The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B5. Beijing 2008 
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I G [0.0,1.0], 
which can be scaled to discrete 12 bit pixel values. In our case, 
the object the ray runs through is the CT volume. 
Usually all DRR pixels would be computed by the line integral. 
However, it is possible that the user defines a Region of Interest 
(ROI) in the X-ray image(s) to exclude certain regions from the 
matching process. This can be the case if an image contains 
features that only occur in one of the modalities (X-ray image or 
projected CT scan) as for example head fixation equipment or 
parts of the patient table, to name but two. In this case a validity 
mask is created to mark valid parts of the X-Ray image. The 
markings are transferred to the image plane of the respective 
DRR image and are used to mask out DRR pixels. The ray 
tracing process for the pre-alignment then skips rays that are not 
included in the ROI (see figure 3). 
Figure 3. Ray-tracing and ROI 
3.2 Automatic Exclusion of DR Portions 
After the pre-alignment we mask out regions of the X-ray image 
and the DRR plane to speed-up the rendering process and to 
concentrate on relevant areas of pixels when performing the 
alignment fine-tuning. As shown in (Olson, 2001) aligning 
entropies of images is a stable way to perform a registration and 
can be considered more reliable than aligning gradients. This 
holds especially in cases (as in our case) where it is not trivial to 
find corresponding gradients in the image pairs, because of 
differences between the two image modalities. However, 
(Olson, 2001) aim a template based matching, whereas we want 
to find the maximal similarity between two different images. 
For this reason we still use MI as measure, but mask out parts of 
the images using the Block Entropy for a certain window W 
around each pixel of the X-ray image. 
The Shannon Entropy is computed by equations 3: 
H ( X )=~YjP g * ,n W (3) 
«=o 
Wlth limn ln(» )=0 
Pg ->o 8 v g 7 
where H(X) = entropy between 0 and 1 
X- respective image (here the X-ray image) 
p g - probability for the occurrence of gray-value g 
We compute the Block Entropies H(W) of the image for each 
pixel in a predefined window W. Therefore we use a window of 
size 7 x 7 = 49 pixels. To reduce computation time and to avoid 
overweighing of small pixel intensity fluctuations we apply 
histogram bins of size 32 gray-levels (the original images have 
12 bit gray-value resolution and are downsampled). The 
entropies of the single pixels are stored in an entropy map with 
the same resolution as the original image. At the same time we 
compute the total entropy H(X) for the whole image by 
summation of the Block Entropies H(W). Because pixels can 
occur twice in different windows, we additionally normalize by 
the number of blocks (which are the number of windows, for 
which the entropy could be computed). 
To make the algorithm more tolerant against noise and to 
further decrease computation time, the entropies are computed 
in half image resolution and the image data is filtered by a 3 x 3 
Gaussian kernel. The low-resolution entropy map is then 
resampled to the original image size. In this way, the 7 x 7 pixel 
area of the Block Entropy window, applied to the lower 
resolution image, covers 14 x 14 pixels in the original 
resolution. Enlargement of the entropy map additionally leads 
to a margin around the masked out areas. This can be 
advantageous because inaccuracies of the previous processing 
steps can still be corrected by aligning only the correct sup-parts 
of these areas in the final matching process. 
The entropy gives the average information per pixel, normalized 
to the range 0 to 1. The Block Entropy H(W) gives the entropy 
for subparts of H(X). Thus we compare the Block Entropies 
with the image entropy and mask out regions where 
H(W) < H(X) 
holds, to exclude image regions with relative low information 
per pixel (see figure 4). 
a b c 
Figure 4. Exclusion of image regions: a) X-ray image of an 
anatomic head-phantom; b) map of Block Entropies 
for 7x7 pixel windows and 32 gray-value bins; c) 
X-Ray image where low Block Entropies have been