Image Processing

Image processing provides the foundation for much work in data analysis. DDMA has made contributions in this area from boundary extraction to de-blurring techniques.

Boundary Finding By Triangulation — by admin — last modified 2007-03-10 03:45

A discussion of Bill Allard’s methods for finding boundaries of shapes by triangulation. This method will allow us to avoid spurious oscillations that may appear for some images in a shape boundary due to the trigonometric polynomial parameterization.

Update on the Analysis of Jets Data, May 2006 — by admin — last modified 2006-12-04 06:23

A summary of our work for Bernie Wilde mid year. In particular, it summarizes our investigation into segmentation techniques. Slides 11-17 show the comparison of k-means, fuzzy c-means, and spatial fuzzy c-means. Slide 18 compares a smoothing operation before k-means (left image) with the output of spatial fuzzy c-means to illustrate the potential extreme effect of preprocessing on subsequent segmentation.

Distinguishing object and background — by admin — last modified 2006-12-04 06:23

A method developed by Tom Asaki to distinguish objects from a background. In these examples, we correct for a low spatial frequency background by removing low frequency components that best minimize the total variation (TV) of the residual. The results show that we can distinguish between object and background because edges contain high frequency components AND are not penalized. The method is not limited to low frequency backgrounds and is robust to noise.

Graduated Adaptive Image Denoising — by admin — last modified 2006-12-04 06:24

Peter F. Schultz, Erik M. Bollt, Rick Chartrand, Selim Esedoğlu and Kevin R. Vixie, "Graduated adaptive image denoising: local compromise between total variation and isotropic diffusion", Submitted., 2005

Carasso Debluring — by admin — last modified 2006-12-04 06:24

A deblurring technique we investigated this year that does an exceptional job of recovering detail.

Numerical differentiation of noisy, nonsmooth data — by Katharine Chartrand — last modified 2007-05-17 15:38

We consider the problem of differentiating a function specified by noisy data. Regularizing the differentiation process avoids the noise amplification of finite-difference methods. We use total-variation regularization, which allows for discontinuous solutions. The resulting simple algorithm accurately differentiates noisy functions, including those which have a discontinuous derivative.