A topological approach for detection of chessboard patterns for camera calibration - Emerging Trends in Image Processing, Computer Vision, and Pattern Recognition - page 442

Chen and Zhang [ 4 ] propose a new detector specially designed to fit x-shaped corners. Con-
sidering the neighborhood of a pixel as a surface, its Hessian matrix can be expressed as:
(3)
where I xx , I xy , and I yy are the second partial derivatives of pixel I ( x , y ). Thus, the x-corner detect-
or is described as:
(4)
where λ 1 and λ 2 are the Eigen values of H .
In order to avoid unnecessary computation, this operator is only applied in regions deined
by the valid vertices of triangle mesh. The real x-corner is the pixel with largest negative value
of S and the refined coordinates [ x 0 + s , y 0 + t ] T is given by:
(5)
6 Experimental Results
In this section, the detector response is evaluated considering an image database and by means
of experimental tests with two different cameras. The image database is provided by the tool-
box for MATLAB prepared by Bouguet [ 12 ] . This database consists of 20 images of a chess-
board calibration patern, accounting 156 x-corners arranged as 12 × 13 matrix, being presen-
ted in different orientations. This set represents a common situation to most of systems where
the patern images are irst captured and calibration is performed in an of-line manner.
Figure 6 shows some examples of these images and Table 1 summarizes the results obtained
for each one. The results are generated by applying the algorithm in each image and counting
the number of corners identified. Analyzing Table 1 , the vast majority of points is detected.