# Which image for DoG filter?

I am studying computer vision and have some trouble with difference of Gaussian filter.

We apply Gaussian filters with different values of sigma on original image then subtracting from them.

However, Gaussian filter blurs image, so some edge might not be identified.

• Why could we use DoG?
• How effective is DoG?
• Which type of images work best for this filter?

The above impulse filter can be seen as the limit of a Gaussian filter whose $\sigma$ tends to $0$.
The DoG filter somehow generalizes the described old edge-enhancement technique, with a pair of blurring filters. Perhaps surprisingly, two blurs, when subtracted, can sharpen edges. The resulting filter acts as a pass-band with appropriate $\sigma_k$ kernel ratios.