Outline

1
Outline

• S. C. Zhu, X. Liu, and Y. Wu, Exploring Texture
  Ensembles by Efficient Markov Chain Monte Carlo,
  IEEE Transactions On Pattern Analysis And Machine
  Intelligence, Vol. 22, No. 6, pp. 554-569, 2000

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Limitations of Linear Representations

• Linear representations do not depend on the
  spatial relationships among pixels
• For example, if we shuffle the pixels and
  corresponding representations, then the
  classification results will remain the same
• But in images spatial relationships are important

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Image Features
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Spectral Representation of Images

• Spectral histogram
• Given a bank of filters F(a), a 1, , K, a
  spectral histogram is defined as the marginal
  distribution of filter responses

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Spectral Representation of Images - continued

• An example of spectral histogram

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Image Modeling - continued

• Given observed feature statistics H(a)obs, we
  associate an energy with any image I as
• Then the corresponding Gibbs distribution is
• The q(I) can be sampled using a Gibbs sampler or
  other Markov chain Monte-Carlo algorithms

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Image Modeling - continued

• Image Synthesis Algorithm
• Compute Hobs from an observed texture image
• Initialize Isyn as any image, and T as T0
• Repeat
• Randomly pick a pixel v in Isyn
• Calculate the conditional probability q(Isyn(v)
  Isyn(-v))
• Choose new Isyn(v) under q(Isyn(v) Isyn(-v))
• Reduce T gradually
• Until E(I) lt e

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A Texture Synthesis Example
Observed image
Initial synthesized image
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A Texture Synthesis Example

• Energy and conditional probability of the marked
  pixel

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A Texture Synthesis Example - continued

• A white noise image was transformed to a
  perceptually similar texture by matching the
  spectral histogram

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A Texture Synthesis Example - continued

• Synthesized images from different initial
  conditions

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Texture Synthesis Examples - continued

• A random texture image

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Texture Synthesis Examples - continued
Observed image
Synthesized image

• An image with periodic structures

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Texture Synthesis Examples - continued
Mud image
Synthesized image

• A mud image with some animal foot prints

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Texture Synthesis Examples - continued
Observed image
Synthesized image

• A random texture image with elements

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Texture Synthesis Examples - continued
Observed image
Synthesized image

• An image consisting of two regions
• Note that wrap-around boundary conditions were
  used

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Texture Synthesis Examples - continued

• A cheetah skin image

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Texture Synthesis Examples - continued
Observed image
Synthesized image

• An image consisting of circles

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Texture Synthesis Examples - continued
Observed image
Synthesized image

• An image consisting of crosses

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Texture Synthesis Examples - continued

• A pattern with long-range structures

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Object Synthesis Examples

• As in texture synthesis, we start from a random
  image
• In addition, similar object images are used as
  boundary conditions in that the corresponding
  pixel values are not updated during sampling
  process

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Object Synthesis Examples - continued
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Object Synthesis Examples - continued
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Linear Transformations of Images

• Linear transformations include
• Principal component analysis
• Independent component analysis
• Fisher discriminant analysis
• Optimal component analysis
• They have been widely used to reduce dimension of
  images for appearance-based recognition
  applications
• Each image is viewed as a long vector and
  projected into a set of bases that have certain
  properties

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Principal Component Analysis

• Defined with respect to a training set such that
  the average reconstruction error is minimized

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Principal Component Analysis - continued
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Eigen Values of 400 Eigen Vectors
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Principal Component Analysis - continued
Reconstructed using 50 PCs
Reconstructed using 200 PCs
Original Image
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Principal Component Analysis - continued

• Is PCA representation a good representation of
  images for recognition in that images that have
  similar principal representations are similar?
• Image generation through sampling
• Roughly speaking, we try to generate images that
  have the given coefficients along PCs

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Principal Component Analysis - continued
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Principal Component Analysis - continued
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Difference Between Reconstruction and Sampling
Reconstruction is not sufficient to show the
adequacy of a representation and sampling from
the set of images with same representation is
more informational
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Object Recognition Experiments

• We compare linear methods in the methods
  including
• Principal component analysis (PCA)
• Independent component analysis (ICA)
• Fisher discriminant analysis (FDA)
• Random component analysis (RCA)
• For fun and to show the actual gain of using
  different bases is relatively small
• Corresponding linear methods in the spectral
  histogram space including
• SPCA, SICA, SFDA, and SRCA

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COIL Dataset
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3D Recognition Results
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Experimental Results - continued

• To further demonstrate the effectiveness of our
  method for different types of images, we create a
  dataset of combining the texture dataset, face
  dataset, and COIL dataset, resulting in a dataset
  of 180 categories with 10160 images in total

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Linear Subspaces of Spectral Representation
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Experimental Results - continued

• Combined dataset continued
• Not only the recognition rate is very good, but
  also it is very reliable and robust, as the
  average entropy of the p0(iI) is 0.60 bit (The
  corresponding uniform distributions entropy is
  7.49 bits)

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Experimental Results - continued

• Combined dataset continued
• Not only the recognition rate is very good, but
  also it is very reliable and robust, as the
  average entropy of the p0(iI) is 0.60 bit (The
  corresponding uniform distributions entropy is
  7.49 bits)