Two dimensional generalized edge detector

Detecting edges in images is one of the most challenging issues in computer vision and image processing due to lack of a robust detector. Gokmen and Jain (1997) have obtained an edge detector called the generalized edge detector (GED), capable of producing most of the existing edge detectors. The original problem was formulated on a two-dimensional hybrid model comprised of the linear combination of membrane and thin-plate functionals. The smoothing problem was then reduced to the solution of two-dimensional partial differential equations (PDE). The filters were obtained for the one-dimensional case assuming a separable solution. This study extends edge detection of images in λτ-space to two-dimensional space. The two-dimensional extension of the representation is important since the properties of images in the space are best modeled by two-dimensional smoothing and edge detector filters. Also since GED filters encompass most of the well-known edge detectors, two-dimensional versions of these filters could be obtained. The derived filters are more robust to noise when compared to the previous one-dimensional filtering scheme in the sense of FOM (figure of merit), missing and false alarm characteristics. Experimental results on synthetic and natural images are presented, including an analysis of the introduced two-dimensional edge detector filters and the behaviour of the detected edges through the λτ-space