Texture Characterization via Joint Statistics of Wavelet Coef cient - - PowerPoint PPT Presentation

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Texture Characterization via Joint Statistics of Wavelet Coef cient - - PowerPoint PPT Presentation

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Texture Characterization via Joint Statistics of Wavelet Coef cient Magnitudes Eero Simoncelli Center for Neural Science, and Courant Institute of Mathematical Sciences New York University Javier Portilla Instituto de Optica Consejo

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Texture Characterization via Joint Statistics

  • f Wavelet CoefÞcient Magnitudes

Eero Simoncelli Center for Neural Science, and Courant Institute of Mathematical Sciences New York University Javier Portilla Instituto de Optica Consejo Superior de Investigaciones CientiÞcas Madrid, SPAIN

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Example Texture Types

structured random periodic 2nd-order Can we derive a statistical model (and sampling technique) to rep- resent all of these?

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Synthesis-by-Analysis

Synthesis Analysis

Transform

measure statistics

Example Texture Random Seed

Statistical Sampler Transform

measure statistics

Synthesized Texture

Choice of statistical measurements crucial Proper transform can simplify statistics Most algorithms are iterative

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Recent Inspirational Approaches

Portilla et. al. (1996): Adaptive Gabor transform, constrained

subband auto-correlation. Weakness: structures.

Heeger & Bergen (1995): Steerable pyramid, constrained sub-

band marginals (histograms). Weakness: periodicity, extended structures.

Zhu, Wu & Mumford (1996): Small set of Þlters, constrained sub-

band marginals, Gibbs sampling (maximal entropy). Weakness: extended structures, efÞciency.

DeBonet & Viola (1997): Laplacian pyramid, coarse-to-Þne boot-

strap sampling from the scale-conditional empirical neighbor- hood statistics. Weakness: random textures, no parameteriza- tion.

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Complex Steerable Pyramid Representation

Fourier spectra of 4-orientation 3-scale complex analytic Steerable pyramid.

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Matched Pixel Marginals

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Matched Subband Variances

Captures smoothed distribution of energy in frequency domain.

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Matched Subband Autocorrelation

Captures periodicity.

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Matched Subband Marginals

Captures some local structure.

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Subband Magnitudes

Correlated or anti-correlated magnitudes capture important struc- ture.

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Texture Model Parameters

CoefÞcient magnitude correlations: E jc i j
  • jc
j j Raw coefÞcient auto-correlation: E c x
  • c
x
  • Pixel statistics: mean, variance, skew, kurtosis, min, max.
  • neighborhoods
  • rientations
scales
  • parameters

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Texture Synthesis System

Synthesis Analysis

build complex pyramid

Sample Texture Gaussian Noise

impose statistics mag collapse real part of pyramid build complex pyramid impose statistics impose moments estimate moments mag mag estimate statistics estimate statistics

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Projection onto Constraint Surfaces

Joint magnitudes : match correlation of local (spatial position,
  • rientation, scale) magnitudes. Find linear transformation
A

minimizing:

E
  • jj
  • Q
  • A
  • Qjj
  • subject to:
E
  • A
  • Q
  • Q
T A T
  • E
  • Q
  • Q
  • T
  • A.

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Synthesis Results

ArtiÞcial textures.

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Synthesis Results

Natural textures, random.

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Synthesis Results

Natural textures, structured.

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Synthesis Failures

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Spatial Extrapolation

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Scale Extrapolation

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