In this paper we present a generalization of geometric moments in scale-spaces derived from the general heat diffusion equation, with a particular interest for the min/max flow. As an application of those theoretical developments, two multiscale moments are used to enhance the classical Euclidean registration process. They are computed from a multiscale representation which preserves the global...

The paper is a short tutorial on the multiscale differential geometric possibilities of the front-end visual receptive fields, modeled by Gaussian derivative kernels. The paper is written in, and interactive through the use of Mathematica 4, so each statement can be run and modified by the reader on images of choice. The notion of multiscale invariant feature detection is presented in detail, w...

Large data sets are often modeled as being noisy samples from probability distributions μ in R, withD large. It has been noticed that oftentimes the supportM of these probability distributions seems to be well-approximated by low-dimensional sets, perhaps even by manifolds. We shall consider sets that are locally well approximated by k-dimensional planes, with k ≪ D, with k-dimensional manifold...

The analysis and detection of edges and interface boundaries is a fundamental problem in applied mathematics and image processing. In the study of the wave equation, for example, one is interested in the evolution of moving fronts; in image processing and computer vision, the detection and analysis of edges is an essential task for applications such as shape recognition, image enhancement and c...

We present an automated system that we have developed for estimation of the bioecological quality of soils using various image analysis methodologies. Its goal is to analyze soilsection images, extract features related to their micromorphology, and relate the visual features to various degrees of soil fertility inferred from biochemical characteristics of the soil. The image methodologies used ...

In this paper, a multiscale virtual particle based elastic network model (MVP-ENM) is proposed for biomolecular normal mode analysis. The multiscale virtual particle model is proposed for the discretization of biomolecular density data in different scales. Essentially, the model works as the coarse-graining of the biomolecular structure, so that a delicate balance between biomolecular geometric...

In a recent paper, we have proposed a novel theory that extends connectivity to a multiscale framework. Although we have presented several examples, we have not provided a systematic approach for constructing multiscale connectivities. In this paper, we introduce three general techniques for constructing multiscale connectivities. The first two start from a given base connectivity and produce m...

The richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency and complexity, while achieving accurate rendering of smooth regions as well as reproducing faithful contours and textures. The most recent ones, proposed i...