Difference of Gaussians
In imaging science, difference of Gaussians (DoG) is a feature enhancement algorithm that involves the subtraction of one Gaussian blurred version of an original image from another, less blurred version of the original. In the simple case of grayscale images, the blurred images are obtained by convolving the original grayscale images with Gaussian kernels having differing width (standard deviations). Blurring an image using a Gaussian kernel suppresses only high-frequency spatial information. Subtracting one image from the other preserves spatial information that lies between the range of frequencies that are preserved in the two blurred images. Thus, the DoG is a spatial band-pass filter that attenuates frequencies in the original grayscale image that are far from the band center. Mathematics of difference of Gaussians Given an n-dimensional gray-scale image The difference of Gaussians (DoG) of the image is the function obtained by subtracting the image convolved with the Gaussian of standard deviation from the image convolved with a Gaussian of narrower standard deviation : where is a Gaussian with standard deviation : Equivalently one can write which represents an image convolved by the difference of two Gaussians, which approximates a Mexican hat function. The relation between the difference of Gaussians operator