Robust and Accurate Calibration Point Extraction with Multi-scale Chess-Board Feature Detector - Advances in Image and Graphics Technologies - page 156

Fig. 3. points on opposite and perpendicular sides [10]

As illustrated in Fig. 4 , taking as a sample point on the circular window, is the
point on the opposite side and on the perpendicular side, N is the number of sam-
pling points on the semicircle, these two energies can be formulated as:

∑ 2

0

(1)

∑ 2

0

(2)

The former energy should be small over the semicircle while the latter relatively
larger.

Fig. 4. Chess-board vertex

3 . 1.2 Multi-scale Annular Chess-Board Detector
If we adopt single-scale detector over the image, the radius of sampling window must
be carefully chosen. Small rings over the blurred region of a vertex can't provide
discriminating features while too large rings risk sampling pixels from unrelated
squares which doesn't form the current features ( Fig. 5 ). This creates a dilemma when
processing different images. It is both unrealistic to apply only one sampling radius
over all images and also inconvenient to choose an appropriate radius for every image.

(a) (b) (c)

Fig. 5. sampling circle (a) ideal vertex (b) vertex with blurriness(c)sampling circles of different
sizes