Harris corner detector

A response function R = det(M) - k*trace(M)^2, built from a window's own gradient products, that classifies a pixel flat/edge/corner with no eigensolver required.

Built from the structure tensor $M=\sum_{(x,y)\in W}\begin{bmatrix}I_x^2 & I_xI_y\\ I_xI_y & I_y^2\end{bmatrix}$ (Chapter 5's own Sobel-derived gradients $I_x,I_y$ , summed over a small window $W$ ), the Harris response is $R=\det(M)-k\,\operatorname{trace}(M)^2$ , with $k$ an empirical sensitivity constant (typically $0.04$ - $0.06$ ). Since $\det(M)=\lambda_1\lambda_2$ and $\operatorname{trace}(M)=\lambda_1+\lambda_2$ for $M$ 's own eigenvalues $\lambda_1,\lambda_2\ge0$ , a small trace classifies the window flat, a large trace with $R<0$ (one eigenvalue much larger than the other) classifies it an edge, and a large trace with $R>0$ (both eigenvalues large and comparable) classifies it a corner -- without ever solving for $\lambda_1,\lambda_2$ directly.