Image matching using generalized scale-space interest points

Tony Lindeberg

Journal of Mathematical Imaging and Vision, volume 52, number 1, pages 3-36, 2015.

Digitally published with DOI:10.1007/s10851-014-0541-0 in October 2014.


The performance of matching and object recognition methods based on interest points depends on both the properties of the underlying interest points and the choice of associated image descriptors. This paper demonstrates advantages of using generalized scale-space interest point detectors in this context for selecting a sparse set of points for computing image descriptors for image-based matching.

For detecting interest points at any given scale, we make use of the Laplacian, the determinant of the Hessian and four new unsigned or signed Hessian feature strength measures, which are defined by generalizing the definitions of the Harris and Shi-and-Tomasi operators from the second moment matrix to the Hessian matrix. Then, feature selection over different scales is performed either by scale selection from local extrema over scale of scale-normalized derivates or by linking features over scale into feature trajectories and computing a significance measure from an integrated measure of normalized feature strength over scale.

A theoretical analysis is presented of the robustness of the differential entities underlying these interest points under image deformations, in terms of invariance properties under affine image deformations or approximations thereof. Disregarding the effect of the rotationally symmetric scale-space smoothing operation, the determinant of the Hessian is a truly affine covariant differential entity and two of the new Hessian feature strength measures have a major contribution from the affine covariant determinant of the Hessian, implying that local extrema of these differential entities will bemore robust under affine image deformations than local extrema of the Laplacian operator or the two other new Hessian feature strength measures.

It is shown how these generalized scale-space interest points allow for a higher ratio of correct matches and a lower ratio of false matches compared to previously known interest point detectors within the same class. The best results are obtained using interest points computed with scale linking and with the new Hessian feature strength measures and the determinant of the Hessian being the differential entities that lead to the best matching performance under perspective image transformations with significant foreshortening, and better than the more commonly used Laplacian operator, its difference-of-Gaussians approximation or the Harris-Laplace operator.

We propose that these generalized scale-space interest points, when accompanied by associated local scale-invariant image descriptors, should allow for better performance of interest point based methods for image-based matching, object recognition and related visual tasks.

PDF: (11.9 Mb)

On-line version: (At the official site of JMIV)

Background and related material: (Earlier conference paper on this topic at SSVM 2013) (Theoretical analysis of scale selection properties of generalized scale-space interest points) (Tutorial article on the use of Laplacian interest points and their difference of Gaussians approximation for computing locally scale adapted SIFT descriptors) (Earlier paper on Laplacian and determinant of the Hessian interest points with automatic scale selection)

Responsible for this page: Tony Lindeberg