Projective Texture Atlas for 3D Photography

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Projective Texture Atlas for 3D Photography
Luiz Velho

• Jonas Sossai Júnior

IMPA
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Motivation

• Texture maps describe surface properties
• Important for Visualization and Modelling
• Surface parameterization(Mapping a 2D domain to
  a 3D surface)
• Difficult to compute / Introduces distortion
• Solution use an atlas structure(set of charts
  individually parameterized)

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Problem Description

• Our work Build texture atlas for 3D photography
• Strategy
• Projective atlas
• Variational optimization
• Applications
• 3D photography
• Attribute editing

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Related Work

• 3D photography (Scopigno et al. 2002)
• Surface representation (Sander et al. 2003)
• Variational approximation (Desbrun et al. 2004)

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Contributions

• Projective texture atlas
• 3D Photography Application
• Optimal Patch Construction
• Texture Compression and Smoothing

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Texture for 3D Photography

• The problem Construct a good texture map from
  photographs
• Requirements
• Minimize texture distortion
• Space-optimized texture
• Reduce color discontinuity
• Variational projective texture atlas
• Surface partitioning (distortion and
  frequency-based)
• Parametrization, discretization and packing
• PDE-based color diffusion
• Texture smoothing

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Overview

• Partitioning Parameterization
  Packing

• Techniques
• Partitioning Variational minimization of
  texture distortion and space
• Parameterization Projective mapping
• Packing Simple algorithm

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Variational Surface Partitioning

• Given a surface S, a desired number of regions n,
  and an error metric E
• An optimal atlas A with a partition R over S,is
  a set of regions Ri, associated with charts Ci,
  that minimizes the total error
  
• E(R, A) ? E(Ri, Ci)
• Error Metrics
• Texture Distortion
• Frequency Dissimilarity

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Lloyds Algorithm

• Clustering by Fixed Point Iteration
• Repeat until done
• Assign points to regions according to centers
• Update centers
• Scheduling
• Chart adding
• Chart growing
• Chart merging

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Minimizing Texture Distortion

• Texture Distortion
• Visibility

Ci Chart ci Camera associate to chart Ci ni
camera direction n(x) surface normal
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Maximizing Frequency Coherency

• Texture has different levels of detail
• Algorithm
• Compute frequency content using wavelet analysis
• Make charts based on frequency similarity
• Scale images according to frequency

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Color Compatibilization

• Problem Color discontinuity between images
  (different exposure)
• SolutionFrontier faces share an edge(color
  from two images)

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PDE-based Diffusion

• Algorithm
• For each frontier edge compute the color
  difference between corresponding texels
• Multigrid diffusion of differences over charts

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Parameterization and Discretization

• Parameterization of each chart is the projective
  mapping of its associated camera
• The discretization is obtained by projecting the
  chart boundary onto its associated image

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Packing

• Output Texture Map
• Simple Algorithm
• For each chart clip the bounding box
• Sort these clipped regions by height
• Place sequentially into rows
• OBS Could use better packing, but frequency
  analysis makes the size of the texture atlas
  small enough

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Results I
(5 charts, distortion5875.18)
220 x 396
(39 charts, distortion4680.54)
750 x 755
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Results II
39 charts
750 x 755
70 charts
320 x 433
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Comparison I
Real photograph
Scopigno et al. 2002
Our results
6 charts, 256 x 512
5 charts, 220 x 396
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Comparison II
Real photograph
Scopigno et al. 2002
Our results
73 charts, 512 x 1024
39 charts, 750 x 755
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Conclusions and Future Work

• Projective texture atlas
• Powerful structure for 3D photography
• Foundation for attribute editing
• Improvements
• Better packing algorithm
• Other surface attributes(normal and displacement)