We use the shape and size attributes of the object for segmentation. It is reasonable to assume that the fiducials are within a certain distance from the four corners or/and the middle of the four sides of the image and have certain eccentricity value. We can also assume the fiducial marks are larger than a certain size or area. The area is the number of pixels that the objects occupy. The eccentricity is defined as the ratio of the lengths of the semi-major and semi-minor axes of the best-fit ellipse, which is the ellipse whose second moment equals that of the object. We also assume that we have some knowledge about the shape of the fiducial marks. We use different methods to segment different kinds of fiducial marks.
For the kinds of images shown in Figure 2(a)(b), the segmentation procedure we used are as follows. Firstly, the images were filtered by using the area-based morphology. This operation had the effect of removing small bumps in the gray scale image. Secondly, the smoothed image was filtered by using ratio attribute of the morphology operation. This operation removed any object that are more or less ``circular''. For circular shapes or those fiducials shown in Figures 3(a) and 4(a), the aspect ratio of the best fitted ellipse is close to 1. Thirdly, a difference image was obtained from the images in the previous two steps. The fiducial mark will show up in this difference image. Finally, the fiducial mark is chosen as the brightest object in the image. This was actually performed by choosing the brightest point in the image and then carrying out a morphological reconstruction to recover the shape of the fiducials. The result is a grey level image rather than a binary image.
For the kind of images shown in Figure 2(c), the
segmentation procedure we used are as follows.
There were some difference for the steps used for segmenting this kind
of fiducials compared to those mentioned earlier. Some preprocessings
were applied to the input image before performing the attribute based
morphology. This preprocessing includes using median filtering and
subtraction of the median filtered image and the input image. After
this preprocessing, the fiducials will become the dominant feature in
the image. We segment the broken `` 
'' by separating the cross
into two parts. Each part contains two line segments oriented in the
same direction. The attributes used include object area, the aspect
ratio, and the orientation of objects (i.e. the line segment size
should larger than a certain threshold; the lines are thin and with a
certain direction). The two parts found were joint together to form
the broken `` ''. After this attribute based morphology step,
the original shape was recovered by using morphological
reconstruction.
For the kind of images shown in Figure 2(d), the segmentation procedure we used was similar to those used for the case in the previous paragraph except the preprocessing step and the formation of the ``+''.