Novel Similarity Measures for Differential Invariant Descriptors for Generic Object Retrieval

Abstract

Local feature matching is an essential component of many image and object retrieval algorithms. Euclidean and Mahalanobis distances are mostly used in order to quantify the similarity of two stipulated feature vectors. The Euclidean distance is inappropriate in the typical case where the components of the feature vector are incommensurable entities, and indeed yields unsatisfactory results in practice. The Mahalanobis distance performs better, but is less generic in the sense that it requires specific training data.In this paper we consider two alternative ways to construct generic distance measures for image and object retrieval, which do not suffer from any of these shortcomings. The first approach aims at obtaining a (image independent) covariance matrix for a Mahalonobis-like distance function without explicit training, and is applicable to feature vectors consisting of partial image derivatives. In the second approach a stability based similarity measure (SBSM) is introduced for feature vectors that are composed of arbitrary algebraic combinations of image derivatives, and likewise requires no explicit training. The strength and novelty of SBSM lies in the fact that the associated covariance matrix exploits local image structure. A performance analysis shows that feature matching based on SBSM outperforms algorithms based on Euclidean and Mahalanobis distances.

Jet-Based Local Image Descriptors

“…We also include J 5 , J 7 as we want to investigate the performance when relying on a single, low-dimensional jet. We do not compare with previously published differential invariant based descriptors, such as [7][8][9], because they have in our experiments (not part of the paper) been shown to be significantly under par.…”

“…If either n or m is odd, the covariance is 0. Finally, we remark that this normalization method is related, but not identical, to the descriptor similarity measure proposed in [8]. After the whitening, the descriptor is L 2 normalized to achieve invariance to affine contrast changes.…”

“…Local image descriptors based on higher order image differentials have previously been proposed [7,8] with little success for feature matching [2]. Compared to our descriptor, these descriptors do not rely on multi-locality and only use differential invariants (functions of the local jet) up to the third order.…”

Image Matching Using Generalized Scale-Space Interest Points

“…Inspired by early theoretical studies by Johansen [60,61] regarding the information content in socalled "top points" in scale space where bifurcations occur, Platel et al [135], Balmashnova et al [5], Balmashnova and Florack [4] and Demirci et al [37] proposed to use such bifurcation events as primitives in graph representations for image matching. Such bifurcations events were also registered in the original scale-space primal sketch concept for intensity data (Lindeberg [90]), in which the bifurcation events delimited the extent of grey-level blobs in the scale direction and provided explicit relations of how neighbouring image features (local extrema with extent) were related across scales.…”

“…Moreover, only features within corresponding scale ranges are evaluated. 4 Tables 2 and 3 show the result of evaluating 2 × 9 different types of scale-space interest point detectors with respect to the problem of establishing point correspondences between 4 The reason for prefiltering the interest points by position and scale is to prevent the performance measures from being primarily dominated by geometric parameters of the experimental setup. For example, with a relative scaling factor of s > 1 between two images, on average 1 − 1/s 2 of the points in the first image will fall outside the domain of the transformed image if the image size is kept constant as in these experiments.…”