Hessian Corner Detector

[Beaudet, 1978]

Searches for image locations that have a strong change in gradient along both orthogonal directions.

The Hessian matrix captures the second-order derivatives of the image intensity:

$H(x,\sigma )=\left[\begin{array}{cc}{I}_{xx}(x,\sigma )& I_{xy}(x,\sigma )\\ I_{xy}(x,\sigma )& I_{yy}(x,\sigma )\end{array}\right]$

Where:

• $I_{xx}$ is the second-order derivative of the image intensity with respect to x.
• $I_{yy}$ is the second-order derivative of the image intensity with respect to y.
• $I_{xy}$ is the mixed second-order derivative with respect to x and y.
• $(x,\sigma )$ represents the location and scale.

The determinant of the Hessian is used as a measure of cornerness:

$\text{det}(H)=I_{xx}{I}_{yy}-I_{xy}^2$

• Non-maximum suppression: A $3\times 3$ window is used. Only points with a determinant value higher than all 8 neighbors are kept.
• Thresholding: Select points where $\text{det}(H)>\theta$, where $\theta$ is a predefined threshold.

Effect: Responses are mainly on corners and strongly textured areas.