Texture Analysis

1
Fac. of Comp., Eng. Tech. Staffordshire
University
Image Processing, Computer Vision, and Pattern
Recognition
Texture Analysis
Dr. Claude C. Chibelushi
2
Outline

• Introduction
• Visual Texture
• Applications
• Texture Description
• Statistical / structural techniques
• Texture Recognition
• Statistical / syntactic approach
• 3D Shape Recovery
• Summary

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Introduction

• Term (visual) texture is difficult to define
• regional image property characterised by
  repetition of a basic pattern
• important for analysis of images such as aerial
  images
• Basic pattern and/or its repetition may be
  deterministic (structural) or probabilistic
  (statistical)

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Introduction
Statistical textures
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Introduction
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Visual Texture

• Two main attributes for texture description
• texture primitive(s)
• spatial dependence or interaction between
  primitives (neighbourhood lay-out)
• Texture characterisation
• number, type, size, shade, ... of primitives
• spatial organisation of neighbourhood of primitive

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Visual Texture

• Typical linguistic descriptors of texture
• fineness, coarseness, smoothness, randomness,
  granulation, ...
• Textures may also be classified as
• weak texture
• strong texture

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Visual Texture

• Weak texture
• displays little spatial interaction between
  primitives
• e.g. majority of natural textures
• Strong texture
• displays non-random spatial interaction between
  primitives
• e.g. majority of human-made textures

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Applications

• Texture is useful attribute for image analysis
• Examples
• image segmentation e.g.
• cell cultures (counting / anomaly detection, ...)
• satellite images (farm-land / water bodies /
  clouds /...)
• surface defects (wood, textile soiling, coated
  metal plates, ...)

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Applications

• Examples (ctd.)
• 3D shape recovery
• shape-from-texture techniques

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Texture Description

• To measure textural properties
• analysis typically applied to sub-images
• Two broad classes of texture descriptions
• statistical description
• based on (pixel) distributions
• structural (syntactical) description
• based on structure / arrangement of primitives

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Texture Description

• Statistical description
• Based on e.g.
• grey-level autocorrelation
• spatial grey-level dependence matrix (SGLDM)
• grey-level mean, median, variance (possibly
  determined from grey-level histogram)
• Fourier or wavelet transform (frequency domain)
• ...

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Texture Description

• Statistical techniques
• Grey-level autocorrelation
• detects repetition / periodicity / frequency of
  primitive(s) similar to spectral transforms
• repetition of texture pattern leads to peaks in
  correlation coefficient

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Texture Description

• Statistical techniques
• Grey-level autocorrelation (ctd.)
• periodicity computation procedure
• (i) consider group of adjacent pixels
• (ii) calculate (auto)correlation coefficient
• (iii) shift group by one pixel
• (iv) if overlap, go to (ii)
• (v) shift giving maximum absolute value of
  coefficient gives possible repetition period
• what if maximum value is low?

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Texture Description

• Statistical techniques
• Grey-level autocorrelation (ctd.)
• Correlation coefficient

• denominator is scaling factor so that -1 ? r ? 1
• hence it can be omitted from computation of
  periodicity

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Texture Description

• Statistical techniques
• Grey-level autocorrelation (ctd.)
• Correlation coefficient numerator can be
  expanded into

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Texture Description

• Statistical techniques
• Grey-level autocorrelation (example 1D image
  segment 0110100101)

Period 4
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Texture Description

• Statistical techniques
• Grey-level autocorrelation pseudo code
• / Calculate texture periodicity for each image
  block /
• for each blockPosRow // row where block starts
  in image
• for each blockPosCol // column where block
  starts
• blockCopy copyBlock(image, blockPosRow,
  blockPosCol, blockWidth, blockHeight)
• // find texture periodicity for image block
• textPeriod findTextPer(image, blockPosRow,
  blockPosCol, blockCopy, blockWidth,
  blockHeight)

