Compression Domain Volume Rendering

Jean Shneider and Rudiger Westermann

Computer graphics and Visualization groupTechnical university Munich

Motivation

Need to deal with data of increasing size:• Large-scale• Multi-dimensional• Multi-parameter

Increasing problems:• Compression• Representation• Rendering

We will adress all three problems!

Talk Outline

The Approach – Vector QuantizationQuality and speed

• Hierachical encoding• PCA-Split• Progressive encoding of time-resolved data

Multi-dimensional data

• Vectors of arbitrary length

Rendering from compressed data

• GPU-based decoding and rendering• Per-fragment evaluation• Interactive framerates

Talk OutlineThe Application – Volume Rendering

• Large-scale volumetric data sets• Time-varying sequences

16 MB / 14 fps 0.78 MB / 11 fps16 MB / 14 fps 0.78 MB / 11 fps

1.4 GB / 20 fps1.4 GB / 20 fps

70 MB / 24 fps70 MB / 24 fps

256^3, rendered from compressed256^3x89 timesteps

Vector Quantization - data fitting

Codebook Codebook CC

with codewordswith codewords

EncoderEncoderXXnn

iinn=E(X=E(Xnn))

Input mappingInput mapping

DecoderDecoder

X‘X‘nn=C(i=C(inn)) Output mappingOutput mapping

iinn

4D vectors

Introduces quantization error

-VQ assymetric, encoding expensive, decoding free => exploit this!

Vector Quantization

LBG-Algorithm• Linde, Buzo and Gray 1980• Iterative refinement of a previous Codebook• Sensitive to quality of first Codebook• Usually computationally expensive

Speed-Up possible (and necessary)• Partial searches• Fast searches• Better initial Codebook (i.e. PCA-Splits)

LBG-Algorithm can be fast!

Vector Quantization

The PCA-Split• Lensch et.al. 2001 – BRDF Compression• Covariance analysis to find optimal splitting plane• Cut a cluster of input vectors in two by this plane.• Plane is given by centroid of current set and largest

Eigenvector (= normal) of the Auto-Covariance Matrix

Vector Quantization

LBG as PCA post-processing• Increases fidelity• Leads to stable Voronoi-Regions• Only a few steps are necessary• Great speed-up compared to LBG only!

A series of LBG steps, codebook from last slide

Example

Full-color confocal microscopy scan, 5122x32xRGB

4D vectors, 2MB4D vectors, 2MBOriginal, 32MBOriginal, 32MB 32D vectors, 1MB32D vectors, 1MB

Hierarchical Vector Quantization

LaplaceLaplace

DecompositionDecomposition

3 freq bands - that is a combination of a smoothening and a difference filter. This results in a three level hierarchy of volumes

full

½ res

¼ res

Hierarchical Vector Quantization

4433 dim. VQ dim. VQ

223 3 dim. VQdim. VQ

Direct CopyDirect Copy

blocks 4^3 scalar samples together into one vectorCodebook

256 8D vectors

256 64D vectors

Hierarchical Vector Quantization

Output:• One RGB Index-Volume• Two Codebooks

RGB Index-Volume RGB Index-Volume 3D Texture 3D Texture

Codebooks Codebooks 2D 2D -Textures-Textures

Example

Visible Human (Male), RGB slice 2048x1216

Compression took 10.0 seconds, PSNR = 34.72dB

Original (7.1MB) Compressed (285KB)

Compression ration - 25:1

Timings

Reference System: P4 2.8GHz, 1GB memory

VHP Slice, 2048x1216 RGB 10.0 sec

Engine 2562x128 CT-Scan 19.0 sec

Skull 2563 CT-Scan 50.6 sec

Vortex Sequence, 1283x100 13 (5) min

Shockwave Sequence, 2563x89 29 (13) min

RenderingGPU-based decoding

• Indices stored in 3D RGB-texture (3/64th original size)• Decode index per block dependent fetch• Decode adress per block 43 adress texture

Decoding process in flatlandDecoding process in flatland

Rendering

Render 3D index and adress texture• Nearest neighbor interpolation for both

• GL_REPEAT for adress texture

Per-fragment decoding• Decode detail components and dependent fetch

• Add the details to average component (Red channel)

• Lookup result in 1D RGB transfer function

Problem:

Complex fragment shader slows down rendering

Rendering

Solution: Deferred Fragment Processing

Avoid decoding in empty regions. „Empty“ means:

a) -Transfer function maps 0 0.• Check on CPU• Switch between two possible rendering modes

b) Average value is 0 (Red channel)• Check in a first, simple fragment program• Fragment‘s depth value is set accordingly• Second pass: discard (early Z-Test) or render fragment• Full decoding only performed in second pass

2562x128 Engine CT Scan

19.0 seconds, PSNR = 36.17dB (P4 2.8GHz)

Original (8MB) – 19 fps Compressed (402KB) – 12 fps

2563 Skull CT Scan

50.6 seconds, PSNR = 35.35dB (P4 2.8GHz)

Original (16MB) – 14 fps Compressed (780KB) – 11 fps

Time-resolved Sequences

Exploit temporal coherences during compression:• Group of Frames (GOF)

First frame in a GOF:• PCA-Split followed by LBG-Refinement

Other frames:• LBG-refinement of last Index-Volume and Codebook

Result:• Great speed-up (factor 2 to 3)• Very large GOFs possible (64+ frames)• Virtually same fidelity as frame-by-frame

1283x100 Vortex-Simulation

5 minutes, PSNR = 34.43dB (P4 2.8 GHz)

Original (200MB) - 28 fps Compressed (11MB) - 16 fps

2563x89 Shockwave-Sequence

13 minutes, PSNR = 51.36dB (P4 2.8 GHz)

Original (1.4GB) - 20 fps Compressed (70MB) - 24 fps

Conclusions

• Compression ratios of approx. 20:1• Interactive rendering possible• Easy random access to each frame• Wide variety of data sets handled

Currently only nearest neighbor interpolation• Mainly limited by performance / instruction count.• Tri-linear interpolation can be done on newer GPUs!