Affine Adaptation of Local Image Features Using the Hessian Matrix

Local feature detectors that make use of derivative based saliency functions to locate points of interest typically require adaptation processes after initial detection in order to achieve scale and affine covariance. Affine adaptation methods have previously been proposed that make use of the second moment matrix to iteratively estimate the affine shape of local image regions. This paper shows that it is possible to use the Hessian matrix to estimate local affine shape in a similar fashion to the second moment matrix. The Hessian matrix requires significantly less computation effort to compute than the second moment matrix, allowing more efficient affine adaptation. It may also be more convenient to use the Hessian matrix, for example, when the Determinant of Hessian detector is used. Experimental evaluation shows that the Hessian matrix is very effective in increasing the efficiency of blob detectors such as the Determinant of Hessian detector, but less effective in combination with the Harris corner detector.