Issues on Displaying 3D Data for Scientific Visualization Thomas Theußl theussl@cg.tuwien.ac.at Institute of Computer Graphics Vienna University of Technology Vienna, Austria

Feature Lines

Using feature lines as a sparse, opaque texture on transparent surfaces [5, 12] was inspired by the ability of gifted artists to define a figure with just a few strokes. The two types of geometric features most often represented in line drawings are discontinuities of depth (silhouettes and contours) and discontinuities of curvature (sharp ridges and valleys). Depicting this small set of meaningful lines gives strong cues on the shape and position of transparent surfaces.
Silhouette and contour curves are the 2D-projection of points on the 3D surface where the direction of the surface normal is orthogonal to the line of sight. Silhouette lines are always visible for they form a closed outline around the projection. Contour curves may be disjoint an can fall within the projective boundary. Although contour curves are important shape descriptors, their use under conditions of stereo and motion are limited. Because they are viewpoint-dependent, they must be recomputed and redrawn every time the viewpoint changes or they will seem to crawl over the surface confusing the perception of the surface data. Furthermore, these contour lines provide little indication of depth distance or surface shape across forward-facing areas.
Another sparse set of descriptive lines, but which remain fixed on the surface under dynamic viewing conditions, are ridge and valley lines. To detect these feature lines some characteristics of surfaces must be examined. At any non-spherical point on a generic, smooth surface is one direction in which the the surface is curving most strongly. This direction is referred to as the first principal direction and the curvature in this direction is referred to as the first principal curvature. These two can easily be computed at arbitrary points on a smoothly curving surface from the eigenvectors and eigenvalues of the second fundamental form [5].
Valley lines now are the locus of points on a surface where the normal curvature assumes a local minimum in the principal direction associated with the largest, negative curvature and ridge lines are the locus of points on a surface where the normal curvature assumes a local maximum in the principal direction associated with the largest, positive curvature. Every point classified to lie on or near a ridge or valley line is assigned an additional amount of opacity and a slightly different color to better distinguish between these two kinds of feature lines.
If all the points identified by the preceding definition are displayed opaquely, the result is not satisfactory, too much lines are displayed. So steps must be taken to selectively emphasize more important ridge and valley regions and de-emphasize the others:

• First, the opacity of the ridge and valley points can be defined as a function of the relative magnitude of the normal curvature in the first principal direction. This emphasizes more sharply curved regions.
• Next, only these ridge or valley points are assigned an additional amount of opacity, which magnitude of the maximum principal curvature at that point exceeds a specified cutoff.
• It is possible, that after these two steps very deep, but extremely narrow spurious ridge or valley lines remain visible. The approach to eliminate these lines is to step away from the point in the first principal direction and look if the approximated surface normals begin to realign before a specified minimum distance has been traversed.

Figure 5 shows a treatment plan for a patient with prostate cancer.

  
Figure 5: An untextured skin surface on the left and the same skin surface with ridge and valley texture on the right.