A topological approach for detection of chessboard patterns for camera calibration - Emerging Trends in Image Processing, Computer Vision, and Pattern Recognition - page 441

4 Point Correspondences
The next step of the algorithm associates each vertex to the real coordinates of the patern. This
is done by analyzing the relative position of each corner. First two neighboring triangles of the
same color are arbitrarily selected: T 1 and T 2 . Three vertices make the triangle T 1 , the origin
of the coordinate system is defined by the vertex that has T 2 as its opposite triangle. For the
remaining, vertices are assigned the directions x and y of the Cartesian plane ( Figure 5 ) .

FIGURE 5 Propagation of coordinates. The triangles T 1 and T 2 define the origin and the dir-
ection of coordinates, respectively.

The propagation of coordinates consists in establishing the relative coordinates of the ver-
tices neighbors. Given a triangle T whose vertices have already defined coordinates, where the
origin is v o , v x and v y are the vertices with the x and y directions, respectively. Triangle T v is
defined as a neighbor triangle of T with a different color. If triangles T v and T are neighbors
then they share an edge e and T v has a opposite vertex to T , named v v . The coordinates of the
opposite vertex needs to be determined, thus:

1. If v x ∈ e , then ;

2. If v y ∈ e , then ;
It is understood by v (⋅) the coordinate (⋅) of vertex v . Similarly, T op shares a border e op with

T v , then , where v h is the third vertex of T v and v op is the opposite vertex

to e op .
For each visited triangle, the vertexes coordinates of the current and opposite triangles are
propagated. The algorithm performs recursively for each neighbor triangle to the pair T v and
T op . It makes the algorithm O ( n /2), where n is the number of triangles in the mesh.

5 Location refinement
The x-corner detector, described in Section 2 , identifies the position of corners with low accur-
acy where the only information available is the position of discrete pixels. Since the quality of
the calibration is directly dependent to the precision which the position of features is found,
there is a need for a refinement [ 1 ] .
Traditional algorithms, such as Harris and Stephens detector [ 27 ] and Shi and Tomasi [ 28 ] ,
run throughout the image and use thresholds to select the features of interest. The subpixel
precision is achieved by maximizing functions ited to the square of the intensity proile of the
local neighborhood of each pixel. The threshold has a direct impact on the quality of response
of these detectors, so corners are usually classified as the N pixels with greater response to the
operator.