The Bidirectional Texture Function (BTF) is the recent most advanced representation of visual properties of surface materials. It specifies their appearance due to varying spatial, illumination, and viewing conditions. Corresponding enormous BTF measurements require a mathematical representation allowing extreme compression but simultaneously preserving its high visual fidelity. We present a no...

This paper presents a review of spectral decomposition of seismic data, since it's inception nearly in 1997. It discusses various techniques and applications of spectral decomposition in seismic data processing and interpretation. It is also known as timefrequency analysis consists of transforming non stationary signal in time/space from time/space domain to time/space vs frequency domain. The ...

Similarity matrix is critical to the performance of spectral clustering. Mercer kernels have become popular largely due to its successes in applying kernel methods such as kernel PCA. A novel spectral clustering method is proposed based on local neighborhood in kernel space (SC-LNK), which assumes that each data point can be linearly reconstructed from its neighbors. The SC-LNK algorithm tries ...

n many applications of color technology such as spectral color reproduction, it is of interest to represent the spectral data with lower dimensions than spectral space dimensions. It is more than half of a century that Principal Component Analysis (PCA) method has been applied to find the number of independent basis vectors of spectral dataset and representing spectral reflectance with lower di...

We offer a spectral analysis for a class of transfer operators. These transfer operators arise for a wide range of stochastic processes, ranging from random walks on infinite graphs to the processes that govern signals and recursive wavelet algorithms; even spectral theory for fractal measures. In each case, there is an associated class of harmonic functions which we study. And in addition, we ...

This paper addresses the problem of mixing spectral bands and space in a smooth, linear, and casual manner. Such properties are of fundamental importance for many basic multi-spectral-image processing algorithms that probe inter-spectral structure. The example of color images is used in a simple spectral perspective. An example is given comparing the deep structure of the color and the gray gra...

Spectral image analysis problems often begin by applying a transformation that generates an alternative representation of the spectral data with the intention of exposing hidden features not discernable in the original space. We introduce and demonstrate a transformation based on a Markov-chain model of a random walk on a graph via application to spectral image clustering. The random walk is qu...

According to [9, 8], the initial datum of noncommutative differential geometry is a spectral triple (A,H, D) (see Section 3.1 for the definition), which provides a description of the corresponding geometrical space in terms of spectral data of geometrical operators on this space. The purpose of this paper is to construct spectral triples given by transversally elliptic operators with respect to...