Intuitive understanding of scale-space extrema detection
LoG and DoG (an approximation of LoG) masks can serve as blob detectors. A blob can exist in an image at a number of locations $(x,y)$-coordinates and scales (some parameter; $t$). In some situation where scale space is divided into 3 discrete 'slices' and there are only 'small,' 'medium' and 'large' sized blobs, a 'medium' sized blob will have some response to both the 'small' and 'large' sized detectors. However, a detector whose scale is matched to the scale of the blob will have the largest response.  For this reason, we want to localize the blob by determining the maximum response in both spatial and scale coordinates.