Why do we need to construct Gaussian pyramid using SIFT detector
Actually, the purpose of all this is to approximate a Laplacian of Gaussian!
This computation is part of the corner detection of SIFT. You can find corners by examining extrema of the Laplacian of Gaussians (2nd order derivative). You use Gaussians for denoising, and a Laplacian to find inflection points. However, it is classical to not deal directly with computing this second order derivative, but to approximate it instead by difference of Gaussians for simplicity. This is sometimnes referred to as Gaussian blob detection.
You can find some illustration of this process here.
With this approach your difference of Gaussians (DoG) will have a fixed (small) size in pixels, so you're bounding the computational cost. But you still want to detect blobs of different sizes (because objects have varyng size,s, and the camera can be closer or further away from the scene), and you achieve this by &quot;zooming out the image&quot; with the various scales of the pyramid and keeping the DoG size fixed, instead of keeping the original image size and changing the size of your blob detector.