A topological approach for detection of chessboard patterns for camera calibration - Emerging Trends in Image Processing, Computer Vision, and Pattern Recognition - page 439

This detector can be seen as a specification of the detector proposed in Rosten and Drum-
mond [ 20 ] , which is considered very fast. Since only a small portion of the neighborhood of
the pixel is analyzed, the computational cost is reduced. Other similar detectors can be found
in Zhao et al. [ 17 ] and Sun et al. [ 21 ]. Figure 2 shows a typical result of this detector over a
chessboard image.
FIGURE 2 X-corner detector response. Light pixels define found corner positions in the im-
age.
Equation (1) does not guarantee that only one pixel is classified as a x-corner in its neigh-
borhood. To deal with this problem, the cost described by Equation (2) is associated with each
corner and a nonmaximum suppression is performed [ 22 ] .
(2)
The classes dark and light contains the dark and light pixels, respectively. The right corner is
the one with the highest associated cost.
3 Topological filter
The identification of valid corners is an important step because not all x-corners present in the
image belong to the calibration patern. In this work, the identiication of valid x-corners is
made considering the regularity neighborhood of the chessboard image. This problem can be
extended to the task of creating geometric meshes in computer graphics. In a mesh composed
of basic components such as triangles, vertices are connected according to their neighborhood
[ 23 ] .
The Delaunay triangulation is a classic problem in computational geometry. Given a set of
points in a plane, the only valid triangulation is one where the circumcircle of each triangle
contains no other vertex [ 24 ] . This constraint ensures that the triangles are formed by the more
closely vertexes. The mesh allows to define the neighborhood of each point. Figure 3 gives an
example of this triangulation. Guibas et al. [ 25 ] present an algorithm for incremental triangu-
lation that runs in time O ( n log( n )).