Line detection in images through regularized Hough transform

The problem of determining the location and orientation of straight lines in images is often encountered in the fields of computer vision and image processing. Traditionally the Hough transform has been widely used to solve this problem for binary images, due to it´s simplicity and effectiveness. In this paper we pose the problem of detecting straight lines in gray-scale images as an inverse problem. We treat the input image as noisy observations, which are related to the underlying transform domain image through the inverse Hough transform operator. We then regularize this inverse problem using constraints that accentuate peaks in the Hough parameter space. We present four different forms of such constraints and demonstrate their effectiveness. Finally we show how our scheme can be alternatively viewed as one of finding an optimal representation of the image in terms of elements chosen from a redundant dictionary of lines, and thus is a form of adaptive signal representation