Color edge detection using the Skellam distribution as a sensor noise model

Conventional edge detectors suffer from inherent image noise and threshold determination. In this paper, we propose a noble edge detector based on the noise distribution for CCD or CMOS cameras. By assuming the dominant photon noise, we model the distribution of intensity differences between two neighborhood pixels. Since it is well known that photon noise follows a Poisson distribution, we introduce a Skellam distribution, which is the difference of two Poisson random variables. We show experimentally that the Skellam distribution can be used to model the noise distribution of pixels that are captured from the same scene radiance. For estimating the noise distribution given a single pixel, we find the important property that the Skellam parameters are linearly related to the intensity value of pixels. This linearity enables us to determine noise parameters according to the intensity value. In addition, parameters of the line are preserved under illumination, scene and camera setting changes except for only a gain change. Based on the noise distributions, we calculate intensity allowances of three channels for each pixel given a confidence interval. We propose a noble edge detector by skipping a pre-processing step of conventional Gaussian smoothing which is the main obstacle for robust and accurate edge detection. If the difference of intensity exceeds the intensity allowance at least in a single channel, the in- between pixel is marked as an edge pixel. We demonstrate that without conventional Gaussian smoothing the noise-model based approach can automatically extract the fine details of image structures, such as edge and corners, independent of camera setting.