Summary of four corner detectors

In this section we give a brief summary of the four alternative corner detection algorithms used in our comparative tests. The summary is based on the survey [4]. Each algorithm inputs a chain-coded curve that is converted into a connected sequence of grid points $\ipt{i}=(x_i,y_i)$, $i=1,2\ldots ,N$. A measure of corner strength (`cornerity') is assigned to each point, then corner points are selected based on this measure. For each approach, we summarize these two main steps and list the parameters of the algorithm and their default (`best') values. Setting of the parameters is discussed in more detail in section 4.

When processing a point $\ipt{i}$, the algorithms consider a number of subsequent and previous points in the sequence, as candidates for the arms of a potential corner in $\ipt{i}$. For a positive integer $k$, the forward and the backward $k$-vectors at point $\ipt{i}$ are defined as

  

$$\aik{i}{k} = (x_i-x_{i+k},y_i-y_{i+k}) = (\Xaik{i}{k}, \Yaik{i}{k})$$ (1)

$$\bik{i}{k} = (x_i-x_{i-k},y_i-y_{i-k}) = (\Xbik{i}{k}, \Ybik{i}{k})$$ (2)

where $\Xaik{i}{k}$, $\Yaik{i}{k}$ and $\Xbik{i}{k}$, $\Ybik{i}{k}$ are the components of $\aik{i}{k}$ and $\bik{i}{k}$, respectively.