This paper presents a quantitative comparison of several multi-view stereo reconstruction algorithms. Until now, the lack of suitable calibrated multi-view image datasets with known ground truth (3D shape models) has prevented such direct comparisons. In this paper, we first survey multi-view stereo algorithms and compare them qualitatively using a taxonomy that differentiates their key properties. We then describe our process for acquiring and calibrating multiview image datasets with high-accuracy ground truth and introduce our evaluation methodology. Finally, we present the results of our quantitative comparison of state-of-the-art multi-view stereo reconstruction algorithms on six benchmark datasets. The datasets, evaluation details, and instructions for submitting new models are available online at http://vision.middlebury.edu/mview.

/pdf/a-comparison-and-evaluation-of-multi-view-stereo-2sd22ycy33.pdf

A Comparison and Evaluation of Multi-View Stereo Reconstruction Algorithms

A heuristic method has been developed for registering two sets of 3-D curves obtained by using an edge-based stereo system, or two dense 3-D maps obtained by using a correlation-based stereo system. Geometric matching in general is a difficult unsolved problem in computer vision. Fortunately, in many practical applications, some a priori knowledge exists which considerably simplifies the problem. In visual navigation, for example, the motion between successive positions is usually approximately known. From this initial estimate, our algorithm computes observer motion with very good precision, which is required for environment modeling (e.g., building a Digital Elevation Map). Objects are represented by a set of 3-D points, which are considered as the samples of a surface. No constraint is imposed on the form of the objects. The proposed algorithm is based on iteratively matching points in one set to the closest points in the other. A statistical method based on the distance distribution is used to deal with outliers, occlusion, appearance and disappearance, which allows us to do subset-subset matching. A least-squares technique is used to estimate 3-D motion from the point correspondences, which reduces the average distance between points in the two sets. Both synthetic and real data have been used to test the algorithm, and the results show that it is efficient and robust, and yields an accurate motion estimate.

/pdf/iterative-point-matching-for-registration-of-free-form-5fl1ftde76.pdf

Iterative point matching for registration of free-form curves and surfaces

Geometric matching in general is a difficult unsolved problem in computer vision. Fortunately, in many pratical applications, some a priori knowledge exists which considerably simplifies the problem. In visual navigation, for example, the motion between successive positions is usually either small or approximately known, but a more precise registration is required for environment modeling. The algorithm described in this report meets this need. Objects are represented by free-form curves, i.e., arbitrary spaces curves of the type found in practice. A curve is available in the form of a set of chained points. The proposed algorithm is based on iteratively matching points on one curve to the closest points on the other. A least-squares technique is used to estimate 3-D motion from the point correspondences, which reduces the average distance between curves in two sets. Both synthetic and real data have been used to test the algorithm, and the results show that it is efficient and robust, and yields an accurate motion estimate. The algorithm can be easily extended to solve similar problems such as 2-D curve matching and 3-D surface matching.

/pdf/iterative-point-matching-for-registration-of-free-form-b0pre910b7.pdf

Iterative point matching for registration of free-form curves

The extremal boundaries, of 3-D curved objects are the images of special curves drawn on the object and are called rims They are viewpoint dependent and characterized by the fact that the optical rays of their points are tangential to the surface of the object The mathematics of the relationship between the extremal boundaries and the surface of the object is studied This study makes it possible to design an algorithm for detecting those boundaries in the images that are likely to be extremal Once this has been done, one can reconstruct the rims and compute the differential properties of the surface of the object along them up to the second order If a qualitative description is sufficient, the sign of the Gaussian curvature of the surface along the rim can be computed in a much simpler way Experimental results are presented on synthetic and real images The work provides a better understanding of the relationship between the apparent and real shape of a 3-D object as well as algorithms for reconstructing the local shape of such an object along the rims >

Using extremal boundaries for 3-D object modeling

This paper describes a new approach to matching geometric structure in 2D point-sets. The novel feature is to unify the tasks of estimating transformation geometry and identifying point-correspondence matches. Unification is realized by constructing a mixture model over the bipartite graph representing the correspondence match and by affecting optimization using the EM algorithm. According to our EM framework, the probabilities of structural correspondence gate contributions to the expected likelihood function used to estimate maximum likelihood transformation parameters. These gating probabilities measure the consistency of the matched neighborhoods in the graphs. The recovery of transformational geometry and hard correspondence matches are interleaved and are realized by applying coupled update operations to the expected log-likelihood function. We evaluate the technique on two real-world problems.

/pdf/graph-matching-with-a-dual-step-em-algorithm-wl261ev2nk.pdf

Graph matching with a dual-step EM algorithm

Representing stereo data with the Delaunay triangulation

A coherent way of interpolating 3-D data obtained by stereo, for example, with a simplicial polyhedral surface is discussed. The method is based on constrained Delaunay triangulation; the polyhedral surface is obtained by using a simple visibility property to mark tetrahedra likely to be empty. The method is intrinsically discontinuity-preserving and yields both a surface representation of objects and a volume representation of free space which may be useful in robotics. Algorithms to implement the method are described and their complexity analyzed in the worst case and average case situations where tools of probabilistic geometry are used. >

https://hal.inria.fr/inria-00075763/document

This article proposes a coherent method of interpolating 3D data obtained for example by stereo, with a polyhedral surface by means of the Delaunay Triangulation. We first give some theoretical properties concerning the approximations of sampled objects we obtain when the sampling rate increases, based on the study of their skeleton using some tools of Mathematical Morphology. Then, we present the algorithms and their complexity analysis which yield both a surface representation of objects and a volume representation of free space which may be useful in Robotics. This goal is achieved by means of a simple visibility criterion. The method is intrinsically discontinuity preserving and can be used for the integration of multiple viewpoints.

E. Le Bras-Mehlman

Papers

Representing stereo data with the Delaunay triangulation

Representing stereo data with the Delaunay triangulation

How the Delaunay Triangulation Can Be used For Representing Stereo Data