Levente Hajder

Weak-perspective structure from motion by fast alternation

This paper addresses the problem of moving object reconstruction. Several methods have been published in the past 20 years including stereo reconstruction as well as multi-view factorization methods. In general, reconstruction algorithms compute the 3D structure of the object and the camera parameters in a non-optimal way, and then a nonlinear and numerical optimization algorithm refines the reconstructed camera parameters and 3D coordinates. In this paper, we propose an adjustment method which is the improved version of the well-known Tomasi–Kanade factorization method. The novelty, which yields the high speed of the algorithm, is that the core of the proposed method is an alternation and we give optimal solutions to the subproblems in the alternation. The improved method is discussed here and it is compared to the widely used bundle adjustment algorithm.

Weak-perspective structure from motion for strongly contaminated data

It is widely known that, for the affine camera model, both shape and motion data can be factorised directly from the measurement matrix containing the image coordinates of the tracked feature points. However, classical algorithms for structure from motion (SfM) are not robust: measurement outliers, that is, incorrectly detected or matched feature points can destroy the result. A few methods to robustify SfM have already been proposed. Different outlier detection schemes have been used. We examine an efficient algorithm by Trajkovic and Hedley [Trajkovic, M., Hedley, M., 1997. Robust recursive structure and motion recovery under affine projection. In: Proc. British Machine Vision Conference. Available from: ] who use the affine camera model and the least median of squares (LMedS) method to separate inliers from outliers. LMedS is only applicable when the ratio of inliers exceeds 50%. We show that the least trimmed squares (LTS) method is more efficient in robust SfM than LMedS. In particular, we demonstrate that LTS can handle inlier ratios below 50%. We also show that using the real (Euclidean) motion data results in more precise SfM than using the affine motion data. Based on these observations, we propose a novel robust SfM algorithm and discuss its advantages and limits. Furthermore, we introduce a RANSAC based outlier detector that also provides robust results. The proposed methods and the Trajkovic procedure are quantitatively compared on synthetic data in different simulated situations. The methods are also tested on synthesised and real video sequences.

Automatic focal length estimation as an eigenvalue problem

Abstract This paper focuses on automatic focal length estimation. In several vision applications one can assume that the utilized cameras are semi-calibrated, which means that all the intrinsic camera parameters but the focal length (aspect ratio, principal point, and skew) are known. In this case the camera calibration procedure reduces to the computation of the focal length(s). The main contribution of the study is a novel automatic focal length estimator algorithm for semi-calibrated cameras which handles both the fixed and the variable focal length cases. The method transforms the focal length estimation problem into the generalized eigenvalue problem class. The input of the algorithm is a set of fundamental matrices. The proposed method is validated on both synthetic and real data. For real sequences, the 3D structure is also reconstructed based on the cameras constructed from the output of the algorithm.

Metric Reconstruction with Missing Data under Weak Perspective

D reconstruction with missing data has been a challenging computer vision task since the late 90s. This paper proposes a novel metric reconstruction al- gorithm dealing with the missing data problem. The algorithm is the adaption of the Fast Alternation method published by us in CAIP2007. We concentrate on metric instead of affine reconstruction because the quality of metric recon- structionissignificantlybetterasitisdemonstratedinthisstudy. Thesolution is an alternation which consists of several substeps. All of these substeps are optimal with respect to the parameters that are being optimized. It is proved that the proposed algorithm converges to a local minimum. The solutions to the optimization subproblems in our approach are given by closed-form formulas, therefore the proposed method is relatively fast.

Fast and precise weak-perspective factorization

We address the problem of moving object reconstruction. Several methods have been published in the past 20 years including stereo reconstruction as well as multi-view factorization methods. In general, reconstruction algorithms estimate the 3D structure of the object and the camera parameters in a non-optimal way and then a nonlinear optimization method refines the estimated camera parameters and 3D object coordinates. n nIn this paper, an adjustment method is proposed which is the fast version of the well-known down-hill alternation method. The novelty which yields the high speed of the algorithm is that the steps of the alternation give optimal solution to the subproblems by closed-form formulas. The proposed algorithm is discussed here and it is compared to the widely used bundle adjustment method.

Normal map recovery using bundle adjustment

Although modern reconstruction methods have advanced considerably, their ability to retrieve fine details, small features of a surface is limited. Applying texture can be used to conceal lack of geometry to some extent, but it becomes apparent when lighting varies. A more sophisticated solution is to map normal vectors to the surface of the model in order to alter the way it is rendered under different illuminations in accordance with the properties of the real object. The principle of photometric stereo is to reconstruct normals from a series of images. By illuminating the object with different directional light sources local surface orientation can be inferred. The contribution of this study is that the authors successfully applied the widely used bundle adjustment algorithm to photometric stereo problems when non-parallel light rays illuminate the objects.

Grouping of articulated objects with common axis

We address the problem of nonrigid Structure from Motion (SfM). Several methods have been published recently which try to solve the task of tracking, segmenting, or reconstructing nonrigid 3D objects in motion. Most of these papers focus on deformable objects. We deal with the segmentation of articulated objects, that is, nonrigid objects composed of several moving rigid objects. We consider two moving objects and assume that the rigid SfM problem has been solved for each of them separately. We propose a method which helps to decide whether an object is rotating around an axis defined by another moving object. The theories of the proposed method is discussed in detail. Experimental results for synthetic and real data are presented.