Computer Vision: Why is Gaussian Filter used in SIFT algorithm?

Talking in general about scale-spaces, the ideas behind scale-space are (from [1])- 1. Fine-scale structures should be successively suppressed 2. Structures at coarser scales should be more generalized representations of structures occurring at finer scales. 3. Importantly, structures at coarser scales should not be an 'accidental' result of suppressing fine-scale structures. If you think about a kernel that does all this for you, a Gaussian kernel would be an obvious and a simple choice. All you have to do is use Gaussian kernels of increasing variance, and you will successively suppress fine-scale structures without creating any accidental artifacts along the way. But that's not all. In SIFT, using Gaussian kernels gives us one more advantage that saves a lot of computation (from [2])- We want to find out points in the image that will give is most stable features. It has been shown that the maxima and minima of the scale-space normalized Laplacian of Gaussian function convolved with the image give us more stable features than a lot of other possible functions such as gradient, Hessian or Harris corners. The solution of the heat diffusion equation (you read it right, heat!) suggests that a difference of Gaussian function is a very close approximation to the Laplacian of Gaussian (if you are interested in the proof check out [1]). So why not use that and kill two birds with one stone? Let me elaborate- Say we create our scale space by convolving our image with Gaussians of different variances. The Difference of Gaussian (DoG) function is nothing but the difference of two successive scale-space representations of the image, divided by the difference in their scales. So we already have the DoG function calculated when we make our scale space (if we make our scale space with Gaussians). As you might have guessed by now, we can simply use this DoG function as an approximation to the scale-space normalized Laplacian of Gaussian, take the DoG's maxima and minima, and therefore, get points where SIFT features will be the most stable. This is a great computational advantage. And hence, Gaussians rule once again! Reference- [1] Tony Lindeberg: "Scale-space: A framework for handling image structures at multiple scales" [2] David G. Lowe: "Distinctive image features from scale-invariant keypoints"

Gaussian filters are used to degenerate noise on image solely or make the image smaller as keeping its pixels as uniform as possible. If you don't use Gaussian while reducing the size some shiny pixels will be occurred. That amiss case can be seen on older image processing tools. General procedure is to applying Gaussian filter to image with some degree setting by a parameter. Than taking some sample pixels for each same range and in that way you re getting smaller image.