Since the imaging plates in the container are only slightly overlapping each other, there is really no need to try to register the images by searching the whole area of the pictures. Instead, to reduce calculation time it is wise to search only from the overlapping parts of the images. To predefine whether certain parts of the images—say certain sides of the images—are overlapping or not, we need information about the container and the placement of the imaging plates. Information for estimating a suitable size for the overlapping area of the image could be used too, but in this particular application it is not needed as the necessary information is actually stored in the images.
Let’s say ai,j corresponds to the amount of radiation that is about to hit
pixels in phosphor imaging plate, but we can assume that the energy of certain surface area of the plate is in the process converted to equivalent energy of corresponding pixel.) If there is no imaging plate above, this pixel on the plate gains the whole radiation ai,j. However, should there be another imaging plate
blocking the rays, our pixel will only gain the radiation of T ai,j, where T is a
transmission coefficient indicating the proportion of radiation passing through the first plate (0 < T < 1).
Since an x-ray image is a negative image of recorded data, the value vi,j of
each pixel in the actual image will be
vi,j =
(
1 − ai,j if no plate is above
1 − T ai,j if another plate is above
(27)
where the values of v and a are both between 0 . . . 1.
We can also state that expected value of ai,j is average of all ai,j (equation
28). From this and equation 27we get expected values (equations 29 and 30) for pixel values v in two different cases.
E(ai,j) = 1 IJ X i,j ai,j = a (28)
E(vi,j, no plate above) = 1 − a (29)
E(vi,j, another plate above) = 1 − T a (30)
Since 0 < T < 1, we can say that
E(1 − T a) > E(1 − a) , or (31) E(vi,j, another plate above) > E(vi,j, no plate above)
or, in other words, gray values of pixels shaded by another imaging plate during the exposure are higher than those not shaded.
The change in the overall gray levels between fully exposured (not shaded) and partly exposured (shaded) areas in the image of the lower plate can be seen
clearly. (See the right side on figure12). Because of the more or less rectangle shape of the plate with other side longer than the other, the imaging plate can be inserted in only two ways into the reading device. As a result, there are only two sides in the image where the border between different exposure amounts may lie, and due to the design of the container, that border is on either of the long sides of the image. Also, the border is more or less aligned with the side of the image because of the design of the container doesn’t allow there to be significant angle between the plates.
Figure 12: Sample image of the imaging plate showing a distinct vertical border—or change in the overall gray levels—on the right side of the image. It has been caused by another imaging plate on top this one during the exposure. To make decision on which one of the images was on top and which one was underneath the other one at the time of the exposure, the algorithm tries to find if there is an area of higher gray values in the image as expected by equation
31. The area of lesser exposure should be on the long side of the image, which means, moving along the i-coordinate should not have an influence whether we are on the fully exposured area or not, assuming the image (matrix) is in upright position and i is taken to be the row coordinate of the matrix.
The values of each row are added up (32). The series from (32) are differ- entiated and since we are interested in the absolute change only rather than direction of the change, the absolute value of the series is taken (33).
s(j) = I X i=1 vi,j (32) ∆s(j) = ks(j) − s(j − 1)k (33)
Differentiated series ∆s shows a distinct peak where the overall gray values of the image changed in the “lower” image. In the “upper” image however, there is no such peak in the differentiated series since the plate has not been shadowed by any other imaging plate. During this thesis, by “lower” image is meant the image acquired from the imaging plate that was underneath during the exposure. By the “upper” image, naturally, is meant the image of the plate that was above the “lower”.
The images are identified as “upper” and “lower” image according the absence or the presence of this peak respectively. (See figure 13)
In practice one must notice that there might be false peaks near the ends of the series. These are formed because the edge of the physical plate is not always sharp, and there might be white pixels as the remainings of the canvas. The ∆s series shows a peak where the empty space changes to actual image since there is a also a change in the overall gray levels.
When searching the peak from the series, the application must omit those false spikes. In this application it is done by excluding circa 10% of both ends of the differentiated ∆s(j) series since the overall change in gray levels should not be there according to the plate container design. Ends of the series has been set to zero in figure 13.
The series ∆s(j) of both lower and upper image are compared and identified so that
is satisfied, where ∆sL presents the series of the lower image and ∆sU of the
upper image.
As seen in figure 13(b), even when teeth (in this case molar teeth)—which show in the image as lighter areas—are situated in a line at the side of the image, the diagram shows no prominent peak which would be mixed with the peak of overall change in gray values in the other diagram.
(a) Image of the lower imaging plate overlaid with dia- gram.
(b) Image of the
upper imaging
plate overlaid with diagram.
Figure 13: Images of the lower (a) and upper (b) imaging plate along with overlaid diagrams. The diagrams represent the values of series ∆s(j) (equation
33) at each column j of the image matrix. A distinct peak can be seen in diagram of the lower image at the very spot where there is a border between fully and partially exposured areas of the image. Diagrams are in the same scale. There is no peak at the diagram of the upper image. The ends of the diagrams are set to zero to avoid possible false peaks near the edges of the images.