Surface Simplification & Edgebreaker Compression for 2D Cel Animations Vivek Kwatra & Jarek Rossignac GVU Center, College of Computing Georgia Institute of Technology

Cel Animations: Example Foreground Cel Background Cel Animation

Motivation Need to compress –To speed up transmission –Want to compress boundary of region –Image/video compression too expensive Compress pixels instead of regions MPEG, RLE, Octree, Gzip Applications –Entertainment: Animations –Web-based instruction: manuals, tutorials, explanations –Visualization: weather, environmental, medical

Cel Animations: Observations Collection of regions Uniform color per region Only few colors/regions Shape of region changes slowly with time Want to encode shape instead of pixels

Voxelization Overview Iso-surface Extraction Simplification Playback Compression Video Clipping Decompression

Prior Art (building blocks) Iso-surface extraction to build 3D model –Marching Cubes [Lorensen & Cline’87] –Tetrahedral Decomposition [Gueziec’95] Surface simplification for lossy compression –[Hoppe’96, Lindstrom & Turk’98, Rossignac & Borrel’93, Ronfard & Rossignac’96…] Geometric Compression –[King & Rossignac’99, King et al’00, Rossignac’99: Edgebreaker, Rossignac & Szymczak’99, Rossignac et al’01, Taubin & Rossignac’98, Touma & Gotsman’98…]

Voxelization Overview SimplificationClipping Compression Decompression Video Iso-surface Playback

Voxelization Assume animation is segmented into regions Pixels P(x,y,t) sample 3D image-time space We could extract the black/white bounding faces –But it would be too jaggy Given region R, we define a scalar field: As t changes, R sweeps a volume V:

Iso-surface Extraction Compute S (bounding surface of V): Interpolate F between pixel centers –piecewise constant –bilinear interpolation –linear interpolation (over triangular elements) Use Marching tetrahedra [Gueziec’95]: simpler and more robust than marching cubes

Marching Tetrahedra Each cube is divided into five tetrahedra The iso-surface of a tetrahedron is either a triangle or a quad Consistent tetrahedral decomposition of cubes ensures a watertight mesh

Marching Tetrahedra (contd…) Tetrahedralization may produce sharp corners; depends upon the particular decomposition Move corner away from the midpoint to smooth it out Result is then independent of tetrahedralization

Voxelization Playback Overview Simplification Clipping Compression Decompression Video Iso-surface

Simplification Triangle count reduced by 95-99% for geometric error of less than 0.2% –Metro [Cignoni et al.’98] Simplify using edge- collapse operations – [Lindstrom & Turk’98] Degenerate cases –Surface folds onto itself Manifold connectivity preserved –Surface remains watertight –Parity preserved Odd parity

Compression Edgebreaker for connectivity compression –Compresses connectivity to 1 bit per triangle Vertex quantization –Span the range represented by the animation Predictive encoding for vertices –Parallelogram prediction rule –Compresses geometry to 13 bits per vertex C R SR LEC R R R L E a b...CRSRLECRRRLE (2T bit code: C=0, L=110, R=101, S=100, E=111)

Playback Voxelization Overview Simplification Clipping Compression Decompression Video Iso-surface

Animation Playback Clip the surface with the plane t = frame # Paint the front-facing triangles (shown in green here) in color of background (black) Paint the back-facing triangles (shown in gray) with the region color Degenerate triangles can causing popping artifacts

Parity: Even Odd View Plane Clipping Plane Even Animation Playback (contd…) Parity checking logic improved to handle overlapping triangles No need for z-buffer Odd parity: point on clipping plane is inside the solid Even parity: Front facing is visible Hardware supported OpenGL stencil buffers to expedite process

Results Technique Human (3.2M) 320x240x337 Sphere (1.4M) 320x240x100 Jello (5.6M) 320x240x590 Compressed SizeRatioSizeRatioSizeRatio MPEG 1.1M M6.61.5M3.8 MRLE (Microsoft Run-Length) 1.2M M81.0M5.8 Gzip (Entropy coding) 78.0K4117.5K800.12M46.4 Gzip on Low Resolution (LR) Video 21.0K1524.1K K217.7 SSEC (Surface simplification & Edgebreaker) 16.8K1903.7K K290.7

Results (contd…)

Show Animation

Summary Input: series of images (uniform regions) Represent each region as pixels Represent its evolution as volume of voxels Compute 3D boundary as iso-surface Simplify while preserving parity test Compress using Edgebreaker Use clipping and stencils to display slices

Conclusion & Future Work Conclusion –Improve cel animation compression Ratios of –Leverage existing techniques Iso-surface extraction for binary voxels Simplification Compression Future work –Compressing multiple regions together –Extensions to other applications: medical imaging, weather visualization etc.

Thank You