Outline

1
Outline

• Texture modeling - continued
• Filtering-based approaches

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Texture Modeling

• The structures of images
• The structures in images are due to the
  inter-pixel relationships
• The key issue is how to characterize the
  relationships

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Representing Textures through Filtering

• Filtering
• Convolving an image with a linear filter yields a
  representation of the image on a different basis
• The advantage of the transformation is that the
  process makes the local structure of the image
  clear
• A filter can be viewed as a template
• There is a strong response when the local image
  pattern looks similar to the filter kernel and a
  weak response when it does not

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Representing Textures through Filtering cont.
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Representing Textures through Filtering cont.
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Representing Textures through Filtering cont.

• Gabor filters
• Gabor filters have been widely in texture
  modeling
• Mathematically, Gabor filters are optimal in the
  sense of local joint spatial/frequency
  representation

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Representing Textures through Filtering cont.
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Representing Textures through Filtering cont.

• Problems with filtering-based approaches
• The filter response itself does not give rise to
  a representation or a model for textures
• Even for homogenous textures, the filter
  responses are not homogenous

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Representing Textures through Filtering cont.
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Representing Textures through Filtering cont.

• Non-linear smoothing
• In order to derive a more homogenous and
  meaningful feature for textures, the filter
  responses are then passed through a non-linear
  stage
• The hope is that smoothed filter response will be
  relative homogenous within a texture region
• This can be used for texture classification,
  texture boundary detection, and texture
  discrimination

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Texture Classification Based on Filtering
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Texture Classification Based on Filtering cont.
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Texture Classification Based on Filtering cont.
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Texture Classification Based on Filtering cont.
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Histograms of Filter Responses as Texture Models

• Histograms as texture features
• For homogenous textures, histograms should not
  change very much
• In other words, texture images with similar
  histograms of filter responses should look
  similar
• Heeger and Bergen proposed a texture synthesis
  algorithm based on this observation

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Histograms of Filter Responses as Texture Models
cont.
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Histograms of Filter Responses as Texture Models
cont.
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Histograms of Filter Responses as Texture Models
cont.
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Histograms of Filter Responses as Texture Models
cont.
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Histograms of Filter Responses as Texture Models
cont.
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Histograms of Filter Responses as Texture Models
cont.
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Histograms of Filter Responses as Texture Models
cont.
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Non-Parametric Sampling

• Non-parametric sampling
• When we need to decide a pixel value, we
  calculate the conditional probability given the
  pixel values in the surrounding neighborhood
• This is done by finding the similar surrounding
  neighborhood in the given texture

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Non-Parametric Sampling cont.
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Non-Parametric Sampling cont.
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Non-Parametric Sampling cont.