Hessian affine region detector

The Hessian affine region detector is a feature detector used in the fields of computer vision and . Like other feature detectors, the Hessian affine detector is typically used as a preprocessing step to algorithms that rely on identifiable, characteristic interest points. The Hessian affine detector is part of the subclass of feature detectors known as affine-invariant detectors: Harris affine region detector, Hessian affine regions, maximally stable extremal regions, Kadir–Brady saliency detector, edge-based regions (EBR) and intensity-extrema-based (IBR) regions. The Hessian affine detector algorithm is almost identical to the Harris affine region detector. In fact, both algorithms were derived by Krystian Mikolajczyk and Cordelia Schmid in 2002, based on earlier work in, see also for a more general overview. The Harris affine detector relies on interest points detected at multiple scales using the Harris corner measure on the second-moment matrix. The Hessian affine also uses a multiple scale iterative algorithm to spatially localize and select scale and affine invariant points. However, at each individual scale, the Hessian affine detector chooses interest points based on the Hessian matrix at that point: where is second partial derivative in the direction and is the mixed partial second derivative in the and directions. It's important to note that the derivatives are computed in the current iteration scale and thus are derivatives of an image smoothed by a Gaussian kernel: . As discussed in the Harris affine region detector article, the derivatives must be scaled appropriately by a factor related to the Gaussian kernel: . At each scale, interest points are those points that simultaneously are local extrema of both the determinant and trace of the Hessian matrix. The trace of Hessian matrix is identical to the Laplacian of Gaussians (LoG): As discussed in Mikolajczyk et al.(2005), by choosing points that maximize the determinant of the Hessian, this measure penalizes longer structures that have small second derivatives (signal changes) in a single direction.