A Total Variation-Morphological Image Edge Detection Approach

We present image edge detection using the total variation functional and morphological methods. First, we derive the total variation functional from first principles and vector gradient method. The total variation functional is then minimized using the Euler-Lagrange optimization method. The steady state equation which results from the minimization of the total variation functional is then used as an anisotrpic filter on images. While the total variation method has proven to be a better edge detector than the Marr-Hildreth method, it also segments the image into regions delineated by strong edges. To achieve results similar to the Marr-Hildreth method, we apply morphological considerations. We develop new operations based on erosion, dilation, opening and closing to achieve morphological edge detection of total variation filtered images.