Difference of Gaussians
The difference of gaussian (DOG) is the convolution of input image by difference of two gaussians usually with different standard devitations($\sigma$). The basic idea behind this is to capture edges or gradients in the images that are simplified by the gaussian with larger $\sigma$  but preserved by the smaller gaussian. This is form of scale space derivative, which basically analyses different frequency components in the image, by changing the $\sigma$s  of gaussians. Thus, its like a band-pass filter that rejects certain frequencies in the input.

If we consider an constant image with its value centered around the means of the gaussians, the result of the DOG would be a zero - indicating no gradient.Try this out for a basic tutorial.