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Computer Vision Metrics: Chapter Three (Part D)

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For Part C of Chapter Three, please click here.

Bibliography references are set off with brackets, i.e. "[XXX]". For the corresponding bibliography entries, please click here.

Statistical Region Metrics

Describing texture in terms of statistical metrics of the pixels is a common and intuitive method. Often a simple histogram of a region will be sufficient to describe the texture well enough for many applications. There are also many variations of the histogram, which lend themselves to a wide range of texture analysis. So this is a good point at which to examine histogram methods. Since statistical mathematics is a vast field, we can only introduce the topic here, dividing the discussion into image moment features and point metric features.

Image Moment Features

Image moments [518,4] are scalar quantities, analogous to the familiar statistical measures such as mean, variance, skew, and kurtosis. Moments are well suited to describe polygon shape features and general feature metric information such as gradient distributions. Image moments can be based on either scalar point values or basis functions such as Fourier or Zernike methods discussed later in the section on basis space.

Moments can describe the projection of a function onto a basis space—for example, the Fourier transform projects a function onto a basis of harmonic functions. Note that there is a conceptual relationship between 1D and 2D moments in the context of shape description. For example, the 1D mean corresponds to the 2D centroid, and the 1D minimum and maximum correspond to the 2D major and minor axis. The 1D minimum and maximum also correspond to the 2D bounding box around the 2D polygon shape (also see Figure 6-29).

In this work, we classify image moments under the term polygon shape descriptors in the taxonomy (see Chapter 5). Details on several image moments used for 2D shape description will be covered in Chapter 6, under “Object Shape Metrics for Blobs and Objects.”

Common properties of moments in the context of 1D distributions and 2D images include:

  • 0th order moment is the mean or 2D centroid.
  • Central moments describe variation around the mean or 2D centroid.
  • 1st order central moments contain information about 2D area, centroid, and size.
  • 2nd order central moments are related to variance and measure 2D elliptical shape.
  • 3rd order central moments provide symmetry information about the 2D shape, or skewness.
  • 4th order...