Edge and line detection as exercises in hypothesis testing

In the standard paradigm for edge or line detection matched filters are used to test for the presence of a specified structure. Longer lines are then produced by linking detections; broader lines by filtering at larger scales. The paper proposes an alternative approach based on characterising general linear features as lines along which the distribution of pixel values and/or pixel differences is significantly different from their distribution in the image as a whole. Detection then becomes an exercise in testing the hypothesis that the two distributions are different. For Gaussian distributions the test reduces to computing one or more Radon transforms. Issues of length and scale are now addressed by multiresolution methods: multiresolution implementations of the Radon transform naturally construct longer lines as unions of shorter ones, while broader lines are detected by applying the detection process to the coefficients in each level of a wavelet decomposition of the image.