We have developed tools for analysis of 3-D volumetric data which allow sensitive characterizations of point clouds containing filamentary structures. Our approach involves multiscale X-ray transforms of the data volume. The idea is that cubes of all different locations and scales are extracted from the data volume and then analyzed by integrating along lines (X-Rays) of all different orientati...

As a novel multiscale geometric analysis tool, sparse representation has shown many advantages over the conventional image representation methods. However, the standard sparse representation does not take intrinsic structure and its time complexity into consideration. In this paper, a new fusion mechanism for multimodal medical images based on sparse representation and decision map is proposed ...

study of the potential fields at different altitudes, constituting a multiscale field is a class of interpretative methods which are used to approximate depth and geometry of sources. interpretation of potential fields by this class of methods is mainly based on the recognition that the gravity or magnetic fields, generated by ideal sources (point mass, line of mass, sheet and contact) are homo...

he Artificial Visual System (AVS) (Figure 1) ~mputational framework for computer vision. [1] n AVS convolves an image with a series of D mtial filters, yielding a series of D filtered aages. While any set of filters can be applied in ds way, families of filters can be designed to .~oduce a compact, task-specific decomposition or a meral, task-independent decomposition of the aage. The filter se...

This paper focuses on the geometric modeling and computational algorithm development of biomolecular structures from two data sources: Protein Data Bank (PDB) and Electron Microscopy Data Bank (EMDB) in the Eulerian (or Cartesian) representation. Molecular surface (MS) contains non-smooth geometric singularities, such as cusps, tips and self-intersecting facets, which often lead to computationa...

Large data sets arise in a wide variety of applications and are often modeled as samples from a probability distribution in high-dimensional space. It is sometimes assumed that the support of such probability distribution is well approximated by a set of low intrinsic dimension, perhaps even a lowdimensional smooth manifold. Samples are often corrupted by high-dimensional noise. We are interest...

We develop a quaternion wavelet transform (QWT) as a new multiscale analysis tool for geometric image features. The QWT is a near shift-invariant, tight frame representation whose coefficients sport a magnitude and three phase values, two of which are directly proportional to local image shifts. The QWT can be efficiently computed using a dual-tree filter bank and is based on a 2-D Hilbert tran...

Geometric modeling of biomolecules plays an essential role in the conceptualization of biolmolecular structure, function, dynamics, and transport. Qualitatively, geometric modeling offers a basis for molecular visualization, which is crucial for the understanding of molecular structure and interactions. Quantitatively, geometric modeling bridges the gap between molecular information, such as th...