MULTIPLE WIDTHS YIELD RELIABLE FINITE-DIFFERENCES

This paper introduces a new finite difference edge finder in which each finite difference is computed at a range of widths, i.e., a range of distances between data points. Although narrow operators are best for describing detailed texture, wide operators report low-amplitude responses more reliably. Thus, if wide operators are used to fill gaps in narrow operator responses, each operator can be restricted to report only statistically reliable responses without losing many real features. This sharply reduces the noise in the final output. The paper presents theoretical bounds on spurious responses in the finite difference outputs, given only weak assumptions about the signal and noise. The expected response of the edge finder to an ideal straight step edge is also analyzed. These performance measures are compared with those of a standard algorithm based on Gaussian smoothing and those of a second new algorithm that also considers the spatial structure of noise. The new algorithms prove equally good at suppressing noise but are better able to detect faint or blurred features. These predictions are confirmed by empirical tests on real images using empirical measurements of camera noise.