Statistical Object Features

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Statistical Object Features

• Jin, Tao

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Introduction

• We have modified the image from the lowest level
  of pixel data into higher-level representations,
  using image segmentation and transforms.
• Image segmentation allows us to look at object
  features.
• Object features include the geometric properties
  of binary objects, histogram features, and color
  features.

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Geometric Object features

• To extract object features, we need an image that
  has undergone image segmentation and any
  necessary morphological filtering. This will
  provide us with clearly defined objects, which
  can then be labeled and processed independently.
• Labeled image is used to extract the features of
  interest.
• The binary object features include area, center
  of area, axis of least second moment, perimeter,
  Euler number, projections, thinness ratio, and
  aspect ratio.
• Area, center of area, axis of least second
  moment, perimeter tell us something about where
  the object is. The other four tell about the
  shape of the objects.

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Area

• The area Ai is measured in pixels and indicates
  the relative size of the object.
• Ai SS Ii(r,c) (0 lt r, c lt N-1)
• Where
• Ii(r, c) 1 if I(r,c) ith object 0 otherwis
  e

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Center of area

• We define the center of area for an object by the
  pair (ri, ci)
• ri (SS rIi(r,c) )/Ai (0 lt r, c lt N-1)
• ci (SS cIi(r,c) )/Ai (0 lt r, c lt N-1)
• (sum of the r,c value of all the pixels divides
  the number of pixels)
• Theses correspond to the row coordinate of the
  center of area for the ith object ri, and the
  column coordinate of the center of area for the
  ith object ci.
• This feature will help to locate an object in the
  two-dimensional image plan.

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Axis of Least Second Moment

• The axis of least second moment provides
  information about the the objects orientation
• This axis corresponds to the line about which it
  takes the least amount of energy to spin an
  object of like shape.
• If we move the origin to the center of area
  (r,c), the axis of least second moment is defined
  as
• tan(2?i) 2 SSrcIi(r,c)/(SSr2Ii(r,c) -
  SSc2Ii(r,c))

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Axis of Least Second Moment(2)
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Perimeter

• The perimeter of the object can help us to locate
  in in space and provide information about the
  shape of the object.
• The perimeter can be found in the original binary
  image by counting the number of 1 pixels that
  have 0 pixels as neighbors.
• Or it can be found by applying an edge detector
  to the object, followed by counting the 1
  pixels. Finding the area of the border.

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Matlab - imfeature

• Matlab image processing toolbox provides the
  imfeature function
• statsimfeature(L,measurements)
• L labeled binary image
• Measurement name of the features
• Output struct array with fields.

• 80x1 struct array with fields
• Area
• Centroid
• BoundingBox
• MajorAxisLength
• MinorAxisLength
• Eccentricity
• Orientation
• ConvexHull
• ConvexImage
• ConvexArea
• Image
• FilledImage
• FilledArea
• EulerNumber
• Extrema
• EquivDiameter
• Solidity
• Extent

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Experiment Get labeled binary image

• Iimread('rice.tif')
• figure('Name', 'Original image'), imshow(I)
• Iim2double(I)
• bkgblkproc(I, 32,32, 'min(x())')
• bkgimresize(bkg, 256,256, 'biliniear')
• I2 I - bkg
• I2 max(min(I2,1),0)
• I3 imadjust(I2, 0 max(I2()), 0 1)
• apply thresholding to the image
• bw I3gt0.2
• label components
• L, numObj bwlabel(bw, 4)
• map hot(numObj1) create a colormap

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Experiment Extract object features

• Compute feature measurements of objects in the
  image
• FeatureData imfeature(L, 'all')

• FeatureData
• 80x1 struct array with fields
• Area
• Centroid
• BoundingBox
• MajorAxisLength
• MinorAxisLength
• Eccentricity
• Orientation
• ConvexHull
• ConvexImage
• ConvexArea
• Image
• FilledImage
• FilledArea
• EulerNumber
• Extrema
• EquivDiameter

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Experiment - Area

• Array FeatureData.Area
• Min min(Array)
• Max max(Array)
• Mean mean(Array)
• Std std(Array)
• figure('Name', 'histogram for area'), hist(Array,
  20)
• idx find(Array lt (Mean-Std))
• L2 ismember(L, idx)
• L2 I.L2
• figure('Name', 'Objects below mean-std area'),
  imshow(L2)
• idx find(Array gt (MeanStd))
• L2 ismember(L, idx)
• L2 I.L2
• figure('Name', 'Objects above meanstd area'),
  imshow(L2)

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Experiment Area(cont.)
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Experiment - centroid

• Array FeatureData.Centroid
• Array reshape(Array, 2, numObj)
• Min min(Array(1,)) min(Array(2,))
• Max max(Array(1,)) max(Array(2,))
• Mean mean(Array(1,)) mean(Array(2,))
• Std std(Array(1,)) std(Array(2,))
• figure('Name', 'histogram for Centroid.row'),
  hist(Array(1,), 20)
• figure('Name', 'histogram for Centroid.col'),
  hist(Array(2,), 20)
• row, col find( (Array(1,) lt
  (Mean(1,1)-Std(1,1))) (Array(2,) lt
  (Mean(2,1)-Std(2,1))))
• L2 ismember(L, col)
• L2 I.L2
• figure('Name', 'Objects below mean-std
  Centroid'), imshow(L2)
• row, col find( (Array(1,) gt
  (Mean(1,1)Std(1,1))) (Array(2,) gt
  (Mean(2,1)Std(2,1))))
• L2 ismember(L, col)
• L2 I.L2

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Experiment centeroid(cont.)
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Experiment Axis of least second moment

• Array FeatureData.Orientation
• Min min(Array)
• Max max(Array)
• Mean mean(Array)
• Std std(Array)
• figure('Name', 'histogram for Orientation'),
  hist(Array, 20)
• idx find((Array lt 0) (Array gt -90))
• L2 ismember(L, idx)
• L2 I.L2
• figure('Name', 'Objects between -90 to 0
  degree'), imshow(L2)
• idx find((Array gt 0) (Array lt 90))
• L2 ismember(L, idx)
• L2 I.L2
• figure('Name', 'Objects between 0 and 90
  degree'), imshow(L2)
• idx find((Array lt 180) (Array gt 90))

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Experiment axis of least second moment(cont.)
Note The orientation of imfeature is different
with the text book, and the value is in degree.