INDEPENDENT COMPONENT ANALYSIS OF TEXTURES

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INDEPENDENT COMPONENT ANALYSIS OF TEXTURES

• based on the article
• R.Manduchi, J. Portilla, ICA of Textures, The
  Proc. of the 7th IEEE Int. Conf. On Comp. Vision,
  1999
• Ramunas Girdziuas, 30.11.2000

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Outline Step-1 Markov Random Fields as texture
models Step-2 Combining MRF with steerable
pyramids Step-3 Optimizing representation by
ICA
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Introduction What is texture? Pickett,1970
...large number of elements, each in some
degree visible, and, on the whole densely and
evenly (possibly randomly) arranged over the
field of view such that there is a distinct
spatial repetitiveness in the pattern.Cross
and Jain,1983 ...stochastic, possibly
periodic, two-dimensional image field. Main
tasks Restoration, Segmentation, Classification,
Synthesis Tools Random Fields Co-occurrence
matrices Reaction-diffusion equations Mosaic
models Fractal parameters Subband
decompositions Higher order statistics We focus
on the classification of image textures using MRF
modeling of steerable pyramid image
representations filtered by ICA.
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• Step-1 Markov Random Field modeling
• of texture
• - Systematic approach based on sound principles.
• Modeling of image through local interaction of
• pixels.
• Texture classification (MAP)
• Problem given an image consisting of more than
• one texture, determine whether the particular
  pixel
• comes from the l-th texture .
• MAP classifier
• According to the Bayes Theorem

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The 1st assumption The 2nd
assumption L is a locally dependent Markov Random
Field (MRF) with pdf p(L)
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• The Iterated Conditional Modes (ICM) algorithm
• (J. Besag, 1983)
• - Fast alternative to MAP.
• - Local deterministic relaxation.
• Algorithm
• Initialize labeling L according to ML decision.
• For every epoch k,
• For every image pixel i,
• Choose label L(i) that maximizes
  
• 2. Repeat step 1 until no label changes occur.

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Step2 Combining MRF modeling with
multiresolution approaches Why? -MRF is only
suitable for micro-texture. -Biological relevance
? -Invariance properties? -High computational
complexity. -Robustness to noise ? What kind
of feature spaces to consider? -Invariance to
slow-varying bias. -Energy separation while
preserving locality. -Steerability
(Shiftability). Steerability Teo, 1998 A
function f(x,y) is steerable under Lie group G if
any transformation of f can be written as as a
linear combination of a fixed, finite set of
basis functions
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• Steerable pyramids
• - Introduced to remove some deficiencies of
  wavelets
• - The code in Matlab and C is available on the
  web
• The Steerable Pyramid is a linear,
  non-orthogonal,
• overcomplete, self inverting, multi-scale,
• multi-orientation image decomposition.
• Why is it useful?
• - The power contained within a subband is
  invariant

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Example three scales and two orientations
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Step-3 Selection of the optimal basis
Motivation - Texture is characterized by joint
feature pdf.- Typical filter based algorithms do
not estimate joint description, marginal
statistics are used. - Does a marginal set
represent joint pdf well? Approach -Find the
basis of a given filter space which generates
the most informative marginals for a given
texture in a sense that the product of marginal
densities most closely approximates the joint
pdf
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The algorithm
-Training For each
texture l, Filter texture with a fixed filter
bank Demix filter outputs by using ICA Compute
the channel histograms -Classification Apply the
fixed filter bank to the test image For texture
model l, Multiply the filter output vectors
by the model ICA matrix W and from channel
histograms obtain marginal likelihoods
. Compute the conditional
likelihoods . Use ICM to obtain
pixel labels from .
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Few words about texture synthesis Problem
generate an image that matches the appearance of
a given texture sample Histogram
matching Texture synthesis algorithm
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• Conclusions
• Texture classification can be performed pixelwise
  
• using MAP classifier
• - conditional independence together with Markov
• property attacks MAP computational problem
• ICM is fast deterministic approximate MAP.
• It is better to consider MRF under different
• scales, for ex. by decomposing an image using
  SP.
• - Classification results can be improved by
  making
• features as independent as possible.
• More textures can be synthesized using shifted
• versions of filters and then performing ICA.
• In general, ICA application in texture analysis
• makes sense
• Textures are non-gaussian intensity processes
• Wavelet representations are non-gaussian too.
• In particular,...

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Is the most informative likelihood the desired
criterion of optimality? Ex. Randen,1997
PCA -gt0.01. MOT -gt
67. More to read Similar ideas without ICA D.
Heeger, J. Bergen, Pyramid based texture
analysis/synthesis, Proc. SIGGRAPH, August
1995. Representation vs. separation T. Randen,
Filter and filter bank design for image texture
recognition, PhD.Thesis, 1997. Naive Bayes can be
optimal even when an independence is
violated Domingos P., Pazzani, M., Beyond
Independence Conditions for the Optimality of
the Simple Bayesian Classifier, Proc. ICML,
1996. http//www.cs.washington.edu/homes/pedrod/
Everything about the steerable pyramids
http//www.cis.upenn.edu/eero/steerpyr.html