Tutorial 4

1. In the classification of some medical dataset, scalar values from 100 to 200 represent skin, 200 to 300 represent muscle, and 300 to 400 represent bone. The colour transfer functions define skin as tan, muscle as red, and bone as white. If we interpolate scalar value and then perform classification, what classification artefacts may appear in the image?
   
   
   
2. You need to create a small image of a volume dataset to include on your web page. The dataset contains 512³ voxels, and the desired image size is 100² pixels. You can use a software object-order method that projects each voxel onto the image or a software ray-casting method that casts one ray for each pixel. Assuming that identical images are created, which method would you select, and why?
   
   
   
3. Decimation is a post-process for reducing the number of triangles (generated by the marching cubes algorithm, for instance) that approximate the surface of an object. In the classification step of decimation, the most common case that you would encounter is when the point (i.e., a triangle vertex) is simple (see lecture notes). Given that you have found a simple point, P. The basic steps for decimation are:
   1. Apply a decimation criterion to determine if P should be removed. This step involves the following sub-steps:
      • fit a plane to the vertices {V_i | i = 1, ... m} (note that P is not included in the set) of all the triangles that share vertex P;
      • compute the distance, d, of P to the fitted plane;
      • if d is less than a predefined threshold then P can be removed.
   2. If it is determined to remove P then collapse P to an arbitrary vertex in the list {V_i | i = 1, ... m}. This step would reduce the number of triangles by 2 (see Fig).
   3. Reassign the triangle vertices and remove P from the global list of vertices.

   

   The above steps should be carried out to all the simple points. It would often require several passes to the point set in order to attain a desirable reduction ratio.

4. In the above example given the m vertices, {V₁, V₂, ..., V_m}, that are approximately planar, derive a procedure for computing the coefficients a, b, c, and d of the plane fitted to the vertices. Recall that the plane equation is
   
   ax + by + cz + d = 0
   where a, b, c, and d are coefficients of the plane.