This paper sets out a new representation of an image which is contrast independent. The image is decomposed into a tree of "shapes" based on connected components of level sets, which provides a full and nonredundant representation of the image. A fast algorithm to compute the tree, the fast level lines transform (FLLT), is explained in detail. Some simple and direct applications of this representation are shown.

Multi-view structure from motion (SfM) estimates the position and orientation of pictures in a common 3D coordinate frame. When views are treated incrementally, this external calibration can be subject to drift, contrary to global methods that distribute residual errors evenly. We propose a new global calibration approach based on the fusion of relative motions between image pairs. We improve an existing method for robustly computing global rotations. We present an efficient a contrario trifocal tensor estimation method, from which stable and precise translation directions can be extracted. We also define an efficient translation registration method that recovers accurate camera positions. These components are combined into an original SfM pipeline. Our experiments show that, on most datasets, it outperforms in accuracy other existing incremental and global pipelines. It also achieves strikingly good running times: it is about 20 times faster than the other global method we could compare to, and as fast as the best incremental method. More importantly, it features better scalability properties.

Abstract. The OpenMVG C++ library provides a vast collection of multipleview geometry tools and algorithms to spread the usage of computer vision and structure-from-motion techniques. Close to the state-of-the-art in its domain, it provides an easy access to common tools used in 3D reconstruction from images. Following the credo "Keep it simple, keep it maintainable" the library is designed as a modular collection of algorithms, libraries and binaries that can be used independently or as bricks to build larger systems. Thanks to its strict test driven development, the library is packaged with unit-test code samples that make the library easy to learn, modify and use. Since its first release in 2013 under the MPL2 license, OpenMVG has gathered an active community of users and contributors from many fields, spanning hobbyists, students, computer vision experts, and industry members.

The RANSAC [2] algorithm (RANdom SAmple Consensus) is a robust method to estimate parameters of a model fitting the data, in presence of outliers among the data. Its random nature is due only to complexity considerations. It iteratively extracts a random sample out of all data, of minimal size sufficient to estimate the parameters. At each such trial, the number of inliers (data that fits the model within an acceptable error threshold) is counted. In the end, the set of parameters maximizing the number of inliers is accepted. The variant proposed by Moisan and Stival [7] consists in introducing an a contrario [1] criterion to avoid the hard thresholds for inlier/outlier discrimination. It has three consequences: 1. The threshold for inlier/outlier discrimination is adaptive, it does not need to be fixed. 2. It gives a decision on the adequacy of the final model: it does not provide a wrong set of parameters if it does not have enough confidence. 3. The procedure to draw a new sample can be amended as soon as one set of parameters is deemed meaningful: the new sample can be drawn among the inliers of this model. In this particular instantiation, we apply it to the estimation of the homography registering two images of the same scene. The homography is an 8-parameter model arising in two situations when using a pinhole camera: the scene is planar (a painting, a facade, etc.) or the viewpoint location is fixed (pure rotation around the optical center). When the homography is found, it is used to stitch the images in the coordinate frame of the second image and build a panorama. The point correspondences between images are computed by the SIFT [5] algorithm.

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We adapt ideas presented by Auscher to impose boundary conditions on the construction of multiresolution analyses on the interval, as introduced by Cohen, Daubechies, and Vial. We construct new orthonormal wavelet bases on the interval satisfying homogeneous boundary conditions. This construction can be extended to wavelet packets in the case of one boundary condition at each edge. We present in detail the numerical computation of the filters and the derivative operators associated with these bases. We derive quadrature formulae in order to study the approximation error at the edge of the interval. Several examples illustrate the present construction. ). Orthonormal wavelet bases on R.We briefly review wavelets and MRA of L 2 (R) (for further details, see [Daub 92, Mall 89, Meye 90]). An MRA is a set (V j ) j∈Z of closed subspaces of L 2 (R) satisfying:it is possible to construct a function Φ (called the scaling function) of V 0 such that {Φ(. − k)} k∈Z is an orthonormal basis of V 0 and +∞ −∞ Φ(x)dx = 1. Moreover, P i (m)h j−2m .

Binocular stereovision estimates the three-dimensional shape of a scene from two photographs taken from different points of view. In rectified epipolar geometry, this is equivalent to a matching problem. This article describes a method proposed by Kolmogorov and Zabih in 2001, which puts forward an energy-based formulation. The aim is to minimize a four-term-energy. This energy is not convex and cannot be minimized except among a class of perturbations called expansion moves, in which case an exact minimization can be done with graph cuts techniques. One noteworthy feature of this method is that it handles occlusion: The algorithm detects points that cannot be matched with any point in the other image. In this method displacements are pixel accurate (no subpixel refinement). Source Code The software rewritten from Kolmogorov's code is available at the IPOL web page of this article 1. A set of stereo pairs is available and Kolmogorov and Zabih's algorithm can be tried on line. In the demo, the algorithm is run on six overlapping slices of the images, for efficiency purpose. Essentially, two parameters are needed: K associated to occlusion cost and λ to data fidelity. By default they are tuned automatically but they can be adapted to get better results. Supplementary Material In the demo, an optional rectification step can be launched before running the algorithm. The source code for this preprocessing step (not reviewed) can be found at the IPOL web page of this article 2 .