1. Electronic Visualization Laboratory University of Illinois at Chicago “Fast And Reliable Space Leaping For Interactive Volume Rendering” by Ming Wan, Aamir Sadiq, Arie Kaufman Presented by: Allan Spale, CAVERN Viz Workshop, May 2004

2. Electronic Visualization Laboratory University of Illinois at Chicago Overview Algorithm that accelerates ray casting during interactive navigation in a complex volumetric scene –Pixel depths derived with a fast cell-based reprojection algorithm during navigation –Remaining pixel depths determined by precomputing the distance from each empty voxel to its nearest object boundary Distance-From-Boundary (DFB) jumping Provide suitable solution to new incoming objects problem during navigation –Updates depth pixels where new objects are exposed

3. Electronic Visualization Laboratory University of Illinois at Chicago Background and Definitions Volumetric Data: 3D grids of voxels –Cell: 3D volumetric region bounded by 8 neighboring grid vertices (voxels) –Algorithm works with cubic, regular, and rectilinear grids Utilizes 2 cell buffers and frame buffers (previous and current frame) –Cell buffer: Stores visible object cell –Depth buffer: Stores depth of each pixel, generated by the previous cell buffer Hole pixel: Pixel not covered by any reprojected point Accelerated ray casting algorithm –Use cell-based reprojection to get pixel depths from previous frame –Perform DFB jumping at a hole pixel to detect its depth –Detect correct depth values from step 1 with incoming objects –Skip over empty regions along each ray

4. Electronic Visualization Laboratory University of Illinois at Chicago Cell-Based Reprojection: Reproject the Cell Center (Fig 1a) E : viewpoint, f : distance from E to image plane Given cell C and cell’s center point V –Calculate projected position of P of V on image plane as… The intersection between image plane Line L passing through V and E

5. Electronic Visualization Laboratory University of Illinois at Chicago Cell-Based Reprojection: Determine Reprojected Region (Fig 1a) Line L is perpendicular to the image plane Bounding sphere of cell C is a circle centered at P with radius S Calculate radius of S –There is tangent plane T of cell C passing through viewpoint E A is a tangent point B is projection of point A on the image plane –Distance of s between B and P –Distance of r between A and V –With right triangles, can use equation s = r * f / (d 2 – r 2 ) 1/2

6. Electronic Visualization Laboratory University of Illinois at Chicago Cell-Based Reprojection: Update the Depth Buffer Determine pixels that the reprojected cell may occupy –If occupied pixel’s depth value is available in the buffer Compare it with the new distance l from the cell being reprojected –If depth value is greater than l The value l will replace old depth value Advantages –Safe estimation of jumping distance without losing pixels –Moderate impact on reprojection cost –Less expensive than splatting because each cell reprojection covers a larger area on the image plane

7. Electronic Visualization Laboratory University of Illinois at Chicago Accelerated Ray Casting If a pixel has its depth value in the depth buffer, ray casting quickens because it can jump to the nearest object voxel –Otherwise, perform DFB-jumping to skip over empty ray segment With volumes, camera is located in empty region Voxel’s DFB value is view-independent and can be calculated as a preprocessing step Whenever the ray sampling point occurs in an empty region, DFB jumping may be applied at that position DFB is not applicable for a camera inside a detailed scene since DFB would skip new objects

8. Electronic Visualization Laboratory University of Illinois at Chicago New Incoming Object Detection 1.Find pixels at edge of the reprojection region in current image 2.Recalculate depth of each peripheral pixel by ray casting and performing DFB until first voxel found 1.New depth < original depth  mark pixel to indicate new object detection 3.Check each marked pixel’s 8 neighboring pixels 1. 1.Look for pixels with depth values in the depth buffer but have not been accessed yet 1. 1.Recalculate their depth values 2. 2.Update depth buffer with new value 3. 3.Mark the pixel so that it indicates the detection of a new object 4. 4.Go to step 3 until no more pixels can be marked

9. Electronic Visualization Laboratory University of Illinois at Chicago Results Implementation –16 processor SGI Power Challenge –Task assigned cell buffer entries and pixels to each processor in interleaved scanline order for reprojection and DFB-jumping –Detection of new object was not parallelized because execution time was short Datasets –Phantom pipe: 512 x 512 x 107 –Colon (from CT data): 512 x 512 x 411

10. Electronic Visualization Laboratory University of Illinois at Chicago Summary Highlights –Fast, reliable space leaping method to accelerate ray casting for large volumes Combines temporal and object space coherence Pros –Notable speedup in rendering –Usable for all volume grid types Cons –Generic algorithm but works well in empty scenes –Questionable image quality (figure 5) or bad PDF image –New object detection tends to fail when view changes too much between adjacent frames