We present a new method for discrimination of data classes or data sets in a high-dimensional space. Our
approach combines two important relatively new concepts in
high-dimensional data analysis, i.e., Diffusion Maps
and Earth Mover's Distance, in a novel manner so that it is more tolerant to noise and honors the characteristic
geometry of the data. We also illustrate that this method can be used for a variety of applications in high
dimensional data analysis and pattern classification, such as quantifying shape deformations and discrimination
of acoustic waveforms.
This work is devoted to new computational models for image segmentation, image restoration and image decomposition. In particular, we partition an image into piecewise-constant regions using energy minimization and curve evolution approaches. Applications of denoising-segmentation in polar coordinates (motivated by impedance tomography) and of segmentation of brain images will be presented. Also, we decompose a natural image into a cartoon or geometric component and an oscillatory or texture component using a variational approach and dual functionals. Thus, new computational methods will be presented for denoising, deblurring and texture modeling.