Curve and corner extraction using the multiresolution Fourier transform

The problem of identifying boundary contours or line structures is an important component in many applications of image analysis and computer vision. The multiresolution Fourier transform (MFT), a `local spectral´ model of line and edge features uses a Markov process defined in the Fourier domain and gives both estimates of the feature parameters and a measure of how well the feature models the data. Use of the MFT allows any arbitrarily compact region to be represented independently of what is present outside of it, and thus an appropriate scale can be chosen for any feature in the image. The work described is an extension of these ideas, in which a given region can contain multiple straight line or edge features or a circular curve segment. The processing takes place entirely within the framework of the MFT and does not require separate edge detection processes, while the resolution of feature parameters is primarily limited by noise and does not affect the computational complexity, as happens with the Hough transform. Because the modelling is performed using an invertible transform it is possible to measure the model error and, if required, produce an approximation of the image based upon the estimated parameters. A method of combining these simple features into more complex curves is also described. The new method is shown to be effective in segmenting a variety of synthetic and natural images