Robust integration of range images is an important task for building high-quality 3D models. Since range images, and in particular range maps from stereo vision, may have a substantial amount of outliers, any integration approach aiming at high-quality models needs an increased level of robustness. Additionally, a certain level of regularization is required to obtain smooth surfaces. Computational efficiency and global convergence are further preferable properties. The contribution of this paper is a unified framework to solve all these issues. Our method is based on minimizing an energy functional consisting of a total variation (TV) regularization force and an L 1 data fidelity term. We present a novel and efficient numerical scheme, which combines the duality principle for the TV term with a point-wise optimization step. We demonstrate the superior performance of our algorithm on the well-known Middlebury multi-view database and additionally on real-world multi-view images. 1.

This paper discusses fast and accurate methods to solve Total Variation (TV) models on the graphics processing unit (GPU). We review two prominent models incorporating TV regularization and present different algorithms to solve these models. We mainly concentrate on variational techniques, i.e. algorithms which aim at solving the Euler Lagrange equations associated with the variational model. We then show that particularly these algorithms can be effectively accelerated by implementing them on parallel architectures such as GPUs. For comparison we chose a state-ofthe-art method based on discrete optimization techniques. We then present the results of a rigorous performance evaluation including 2D and 3D problems. As a main result we show that the our GPU based algorithms clearly outperform discrete optimization techniques in both speed and maximum problem size. 1.

Abstract We propose a generative model based method for recovering both the shape and the reflectance of the surface(s) of a scene from multiple images, assuming that illumination conditions and cameras calibration are known in advance. Based on a variational framework and via gradient descents, the algorithm minimizes simultaneously and consistently a global cost functional with respect to both shape and reflectance. The motivations for our approach are threefold. (1) Contrary to previous works which mainly consider specific individual scenarios, our method applies indiscriminately to a number of classical scenarios; in particular it works for classical stereovision, multiview photometric stereo and multiview shape from shading. It works with changing as well as static illumination. (2) Our approach naturally combines stereo, silhouette and shading cues in a single framework. (3) Moreover, unlike most previous methods dealing with only Lambertian surfaces, the proposed

New image denoising models based on non-local image information have been recently introduced in the literature. These so-called ”non-local” denoising models provide excellent results because these models can denoise smooth regions or/and textured regions simultaneously, unlike standard denoising models. Standard variational models s.a. Total Variation-based models are defined to work in a small local neighborhood, which is enough to denoise smooth regions. However, textures are not local in nature and requires semi-local/non-local information to be denoised efficiently. Several papers have introduced non-local filters and non-local variational models for image denoising. Yet, few studies have been done to develop unsupervised image segmentation models based on non-local information. This will be the goal of this paper. We define and study three unsupervised non-local segmentation models. These models will be based on the continuous global minimization approach for image segmentation recently introduced in [10, 6]. The energy of [10, 6] is a first order energy composed of the weighted Total Variation norm and a linear term. The first proposed non-local segmentation model will extend

Abstract. In this paper, a generative model based method for recovering both the shape and the reflectance of the surface(s) of a scene from multiple images is presented, assuming that illumination conditions are known in advance. Based on a variational framework and via gradient descents, the algorithm minimizes simultaneously and consistently a global cost functional with respect to both shape and reflectance. Contrary to previous works which consider specific individual scenarios, our method applies to a number of scenarios – mutiview stereovision, multiview photometric stereo, and multiview shape from shading. In addition, our approach naturally combines stereo, silhouette and shading cues in a single framework and, unlike most previous methods dealing with only Lambertian surfaces, the proposed method considers general dichromatic surfaces. 1 Introduction and Related Work Many methods have been proposed to recover the three-dimensional surface shape using multiple images during these last two decades [1]. On the other hand, for a long time, the estimation of surface radiance/reflectance was secondary. Even some recent

Abstract. In this work the weighted minimal surface model traditionally used in multiview stereo is revisited. We propose to generalize the classical photoconsistency-weighted minimal surface approach by means of an anisotropic metric which allows to integrate a specified surface orientation into the optimization process. In contrast to the conventional isotropic case, where all spatial directions are treated equally, the anisotropic metric adaptively weights the regularization along different directions so as to favor certain surface orientations over others. We show that the proposed generalization preserves all properties and globality guarantees of continuous convex relaxation methods. We make use of a recently introduced efficient primal-dual algorithm to solve the arising saddle point problem. In multiple experiments on real image sequences we demonstrate that the proposed anisotropic generalization allows to overcome oversmoothing of small-scale surface details, giving rise to more precise reconstructions. 1

Abstract. We propose a convex optimization framework delivering intuitive and reasonable 3D meshes from a single photograph. For a given input image, the user can quickly obtain a segmentation of the object in question. Our algorithm then automatically generates an admissible closed surface of arbitrary topology without the requirement of tedious user input. Moreover we provide a tool by which the user is able to interactively modify the result afterwards through parameters and simple operations in a 2D image space. The algorithm targets a limited but relevant class of real world objects. The object silhouette and the additional user input enter a functional which can be optimized globally in a few seconds using recently developed convex relaxation techniques parallelized on state-of-the-art graphics hardware. 1

We introduce a continuous global optimization method to the field of surface reconstruction from discrete noisy cloud of points with weak information on orientation. The proposed method uses an energy functional combining flux-based data-fit measures and a regularization term. A continuous convex relaxation scheme assures the global minima of the geometric surface functional. The reconstructed surface is implicitly represented by the binary segmentation of vertices of a 3D uniform grid and a triangulated surface can be obtained by extracting an appropriate isosurface. Unlike the discrete graph-cut solution, the continuous global optimization entails advantages like memory requirements, reduction of metrication errors for geometric quantities, allowing globally optimal surface reconstruction at higher grid resolutions. We demonstrate the performance of the proposed method on several oriented point clouds captured by laser scanners. Experimental results confirm that our approach is robust to noise, large holes and non-uniform sampling density under the condition of very coarse orientation information.

This work proposes a method to reconstruct surfaces with higher-order smoothness from noisy 3D measurements. The reconstructed surface is implicitly represented by the zero level-set of a continuous valued embedding function. The key idea is to find a function whose higher-order derivatives are regularized and whose gradient is best aligned with a vector field defined by the input point set. In contrast to methods based on the first-order variation of the function that are biased towards the constant functions and treat the extraction of the isosurface without aliasing artifacts as an afterthought, we impose higher-order smoothness directly on the embedding function. After solving a convex optimization problem with a multi-scale iterative scheme, a triangulated surface can be extracted using the marching cubes algorithm. We demonstrated the proposed method on several data sets obtained from raw laser-scanners and multi-view stereo approaches. Experimental results confirm that our approach allows us to reconstruct smooth surfaces from points in the presence of noise, outliers, large missing parts and very coarse orientation information.

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