Freeman and Davis FD77

Corner strength. In a point $i$, the angle between the $x$-axis and the backward $k$-vector defined in (2) is given as

$$\theta_{ik} = \begin{cases} \tan^{-1}{({\Ybik{i}{k}}/{\Xbik... ...({\Xbik{i}{k}}/{\Ybik{i}{k}})} & \text{otherwise}, \end{cases}$$

The incremental curvature is then defined as

$$\delta_{ik} = \theta_{i+1,k} - \theta_{i-1,k}$$ (4)

Finally, the $k$-strength in $i$ is computed as

$$S_{ik} = \ln{t_1} \cdot \ln{t_2} \cdot \sum\limits_{j=i}^{i+k}\delta_{jk}$$ (5)

where
$$\begin{align*}t_1 &= \max{\{t:\delta_{i-v,k} \in (-\Delta,\Delta), \forall~1 \le... ...:\delta_{i+k+v,k} \in (-\Delta,\Delta), \forall~1 \leq v \leq t \}} \end{align*}$$
account for the effect of the forward and backward arms as the maximum spacings (numbers of steps from $i$) that still keep the incremental curvature $\delta_{ik}$within the limit $\pm \Delta$. The latter is set as

$$\Delta = \arctan{\frac{1}{k-1}}$$ (6)

Selection procedure. A point $i$ is selected as a corner if $S_{ik}$ exceeds a given threshold $S$ and individual corners are separated by a spacing of at least $k+1$ steps.
Parameters. The two parameters are the spacing $k$ and the corner strength threshold $S$. The default values are $k=5$ and $S=1500$.