Stability of Top-Points in Scale Space

Abstract. This paper presents an algorithm for computing stability of top-points in scale-space. The potential usefulness of top-points in scalespace has already been shown for a number of applications, such as image reconstruction and image retrieval. In order to improve results only reliable top-points should be used. The algorithm is based on perturbation theory and noise propagation

A new tensorial framework for single-shell high angular resolution diffusion imaging

Single-shell high angular resolution diffusion imaging data (HARDI) may be decomposed into a sum of eigenpolynomials of the Laplace-Beltrami operator on the unit sphere. The resulting representation combines the strengths hitherto offered by higher order tensor decomposition in a tensorial framework and spherical harmonic expansion in an analytical framework, but removes some of the conceptual weaknesses of either. In particular it admits analytically closed form expressions for Tikhonov regularization schemes and estimation of an orientation distribution function via the Funk-Radon Transform in tensorial form, which previously required recourse to spherical harmonic decomposition. As such it provides a natural point of departure for a Riemann-Finsler extension of the geometric approach towards tractography and connectivity analysis as has been stipulated in the context of diffusion tensor imaging (DTI), while at the same time retaining the natural coarse-to-fine hierarchy intrinsic to spherical harmonic decomposition. Keywords: Diffusion tensor imaging; High angular resolution diffusion imaging; Orientation distribution function; Riemann-Finsler geometry; Tikhonov regularization

Using multiscale top points in image matching

In this paper we discuss the feasibility of using singular points in a scale space representation (referred to as top points) for image matching purposes. These points are easily extracted from the scale space of an image and they form a compact description of the image. The image matching problem thus becomes a point cloud matching problem. This is related to the transportation problem known from linear optimization and we solve it by using an earth movers distance algorithm. To match points in scale space a distance measure is needed as Euclidean distance no longer applies. In this article we suggest a metric that can be used in scale space and show that it indeed performs better than a Euclidean distance measure. To distinguish between stable and unstable top points we derive a stability norm based on the total variation norm which only depends on the second order derivatives at the top point. To further improve matching results we show that other features at the top points can also increase the accuracy of matching. 1

Object matching in the presence of non-rigid deformations close to similarities

In this paper we address the problem of object retrieval based on scale-space interest points, namely top-points. The original retrieval algorithm can only cope with scale-Euclidean transformations. We extend the algorithm to the case of non-rigid transformations like affine and perspective transformations and investigate its robustness. The proposed algorithm is proven to be highly robust under various degrading factors, such as noise, occlusion, rendering artifacts, etc. and can deal with multiple occurrences of the object