Blob Detection - The Determinant of The Hessian

The Determinant of The Hessian

By considering the scale-normalized determinant of the Hessian, also referred to as the Monge–Ampère operator,

where denotes the Hessian matrix of and then detecting scale-space maxima of this operator one obtains another straightforward differential blob detector with automatic scale selection which also responds to saddles (Lindeberg 1994, 1998)

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The blob points and scales are also defined from an operational differential geometric definitions that leads to blob descriptors that are covariant with translations, rotations and rescalings in the image domain. In terms of scale selection, blobs defined from scale-space extrema of the determinant of the Hessian (DoH) also have slightly better scale selection properties under non-Euclidean affine transformations than the more commonly used Laplacian operator (Lindeberg 1994, 1998). In simplified form, the scale-normalized determinant of the Hessian computed from Haar wavelets is used as the basic interest point operator in the SURF descriptor (Bay et al. 2006) for image matching and object recognition.