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Data Representation and Approximation Techniques for RealTime Visual Data Rendering

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Title: Data Representation and Approximation Techniques for RealTime Visual Data Rendering


1
Data Representation and Approximation Techniques
for Real-Time Visual Data Rendering
Student Yu-Ting Tsai Advisor Prof. Zen-Chung
Shih Department of Computer Science National
Chiao Tung University, Taiwan
2
Outline
  • Introduction
  • Data Representation
  • Spherical Radial Basis Functions
  • Approximation Techniques
  • Generalized Multi-Way Analysis
  • SRBF-Based Spherical Wavelets
  • Permuted PCA
  • Unstructured K-ary Wavelets
  • Conclusion

3
Introduction
4
Visual Data Rendering
  • Analytic Models
  • Render visual effects from formulae, procedures,
    or algorithms
  • Data-Driven Models
  • Render visual effects from data
  • Data sources
  • Measured data
  • Image-based data
  • Precomputed data

5
Visual Data Rendering
  • Challenges
  • Data size
  • Real-time performance
  • Scalability
  • Edibility
  • Meaningful factors
  • Special data sets

6
Previous Proposals
  • Novel Data Representation
  • Spherical Radial Basis Functions (SRBFs)
  • Sophisticated Approximation Technique
  • Clustered Tensor Approximation (CTA)

Vertex
Transfer Matrix
Light
View
7
Data Representation
8
Related Work
  • Data Representation
  • Primitive elements
  • Points, lines, polygons, voxels, …, etc.

9
Related Work
  • Data Representation
  • Topological structures
  • Meshes, graphs, hierarchical structures, …, etc.

10
Related Work
  • Data Representation
  • Parametric models
  • Splines, parametric surfaces, analytic models, …,
    etc.

Lambertian Reflectance Model
11
Related Work
  • Data Representation
  • Functional models
  • Fourier series, harmonic functions, wavelets,
    radial basis functions, …, etc.

Green, GDC 03
12
Related Work
  • Data Representation
  • Functional models
  • Spherical harmonics Ramamoorthi and Hanrahan,
    SIGGRAPH 01 Sloan et al., SIGGRAPH 02
  • Wavelets Matusik et al., SIGGRAPH 03 Ng et
    al., SIGGRAPH 03, 04
  • Radial basis functions Carr et al., SIGGRAPH
    01 Turk and OBrien, ACM TOG 02

SRBFs
13
Spherical Radial Basis Functions
  • Simple Example

Center
Coefficient
Bandwidth
14
Spherical Radial Basis Functions
  • SRBF Representation

15
Spherical Radial Basis Functions
  • SRBF Representation

16
Spherical Radial Basis Functions
  • SRBF Representation

17
Spherical Radial Basis Functions
  • SRBF Representation

18
Spherical Radial Basis Functions
  • SRBF Representation

19
Spherical Radial Basis Functions
  • SRBF Representation

20
Spherical Radial Basis Functions
  • SRBF Representation

21
Spherical Radial Basis Functions
  • SRBF Representation

22
Spherical Radial Basis Functions
  • Rotation-invariant and axis-symmetric functions
  • Radiance functions can be represented in
    intrinsic domain
  • Adaptive to spatial variation by adjusting
    centers and bandwidth parameters
  • Spherical integrals can be efficiently computed

Gaussian SRBFs with different bandwidth
parameters 2D Plot
A Gaussian SRBF 3D plot
23
Applications
  • Measured BRDFs

Weng, Master Thesis 06
24
Applications
  • Importance Sampling

Weng, Master Thesis 06
25
Applications
  • Image-Based Lighting
  • SRBFs behave as filtering kernels

Larger Bandwidth
26
Applications
  • HDR Environment Approximation
  • Alternating least-squares optimization
  • Precondition / initial guess
  • Multi-resolution optimization
  • Color space (LAB)
  • Separate analysis
  • Sub-block, sub-band, sub-energy
  • Simplification
  • Statistical methods
  • Bayesian, HMM, MLS

Reference Image
Our Approach
27
Applications
  • More Applications
  • Dynamic PRT
  • Image-based data sets
  • Normal / tangent / bump map estimation
  • Any radiance / spherical functions

28
Multi-Variate SRBFs
  • Anisotropic SRBFs
  • Bandwidth changes with azimuthal angle around
    center
  • More degrees of freedom
  • Contour function
  • Constructed from multiple uni-variate SRBFs
  • Spherical integrals?

