A Statistical Approach to the Matching of Local Features

Abstract

Abstract. This paper focuses on the matching of local features between images. Given a set of query descriptors and a database of candidate descriptors, the goal is to decide which ones should be matched. This is a crucial issue, since the matching procedure is often a preliminary step for object detection or image matching. In practice, this matching step is often reduced to a specific threshold on the Euclidean distance to the nearest neighbor.Our first contribution is a robust distance between descriptors, relying on the adaptation of the Earth Mover's Distance to circular histograms. It is shown that this distance outperforms classical distances for comparing SIFT-like descriptors, while its time complexity remains reasonable. Our second and main contribution is a statistical framework for the matching procedure, which yields validation thresholds automatically adapted to the complexity of each query descriptor and to the diversity and size of the database. The method makes it possible to detect multiple occurrences, as well as to deal with situations where the target is not present. Its performances are tested through various experiments on a large image database.Key words. Statistical analysis of matching processes, local feature matching, dissimilarity measure, Earth Mover's Distance, a contrario.AMS subject classifications. 62H35, 68T45, 68T10 [26,16], and 3D object modeling [19]. One of the most classical approaches to this problem consists in using local features around interest points or regions. The locality of the features ensures robustness to occlusion or context change, while the coding of the features should be invariant or robust to various geometrical, photometric or radiometric changes. Numerous local approaches have been proposed in the literature, the exhaustive study of which is beyond the scope of the present paper. In two relatively recent comparative studies [30,33], the SIFT descriptor [26] has been proven to be one of the most robust and invariant representation methods. As a result, the problem of finding correspondences between images often boils down to the matching of such local features. Nevertheless, whereas the extraction and representation of local descriptors has been thoroughly studied (see e.g. the references in [30]), their matching has not been the object of a systematic study. In practice, the matching step relies on simple but somehow limited procedures, as detailed further in the paper.In many applications, this matching procedure is yet a crucial preliminary step. It can for instance be used as a pre-processing stage (before resorting to some geometric consistency algorithm like RANSAC [9,43,5] or some mean square error minimization [26]) for finding common objects between images. The matching step is at the core of many recent methods relying on image similarities, see e.g.

SAR-SIFT: A SIFT-Like Algorithm for SAR Images

“…In this paper, following [28], we select the main modes of the local orientation histogram thanks to an a contrario approach. As in the original SIFT algorithm, different keypoints can be obtained with the same position and scale but with different orientations θ.…”

“…In [28], a probability of false alarm is computed for all possible matches using an a contrario method. This approach allows different matches for one keypoint and permits to recognize multiple occurences of one object.…”

SAR-SIFT: A SIFT-like algorithm for applications on SAR images

“…Except from the computation of the gradient, the remaining computations are left unchanged compared to the classical SIFT or its variations. In this paper, we use the variant of the descriptor introduced in [9], where a circular neighborhood is used. We call the resulting descriptor a Ratio Descriptor.…”

A contrario edge detection with edgelets

“…Among the exceptions, we can cite for example [10], in which the P F A distribution is learned from a database. In [14], random simulations are used to estimate a joint P F A distribution.…”

“…Desolneux et al proposed to apply their statistical framework to detect alignments in images [3], clusters [5], and edges [6]. Since then, the a contrario framework have been used in various purposes, such as motion detection [7], shape recognition [8], object matching [9], and local features matching [10].…”