Edge detection based on the Multiresolution Fourier Transform

In this work, an edge detection technique is proposed by using the Multiresolution Fourier Transform (MFT) to analyze the local properties in the spatial frequency domain. Five major steps are adopted to implement the detection of edges. First, the Laplacian Pyramid method is used to create a high-pass filtered image. Secondly, the Multiresolution Fourier Transform (MFT) is applied to divide the high-pass filtered image into blocks and transform each of the blocks into spatial frequency domain. Thirdly, single-feature and non-single-feature blocks are differentiated. Subsequently, the blocks containing single feature are then subject to a process for estimating the orientation and the centroid of the feature in order to locate it. Finally, the accuracy of the estimated centroid of the local feature is checked. Once all the blocks are analyzed at a resolution level, the overall procedure is repeated at the next resolution level and the blocks with their father block being classified as non-single-feature or being rejected in the accuracy check stage at the previous level are analyzed. The algorithm stops when a specific level is reached.