Shape detection in images exploiting sparsity

Detection of different kinds of shapes, i.e. lines, circles, hyperbolas etc., in varying kinds of images arises in diverse areas such as signal and image processing, computer vision or remote sensing. The generalized Hough Transform is a traditional approach to detect a specific shape in an image by transforming the problem into a parameter space representation. In this paper we use the observation that the number of shapes in an image is much smaller than the number of all possible shapes. This means the shapes are sparse in the parameter domain. Rather than forming the parameter space from the image as in the HT, we take a reverse approach and ask “which combination of parameter space cells represent my data best?”. This leads us to generate a dictionary of shapes and use additional information about sparsity of shapes within a basis pursuit framework. The results indicate enhanced shape detection performance, increased resolution, joint detection of different shapes in an image and robustness to noise. In addition to this, combining the sparsity of shapes with the Compressive Sensing ideas shows that it is possible to directly find the shapes in an image from small number of random projections of the image without first reconstructing the image itself.