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.