Continuity of line detection methods based on the Radon transform

The Radon transform is one of the most well-known tools for line detection methods. The drawback of the Radon transform is that it is not continuous. So slight change in an image may lead to a considerable difference in the detection line. This is undesirable. We solve this problem by the modified version of the Radon transform called the d-Radon transform. Several mathematical properties of this modified transform, especially a continuity property of line detection methods, were studied. We focus on a space of image containing several sizes of circles. A metric function on that space is proposed to measure the change of images. By this new transformation, continuity property is obtained.