Defect detection in patterned wafers using anisotropic kernels
Machine Vision and Applications
A Bias-Variance Approach for the Nonlocal Means
SIAM Journal on Imaging Sciences
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In the first part of this thesis, we study the use of anisotropic diffusions on datasets as a tool for signal processing and machine learning. We modify the geometry of the data by adding feature coordinates derived from a function or set of functions which are to be studied. The anisotropic diffusion on the data is just the isotropic diffusion on its modification. We thus transfer some of the complexity of the functions to the geometry of the dataset. This gives a notion of smoothness on the dataset which is adapted to the function(s) under study. We show applications to image denoising and semi-supervised learning problems. In the second part, we study the construction of local and multiscale bases on datasets which are adapted to dyadic partitions of the dataset. Some progress is made towards generalizing the local cosines construction from R . Simpler constructions, like the Haar basis, or block local cosines, generalize easily, and we show applications of the use of these bases in the analysis of functions on datasets and image denoising.