Why is scale space (DoG) needed to detect scale invariant features?

1. How we achieve the scale invariant when computing SIFT features?
2. What is scale space extrema detection?
3. What is scale invariant in image processing?
4. What is scale space in SIFT?

How we achieve the scale invariant when computing SIFT features?

The response of a derivative of Gaussian filter to a perfect step edge decreases as σ increases. To keep response the same(scale-invariant), must multiply Gaussian derivative by σ. Laplacian is the second Gaussian derivative, so it must be multiplied by σ2.

What is scale space extrema detection?

Scale-Space Extrema Detection

To detect the local maxima and minima of D(x, y, σ) each point is compared with its 8 neighbours at the same scale, and its 9 neighbours up and down one scale. If this value is the minimum or maximum of all these points then this point is an extrema.

What is scale invariant in image processing?

Scale-Invariant Feature Transform (SIFT)—SIFT is an algorithm in computer vision to detect and describe local features in images. It is a feature that is widely used in image processing. The processes of SIFT include Difference of Gaussians (DoG) Space Generation, Keypoints Detection, and Feature Description.

What is scale space in SIFT?

Scale spaces in SIFT

SIFT takes scale spaces to the next level. You take the original image, and generate progressively blurred out images. Then, you resize the original image to half size. And you generate blurred out images again.