Template-Based Volume Viewing []

Exploiting coherence between rays in parallel projection.

• They use discrete Ray tracing. discrete line (constant interpolation) or continuos line (multiple samples per voxel and higher order interpolation).
  They use the first approach valid when you have binary data (synthetic objects voxelization with the second approach will give wrong results ).
• Simple algorithm ( See figure ).
• 3D line-voxelization algorithm 6-line or 26-line.
• Desired line characteristics.
  We want the same form for all the rays independent of the length.(The discretization error is distributed along the line).
  Problem with round errors. Entry point to the volume calculated in floating point but the discrete line algorithm is activated from the initial integer point of the grid on.
• Template based approach solve the previous problems.
  If all the rays have the same form there is not need to reactivate the line algorithm for every ray. We use ray templates computed just once.
  

    
  Figure: View dependent artifacts : first image some voxels between ray a and b are skipped while others are being visited by two of the rays b c. A whole ray of voxels is skipped between rays d and c.
  

  PROBLEMS:
  The rays differ in the exact initial position. The naive way can skip some voxels for 26-rays and multiple traversal for 6-rays ( See figure ).
  SOLUTION:
  Plane parallel to one of the volume faces (base-plane for the template placement). Guarantees a complete and uniform tessellation of the volume.
  

  26-rays:

  • Fewer voxels. 6-line (plus) twice as many voxels as a 26-line (max).
  • 26-rays uniformly sampling the space.

    
  Figure: Principles of Template-based volume viewing
  

• Efficient parallel projection.( See figure ).
  1. Initialization Determine the base plane.
     Computes the extend of the projected image. How big the projection plane must be.
     Computes parallel ray template (saving increments).
  2. Ray Casting (Trace the rays).
  3. 2D Mapping ( From the base plane to the screen plane).

  In average 2 times faster than using a 26-line algorithm grows with the number of rays traced.