Computational and Applied Math Proseminar

Thursday, February 14, 12:15 p.m. PSA 206

Rishu Saxena

Dept Math & Stats

High-Order Edge Detection from Scattered Data

Abstract
Detection of edges in piecewise smooth functions is important in many applications such as image processing, computer vision and seismology. Unfortunately, most of the algorithms available until recently are first order and depend on external factors such as the choice of appropriate filters and thresholds. Further, their use is mostly limited to digital images. On the other hand, extensive research has been done for high order methods in the Numerical Partial Differential Equations community.

The polynomial annihilation edge detection method (Archibald, Gelb and Yoon, 2005) was the first attempt to make edge detection a high order venture from physical data. The method has several advantages over already existing methods, the most important being that it is applicable to multi-dimensional scattered data. This talk discusses the polynomial annihilation edge detection method and then expands it for several applications, as needed not only in the field of image processing, but also in a broad range of other applications including determining edges in derivatives of functions for post processing partial differential equations as well as determining discontinuities in greater than three dimensions which arise in stochastic partial differential equations. The focus of this study is on functions that are continuous but not smooth and are irregularly sampled.

For further information please contact: mittelmann@asu.edu