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Texture Description

• Statistical techniques
• Grey-level autocorrelation pseudo code
• / Calculate texture periodicity for image block
  /
• findTextPer(image, blockPosRow, blockPosCol,
  blockCopy, blockWidth, blockHeight)
• overlapWidth blockWidth overlapHeight
  blockHeight
• rMax 0 period.row period.col 0
• for rowLag from 0 to (blockHeight - 1) //
  downward shift
• for colLag from 1 to (blockWidth - 1) //
  rightward shift
• overlapWidth - 1 // reduce width of overlap
  region
• r calcCorrelCoeff(image, blockPosRow
  rowLag,
• blockPosCol colLag, blockCopy,
  overlapWidth, overlapHeight)
• absR fabs(r)
• if (absR gt rMax) // find maximum
  autocorrelation coefficient
• rMax absR
• period.row rowLag period.col colLag
• overlapHeight - 1 // reduce height of
  overlap region

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Texture Description

• Statistical techniques
• Grey-level autocorrelation pseudo code
• / Calculate correlation coefficient for given
  block and specified lag /
• calcCorrelCoeff(image, rowOffset, colOffset,
  rowLag, colLag, blockCopy, overlapWidth,
  overlapHeight)
• sumOrigPix sumShiftedPix sumOfPixProd 0
• for blockRow from 0 to (overlapHeight - 1)
• for blockCol from 0 to (overlapWidth - 1)
• origPix imagerowOffset blockRowcolOffset
  blockCol
• shiftPix blockCopyblockRowblockCol
• sumOrigPix origPix
• sumShiftedPix shiftPix
• sumOfPixProd origPix shiftPix
• overlapSize overlapWidth overlapHeight
• r sumOfPixProd - (sumOrigPix sumShiftedPix)
  / overlapSize
• return r

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Texture Description

• Statistical techniques
• SGLDM
• characterises texture by spatial relationship of
  grey-level pairs
• counts co-occurrence of grey-level pairs
• relationship specified by distance / angle
  between the two pixels
• good characterisation of lay-out but poor
  characterisation of shape of primitives (e.g.
  large-area primitives)

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Texture Description

• Statistical techniques
• SGLDM (ctd.)
• procedure
• (i) set distance and angle between pixels
• (ii) count number of occurrences of grey-level
  pairs

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Texture Description

• Statistical techniques
• SGLDM (ctd.)
• SGLDM can be generalised to co-occurrence of
  properties of primitives consisting of connected
  pixels (e.g. line segment)
• counts co-occurrence of pairs of values (for
  properties such as size, average grey-level of
  primitive)
• spatial relationship typically specified by
  distance or adjacency

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Texture Description

• Statistical techniques
• SGLDM (example 1D image segment 0110100101)

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Texture Description

• Statistical techniques
• SGLDM code
• // initialise SGLDM elements to 0
• ...
• // set rStep cStep based on pixels distance and
  angle
• ...
• / calculate SGLDM /
• for (row 0 row lt IM_HEIGHT row)
• for (col 0 col lt IM_WIDTH col)
• pix1 imagerowcol
• pix2 imagerow rStepcol cStep
• SGLDMpix1pix2

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Texture Description

• Statistical techniques
• SGLDM (ctd.)
• texture discrimination often based on
  measurements derived from SGLDMs, e.g.
• energy or uniformity sum of squares of matrix
  entries
• contrast sum of multiplication of each matrix
  entry by difference between corresponding grey
  levels
• maximum of matrix entries

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Texture Description

• Structural techniques
• Best for texture with primitives in almost
  regular repetitive spatial arrangement
• Typical procedure
• (i) identify primitives (e.g. line segments,
  polygons, circles, ...)
• set of primitives is equivalent to alphabet or
  vocabulary
• (ii) define spatial arrangement rule(s) using
  graphs, trees,
• equivalent to lay-out grammar or syntax

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Texture Description

• Structural techniques

Example of textures suitable for
structural analysis
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Texture Recognition
Statistical approach training phase
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Texture Recognition
Statistical approach recognition phase
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Texture Recognition
Syntactic approach training phase
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Texture Recognition
Syntactic approach recognition phase
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3D Shape Recovery
Surface depth cue textural variation (texel size
change / shape distortion)
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3D Shape Recovery

• Texture gradient
• maximum rate of change of texture-primitive size
• can convey information about orientation of
  object surface or viewing angle
• may be useful for recovery of 3-D information
• 3-D shape
• viewing position / direction

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Summary

• Texture relates to repetition of basic pixel
  pattern
• Texture can be statistical, deterministic, or
  hybrid
• Texture analysis techniques
• statistical (grey-level autocorrelation, SGLDM,
  ...)
• structural
• hybrid
• Texture can convey 3D cues