Line and circle detection using dense one-to-one Hough transforms on greyscale images

By estimating the first-order (direction) and second-order (curvature) derivatives in an image, the parameters of a line or circle passing through a point may be uniquely defined in most cases. This allows to compute a one-to-one Hough transform, every point in the image space voting for one unique point in the parameter space. Moreover, those parameters can be directly estimated on the greyscale image without the need to calculate the contour and without reducing the spatial support of the Hough transform, i.e. densely on the whole image. The general framework using multiscale derivatives is presented, and the one-to-one Hough dense transforms for detecting lines and circles are evaluated and compared with other variants of Hough transforms, from qualitative and computational points of view.