Robust and Accurate Calibration Point Extraction with Multi-scale Chess-Board Feature Detector - Advances in Image and Graphics Technologies - page 158

Fig. 8. Vertices detected

3 . 1.4 Speed-Up Strategy
We propose two strategies to speed up the detection scheme. Instead of constructing
our detector over every pixel of the image, we consider those positions where sobel
responses are relatively high. Anyway, the threshold should be low enough to not risk
eliminating the accurate positions of the vertices when blurring exists. Down-sampling
the image can notably accelerate the computation, but an additional step to find the
accurate positions of the vertices in the original image should be added.

3.2 Mapping the Vertices to 3D Board

After the vertices are detected, we must find out their locations in the 3D board before
camera calibration. As shown in Fig. 9 , the vertices form 12 lines along the periphery
of the marker and each 3 lines make up a group. Usually at most two groups are in-
visible because of the occlusion of the objects, so we have at least two intersecting
groups to locate an ID in the corner of the board. Hough transform [14] is the most
widely used method when dealing with line fitting problems, but it is at great disad-
vantage when there's remarkable camera distortion. Inspired by [6], we design a bidi-
rectional growth algorithm to fit these lines.

Fig. 9. 12 lines along the periphery

The algorithm is demonstrated in Fig. 10 . For a vertex A, we find the closest vertex,
named B, with which can form a path along the edge of the square (consider the sobel
response). Put A and B in the inlier set and make growth along : If another vertex

and the last two inlier vertices lie along the edges of square, then put it into the set and
keep looking for the next one . This process ends before the growth along the other
direction

starts. One-direction growth is enough when the vertices are ordered
along the x or y axis.