# Scale space

## What's that?

The Gaussian scale space is the set of images L(x,y;s), where the original image I(x,y) is convolved with Gaussians G(x,y;s) at different scales s.

This slide from a talk by Daniela Hall visualizes this:

## Why should we generate such a scale space?

It is useful to help to find the characteristic scale of an image structure!

It was shown that the extrema of the LoG responses (blob filter) to an image give very stable keypoints.

And the LoG can be approximated by the Difference of Gaussians (DoG), i.e., the difference of two scale space images at successive levels in the scale space.

So we can construct a scale space representation for a given image, compute the differences of two successive scale levels and search for maxima/minima, to detect (blob-like) keypoints.

## Charateristic scale

The scale space helps to determine the characteristic scale of an image structure simply by taking the scale s where the Laplacian of Gaussian (a blob filter) has the strongest response: 