Fast Volume Rendering Using a Shear-Warp Factorization of the Viewing Transform []

Shear-warp optimized using object and image coherence for parallel projection.( See figure ).

  
Figure: Parallel projection in sheared object space.

• Parallel projection of rendering algorithm. Scanline-based coherence.
  
• Make use of the property that sheared volume lines are aligned with pixels scanlines in the intermediate image. The volume and the image data both can be traversed in scanline order.( See figure ).
• Scan-line based coherence data run-length: skipping runs of transparent voxels. Computed in a preprocessing step it is view independent.
  Two types of runs depending of a user defined threshold:
  1. transparent
  2. non-transparent voxels.
• To take advantage of coherence in the intermediate image, store scanlines for each opaque pixel (exceeds a user defined threshold) and offset to the next non-opaque pixel in the same scan-line. ( See figure ).
  Pixel array and offsets of the intermediate image form a run-length encode structure computed on the fly.

    
  Figure: Scanline of pixels in the intermediate image are parallel to scanlines of voxels in the volume data. In parallel projection every voxel has the same scale factor and this can be choose so that for a given voxel scanline there is a one to one mapping between voxel and intermediate image pixel
  

• Offset in image pixels used to skip pixels which are occluded without examining every pixel.
• The previous structures leads to a fast scanline based rendering algorithm ( See figure ). Marching simultaneously through the volume and through the image in scanline order.
• The only voxels that are treated are this ones which are non transparent and visible.
• For voxels runs that are not skipped it is performed shading, resampling and composition.
  Since all the voxels in a voxel slice are scaled by the same factor. The resampling weights are the same for every voxel in a slice (bilinear interpolation).
  For shading look-up table based system.
  Look-up table to correct voxels opacity.

    
  Figure: Offsets with opaque pixels in the intermediate image allow occluded voxels to be skipped efficiently
  

    
  Figure: Resampling and composing by steaming intermediate image in scanline order, skipping over voxels which are transparent and pixels which are opaque
  

• Some properties.
  The opaque pixels runs usually are large so that many pixels can be skipped at once.
  
• Finally the image must be warp.
• Three run-length encoding of the volume are computed in a pre-processing step one for each possible principal viewing.