Bérenger Stival

Bio: Bérenger Stival is an academic researcher from École normale supérieure de Cachan. The author has contributed to research in topics: RANSAC & Fundamental matrix (computer vision). The author has an hindex of 1, co-authored 1 publications receiving 196 citations.

A Probabilistic Criterion to Detect Rigid Point Matches Between Two Images and Estimate the Fundamental Matrix

Abstract: The perspective projections of n physical points on two views (stereovision) are constrained as soon as n ≥ 8 However, to prove in practice the existence of a rigid motion between two images, more than 8 point matches are desirable in order to compensate for the limited accuracy of the matches In this paper, we propose a computational definition of rigidity and a probabilistic criterion to rate the meaningfulness of a rigid set as a function of both the number of pairs of points (n) and the accuracy of the matches This criterion yields an objective way to compare, say, precise matches of a few points and approximate matches of a lot of points It gives a yes/no answer to the question: “could this rigid points correspondence have occurred by chance?”, since it guarantees that the expected number of meaningful rigid sets found by chance in a random distribution of points is as small as desired It also yields absolute accuracy requirements for rigidity detection in the case of non-matched points, and optimal values of n, depending on the expected accuracy of the matches and on the proportion of outliers We use it to build an optimized random sampling algorithm that is able to detect a rigid motion and estimate the fundamental matrix when the set of point matches contains up to 90% of outliers, which outperforms the best currently known methods like M-estimators, LMedS, classical RANSAC and Tensor Voting

From Gestalt Theory to Image Analysis: A Probabilistic Approach

Abstract: This book introduces the reader to a recent theory in Computer Vision yielding elementary techniques to analyse digital images. These techniques are inspired from and are a mathematical formalization of the Gestalt theory. Gestalt theory, which had never been formalized is a rigorous realm of vision psychology developped between 1923 and 1975. From the mathematical viewpoint the closest field to it is stochastic geometry, involving basic probability and statistics, in the context of image analysis. The authors maintain a public software, MegaWave, containing implementations of most of the image analysis techniques developped in the book. The book is intended for researchers and engineers. It is mathematically self-contained and requires only the basic notions in probability and calculus.

Global Fusion of Relative Motions for Robust, Accurate and Scalable Structure from Motion

Abstract: 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.

ASIFT: An Algorithm for Fully Affine Invariant Comparison

Abstract: If a physical object has a smooth or piecewise smooth boundary, its images obtained by cameras in varying positions undergo smooth apparent deformations. These deformations are locally well approximated by affine transforms of the image plane. In consequencethe solid object recognition problem has often been led back to the computation of affine invariant image local features. The similarity invariance (invariance to translation, rotation, and zoom) is dealt with rigorously by the SIFT method The method illustrated and demonstrated in this work, AffineSIFT (ASIFT), simulates a set of sample views of the initial images, obtainable by varying the two camera axis orientation parameters, namely the latitude and the longitude angles, which are not treated by the SIFT method. Then it applies the SIFT method itself to all images thus generated. Thus, ASIFT covers effectively all six parameters of the affine transform. Source Code The source code (ANSI C), its documentation, and the online demo are accessible at the IPOL web page of this article 1 .

Adaptive structure from motion with a contrario model estimation

Abstract: Structure from Motion (SfM) algorithms take as input multi-view stereo images (along with internal calibration information) and yield a 3D point cloud and camera orientations/poses in a common 3D coordinate system. In the case of an incremental SfM pipeline, the process requires repeated model estimations based on detected feature points: homography, fundamental and essential matrices, as well as camera poses. These estimations have a crucial impact on the quality of 3D reconstruction. We propose to improve these estimations using the a contrario methodology. While SfM pipelines usually have globally-fixed thresholds for model estimation, the a contrario principle adapts thresholds to the input data and for each model estimation. Our experiments show that adaptive thresholds reach a significantly better precision. Additionally, the user is free from having to guess thresholds or to optimistically rely on default values. There are also cases where a globally-fixed threshold policy, whatever the threshold value is, cannot provide the best accuracy, contrary to an adaptive threshold policy.