DoGsigma1sigma2I

DoGsigma1sigma2I refers to the Difference of Gaussians operation applied to an image I, using two Gaussian blur kernels with standard deviations sigma1 and sigma2. It is commonly used in image processing to highlight features at a specific range of spatial scales and to serve as a simple, efficient edge and blob detector.

Mathematically, DoG_sigma1_sigma2(I) is defined as the difference between two Gaussian-blurred versions of I: DoG_sigma1_sigma2(I) = G_sigma1 * I − G_sigma2 * I, where * denotes convolution and G_sigma is the Gaussian kernel with standard deviation sigma. For two-dimensional images, this is typically computed by applying Gaussian blur in both directions. Practically, the Gaussian blur can be implemented efficiently as a separable 2D filter.

DoG is an approximation to the Laplacian of Gaussian (LoG). By choosing sigma2 relative to sigma1 (commonly with sigma2 ≈ k * sigma1, where k ~ 1.5–2, and a common value around 1.6 in scale-space methods), the DoG emphasizes structures whose sizes fall between the two scales. This makes it useful for multi-scale feature detection and noise suppression.

Applications include blob and edge detection, feature detection in computer vision, and as a component in scale-space pipelines such as the DoG pyramid used in keypoint detectors like SIFT. The method is simple, fast, and widely used due to its effectiveness across a range of imaging contexts. Related concepts include Gaussian blur, LoG, and scale-space representations.