These yield approximate 3D reconstructions of points within each patch up to a scale factor. Since we consider overlapping patches, we can enforce them to be consistent over the whole surface. Finally, a local deformation model is used to fit a triangulated mesh to the 3D point cloud, which makes the reconstruction robust to both noise and outliers in the image data.