Biomolecular structure comparison not only reveals evolutionary relationships, but also sheds light on biological functional properties. However, traditional definitions of structure or sequence similarity always involve superposition or alignment and are computationally inefficient. In this paper, I propose a new method called persistent similarity, which is based on a newly-invented method in...

Due to ever more efficient and accurate laser scanning technologies, the analysis of 3D point clouds has become an important task in modern photogrammetry and remote sensing. To exploit the full potential of such data for structural analysis and object detection, reliable geometric features are of crucial importance. Since multiscale approaches have proved very successful for image-based applic...

Thanks to the explosive growth of sensing devices and capabilities, multidimensional (MD) signals — such as images, videos, multispectral images, light fields, and biomedical data volumes — have become ubiquitous. Multidimensional filter banks and the associated constructions provide a unified framework and an efficient computational tool in the formation, representation, and processing of thes...

In this paper, generalized granulometric size distributions and size histograms (a.k.a ‘pattern spectra’) are developed using generalized multiscale lattice operators of the opening and closing type. The generalized size histograms are applied to granulometric analysis of soilsection images. An interesting structure is obtained when the histogram is based on area openings. Furthermore, a fast i...

We introduce multiscale covariance fields associated with probability measures on Euclidean space and use them to define local scales at a point and to construct shape transforms. Local scales at x may be interpreted as scales at which key geometric features of data organization around x are revealed. Shape transforms are used to identify points that are most salient in terms of the local-globa...

In this abstract, we propose a multiscale fusion technique to enhance seismic geometric attributes, such as dip and curvature, which are very sensitive to noise present in seismic data. For a give seismic section, first, we construct a Gaussian pyramid that allows us to generate the seismic attribute at different resolutions (scales). Then, all attributes at the different scales are fused toget...

Coherent Multiscale Image Processing using Quaternion Wavelets by Wai Lam Chan This thesis develops 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 phases: two phases encode local image shifts while the third contains textural informati...

With the ever increasing computational power of modern day processors, it has become feasible to use more robust and computationally complex algorithms that increase the resolution of images without distorting edges and contours. We present a novel image interpolation algorithm that uses the new contourlet transform to improve the regularity of object boundaries in the generated images. By usin...

We develop a novel geometric multiresolution analysis for analyzing intrinsically low dimensional point clouds in high-dimensional spaces, modeled as samples from a d-dimensional set M (in particular, a manifold) embedded in R, in the regime d D. This type of situation has been recognized as important in various applications, such as the analysis of sounds, images, and gene arrays. In this pape...