29
Approximation Techniques
30
Related Work
  • Basis Pursuit
  • Clustering, vector quantization, Fourier series,
    wavelets, radial basis functions
  • Matrix Factorization
  • Singular value decomposition, homo-morphic
    factorization, non-negative factorization
  • Dimensionality Reduction
  • Principal components analysis
  • Clustered PCA, locally linear embedding, iso-map,
    Laplacian eigen-map
  • Multi-way analysis, sub-space analysis

31
Approximation Techniques
  • Common Essence
  • Transformations
  • Basis functions
  • Sparse solutions

Coherence!
32
Approximation Techniques
  • Maximize Coherence
  • Linear / non-linear transformations
  • Orthogonal / non-orthogonal basis functions
  • Local / global coherence
  • Uniform / adaptive approximations
  • Prior knowledge
  • Latent variables

33
Approximation Techniques
  • Generalized Multi-Way Analysis
  • SRBF-Based Spherical Wavelets
  • Permuted PCA
  • Unstructured K-ary Wavelets

34
Generalized Multi-Way Analysis
35
Two-Way Analysis
  • BRDF Matrix

Light
View
Sampled BRDF
36
Two-Way Analysis
  • Principal Component Analysis

Light-Dependent
View-Dependent
Sampled BRDF
37
Two-Way Analysis
  • Advantages
  • Low computational costs
  • Global optimum (least-squares errors)
  • Efficient reconstruction
  • Disadvantages
  • Only for two-way data sets
  • Global coherence
  • Uniform approximations

38
Multi-Way Analysis
Light
View
39
Multi-Way Analysis
Texel
…
Texel Basis Matrix
Light
Light Basis Matrix
View Basis Matrix
Core Tensor
View
40
Clustered Multi-Way Analysis
Texel
…
…
Light
Cluster C
View
41
Clustered Multi-Way Analysis
Iterative Process
…
Texel Basis Matrix
Tensor Approximation
Light Basis Matrix
View Basis Matrix
Core Tensor
Cluster C
42
Multi-Way Analysis
  • Advantages
  • For high-dimensional data sets
  • High compression ratio
  • Coherence exploitation in each sub-space
  • Efficient reconstruction
  • Disadvantages
  • High computational costs
  • Local optimum

43
Multi-Way Analysis
  • Major Drawbacks
  • Alternating least-squares
  • Local optimum
  • Best rank of each sub-space is unknown
  • Linear analysis in each sub-space
  • Clustering along only one dimension

44
Generalized Multi-Way Analysis
Texel
…
Texel Basis Matrix
Light
Light Basis Matrix
View Basis Matrix
Core Tensor
View
45
Generalized Multi-Way Analysis
  • No independence assumptions
  • Alternating vs. simultaneous analysis
  • Correlation model
  • Simultaneously derive all the basis matrices

46
Generalized Multi-Way Analysis
  • Adaptive Shrinkage
  • Simple, intuitive, and practical
  • Correlation model
  • Closed-form solutions?

47
Generalized Multi-Way Analysis
  • Generalization of CTA
  • Non-linear extension
  • Clustering along more than one dimension
  • Destruction before construction

48
Generalized Multi-Way Analysis
…
49
Generalized Multi-Way Analysis
…
50
Applications
Light
View
51
Applications
Raw BTFs (192x192x120x270) 1.1 GB
Compressed BTFs (96x96x32x32) 18.1 MB (Multi-way
factorization) SE 0.61
52
Applications
  • All-Frequency Bi-Scale PRT

53
Applications
  • All-Frequency Bi-Scale PRT

54
Applications
  • More Applications
  • Time-varying appearance analysis
  • Image-based rendering on GPUs
  • All-frequency PRT
  • More complex surface appearance
  • View-dependent bump and displacement maps
  • Time-varying appearance
  • Real-time dynamic all-frequency PRT

55
Conclusion
56
Conclusion
  • RBF-based methods can be easily extended to SRBFs
  • Generalized multi-way analysis aims at overcoming
    major drawbacks of previous multi-way analysis
  • Destruct the structure before construction to
    maximize coherence

57
The End
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