Abstract. This paper presents a novel approach for detecting affine invariant interest points. Our method can deal with significant affine transformations including large scale changes. Such transformations introduce significant changes in the point location as well as in the scale and the shape of the neighbourhood of an interest point. Our approach allows to solve for these problems simultaneously. It is based on three key ideas: 1) The second moment matrix computed in a point can be used to normalize a region in an affine invariant way (skew and stretch). 2) The scale of the local structure is indicated by local extrema of normalized derivatives over scale. 3) An affine-adapted Harris detector determines the location of interest points. A multi-scale version of this detector is used for initialization. An iterative algorithm then modifies location, scale and neighbourhood of each point and converges to affine invariant points. For matching and recognition, the image is characterized by a set of affine invariant points; the affine transformation associated with each point allows the computation of an affine invariant descriptor which is also invariant to affine illumination changes. A quantitative comparison of our detector with existing ones shows a significant improvement in the presence of large affine deformations. Experimental results for wide baseline matching show an excellent performance in the presence of large perspective transformations including significant scale changes. Results for recognition are very good for a database with more than 5000 images.

This paper presents a new method for detecting scale invariant interest points. The method is based on two recent results on scale space: 1) Interest points can be adapted to scale and give repeatable results (geometrically stable). 2) Local extrema over scale of normalized derivatives indicate the presence of characteristic local structures. Our method first computes a multi-scale representation for the Harris interest point detector. We then select points at which a local measure (the Laplacian) is maximal over scales. This allows a selection of distinctive points for which the characteristic scale is known. These points are invariant to scale, rotation and translation as well as robust to illumination changes and limited changes of viewpoint. For indexing, the image is characterized by a set of scale invariant points; the scale associated with each point allows the computation of a scale invariant descriptor. Our descriptors are, in addition, invariant to image rotation, to affine illumination changes and robust to small perspective deformations. Experimental results for indexing show an excellent performance up to a scale factor of 4 for a database with more than 5000 images. 1

Over the past few years, several methods for segmenting a scene containing multiple rigidly moving objects have been proposed. However, most existing methods have been tested on a handful of sequences only, and each method has been often tested on a different set of sequences. Therefore, the comparison of different methods has been fairly limited. In this paper, we compare four 3-D motion segmentation algorithms for affine cameras on a benchmark of 155 motion sequences of checkerboard, traffic, and articulated scenes. 1.

We study the problem of estimating the number of independent motions for segmentation based on feature tracking. We elucidate the mathematical structure of the problem and present an estimation method using model selection by the geometric AIC, the geometric MDL, and the OIC. We compare their performance using synthetic and real data. We also present techniques for evaluating the reliability of segmentation a posteriori, using the standard F test and model selection by the geometric AIC and the geometric MDL. 1.

Abstract—We first investigate the meaning of “statistical methods ” for geometric inference based on image feature points. Tracing back the origin of feature uncertainty to image processing operations, we discuss the implications of asymptotic analysis in reference to “geometric fitting ” and “geometric model selection ” and point out that a correspondence exists between the standard statistical analysis and the geometric inference problem. Then, we derive the “geometric AIC ” and the “geometric MDL ” as counterparts of Akaike’s AIC and Rissanen’s MDL. We show by experiments that the two criteria have contrasting characteristics in detecting degeneracy. Index Terms—statistical method, feature point extraction, asymptotic evaluation, geometric AIC, geometric MDL. 1

Abstract. We present a scheme for simultaneous calibration of a continuously moving and continuously zooming camera: placing an easily distinguishable pattern in the scene, we calibrate the camera from an unoccluded portion of the pattern image in each frame. We describe an optimal method which provides an evaluation of the reliability of the solution. We then propose a technique for avoiding the inherent degeneracy and statistical uctuations by model selection using the geometric AIC and the geometric MDL. 1

Many techniques have been proposed for separating feature point trajectories tracked through a video sequence into independent motions, but objects are usually assumed to undergo general 3-D motions. As a result, the separation accuracy considerably deteriorates in realistic video sequences in which object motions are nearly degenerate. In this paper, we introduce unsupervised learning assuming degenerate motions followed by unsupervised learning assuming general 3-D motions. This multi-stage optimization allows us to not only separate simple motions that we frequently encounter with high precision but also preserve the high performance for considerably general 3-D motions. Doing simulations and real video experiments, we demonstrate that our method is superior to all existing methods. 1.

Abstract. Many techniques have been proposed for segmenting feature point trajectories tracked through a video sequence into independent motions. It has been found, however, that methods that perform very well in simulations perform very poorly for real video sequences. This paper resolves this mystery by analyzing the geometric structure of the degeneracy of the motion model. This leads to a new segmentation algorithm: a multi-stage unsupervised learning scheme first using the degenerate motion model and then using the general 3-D motion model. We demonstrate by simulated and real video experiments that our method is superior to all existing methods in practical situations. 1

Many techniques have been proposed for segmenting feature point trajectories tracked through a video sequence into independent motions, but objects in the scene are usually assumed to undergo general 3-D motions. As a result, the segmentation accuracy considerably deteriorates in realistic video sequences in which object motions are nearly degenerate. In this paper, we propose a multi-stage unsupervised learning scheme first assuming degenerate motions and then assuming general 3-D motions and show by simulated and real video experiments that the segmentation accuracy significantly improves without compromising the accuracy for general 3-D motions.

In this paper, we address the problem of structure and motion recovery from two views of a scene containing planes, i.e. sets of coplanar points. Most of the existing works do only exploit this constraint in a sub-optimal manner. We propose to parameterize the structure of such scenes with planes and points on planes and derive the MLE (Maximum Likelihood Estimator) using a minimal parameterization based on 2D entities. The result is the estimation of camera motion and 3D structure in projective space, that minimizes reprojection error, while satisfying the piecewise planarity. We propose a quasi-linear estimator that provides reliable initialization values for plane equations. Experimental results show that the reconstruction is of clearly superior quality compared to traditional methods based only on points, even if the scene is not perfectly piecewise planar. 1.