Multiscale Edge Detection using a Finite Element Framework for Hexagonal Pixel-based Images

In recent years the processing of hexagonal pixel-based images has been investigated, and as a result, a number of edge detection algorithms for direct application to such image structures have been developed. We build on this research by presenting a novel and efficient approach to the design of hexagonal image processing operators using linear basis and test functions within the finite element framework. Development of these scalable first order and Laplacian operators using this approach presents a framework both for obtaining large-scale neighbourhood operators in an efficient manner and for obtaining edge maps at different scales by efficient reuse of the 7-point Linear operator. We evaluate the accuracy of these proposed operators and compare the algorithmic performance using the efficient linear approach with conventional operator convolution for generating edge maps at different scale levels.