Algorithms

The typical algorithms used in computer graphics can be applied after the approximation of the surface with polygons. But this two-step method can be enduring and full of errors due to the approximations.

The most simple is to find d and φ to each pixel of the screen. This requires O(n3) operations in the case of n pictures with a size of n*n.

In order to create the view from several directions, an algorithm with O(n2) operations can be applied after a preprocessing. To achieve this, the theoretically visible voxels and their faces have to be found and collected in a list. A different list should be made for each eight of space. The faces which are further away from the point of view than the others come sooner on the list.

We talk about theoretically visible voxels, because it is not sure that they can be really seen, as the attached two dimensional figure shows below.

Figure 43.

Composing the list requires O(n3) operations, but afterwards O(n2) operations are enough for the preparation of other views.

The corresponding color and the place of the pixel that need to be used are determined for every element of the list. It is possible that the place where the algorithm has to draw is not empty. It is not really a problem, because the order of the list elements assures that the voxel drawn later is closer to the point of view and it hides the voxel drawn before.

It can happen that inside the visualized object on the screen empty pixels remain. The reason of this is that in the case of inclined view the projection of adjoining voxels are placed further from each other than one pixel, and thanks to the rounding one pixel is left out. An easy solution for this is to plot the projection of the voxel on at least 21/3 times larger square than the length of the voxel’s edge.

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Figure 44. Image from a fetus done by ultrasound. Present-day techniques make it possible to create quickly a three dimensional image, therefore placing them after each other, a moving picture can be composed. With the transformation of the data, arbitrary point of view can be achievable.

After the registration of three-dimensional images made by different recording techniques, there is an opportunity to represent all of the information from the images together. E. g. brain tumor can be seen the best on the MR image, bone system on the CT image, large vessels of the brain on MRA image. Illustrating in one picture all of these images together is a great help for the planning and the execution of tumor’s surgical removal. The formations of the different records are drawn with different colors (green, grey, red).

 MR CT MRA tumor bone large blood vessels

Figure 45.