HistogramThresholding.jl Documentation

t = find_threshold(Otsu(), histogram, edges)

Under the assumption that the histogram is bimodal the threshold is set so that the resultant inter-class variance is maximal.

Output

Returns a real number t that specifies the threshold.

Arguments

The function arguments are described in more detail below.

histogram

An AbstractArray storing the frequency distribution.

edges

An AbstractRange specifying how the intervals for the frequency distribution are divided.

Example

Compute the threshold for the "cameraman" image in the TestImages package.

using TestImages, ImageContrastAdjustment, HistogramThresholding

img = testimage("cameraman")
edges, counts = build_histogram(img,256)
#=
  The `counts` array stores at index 0 the frequencies that were below the
  first bin edge. Since we are seeking a threshold over the interval
  partitioned by `edges` we need to discard the first bin in `counts`
  so that the dimensions of `edges` and `counts` match.
=#
t = find_threshold(Otsu(), counts[1:end], edges)

Reference

1. Nobuyuki Otsu (1979). "A threshold selection method from gray-level histograms". IEEE Trans. Sys., Man., Cyber. 9 (1): 62–66. doi:10.1109/TSMC.1979.4310076

t = find_threshold(MinimumIntermodes(), histogram, edges; maxiter = 8000)

Under the assumption that the histogram is bimodal the histogram is smoothed using a length-3 mean filter until two modes remain. The threshold is then set to the minimum value between the two modes.

Output

Returns t, a real number that specifies the threshold.

Details

If after maxiter iterations the smoothed histogram is still not bimodal then the algorithm will fall back to using the UnimodalRosin method to select a threshold.

Arguments

The function arguments are described in more detail below.

histogram

An AbstractArray storing the frequency distribution.

edges

An AbstractRange specifying how the intervals for the frequency distribution are divided.

maxiter

An Int that specifies the maximum number of smoothing iterations. If left unspecified a default value of 8000 is used.

Example

Compute the threshold for the "cameraman" image in the TestImages package.

using TestImages, ImageContrastAdjustment, HistogramThresholding

img = testimage("cameraman")
edges, counts = build_histogram(img,256)
#=
  The `counts` array stores at index 0 the frequencies that were below the
  first bin edge. Since we are seeking a threshold over the interval
  partitioned by `edges` we need to discard the first bin in `counts`
  so that the dimensions of `edges` and `counts` match.
=#
t = find_threshold(MinimumIntermodes(), counts[1:end], edges)

Reference

1. C. A. Glasbey, “An Analysis of Histogram-Based Thresholding Algorithms,” CVGIP: Graphical Models and Image Processing, vol. 55, no. 6, pp. 532–537, Nov. 1993. doi:10.1006/cgip.1993.1040
2. J. M. S. Prewitt and M. L. Mendelsohn, “THE ANALYSIS OF CELL IMAGES,” *Annals of the New York Academy of Sciences, vol. 128, no. 3, pp. 1035–1053, Dec. 2006. doi:10.1111/j.1749-6632.1965.tb11715.x

t = find_threshold(Intermodes(), histogram, edges; maxiter = 8000)

Under the assumption that the histogram is bimodal the histogram is smoothed using a length-3 mean filter until two modes remain. The threshold is then set to the average value of the two modes.

Output

Returns a real number t that specifies the threshold.

Details

If after maxiter iterations the smoothed histogram is still not bimodal then the algorithm will fall back to using the UnimodalRosin method to select a threshold.

Arguments

The function arguments are described in more detail below.

histogram

An AbstractArray storing the frequency distribution.

edges

An AbstractRange specifying how the intervals for the frequency distribution are divided.

maxiter

An Int that specifies the maximum number of smoothing iterations. If left unspecified a default value of 8000 is used.

Example

Compute the threshold for the "cameraman" image in the TestImages package.

using TestImages, ImageContrastAdjustment, HistogramThresholding

img = testimage("cameraman")
edges, counts = build_histogram(img,256)
#=
  The `counts` array stores at index 0 the frequencies that were below the
  first bin edge. Since we are seeking a threshold over the interval
  partitioned by `edges` we need to discard the first bin in `counts`
  so that the dimensions of `edges` and `counts` match.
=#
t = find_threshold(Intermodes(), counts[1:end], edges)

Reference

1. C. A. Glasbey, “An Analysis of Histogram-Based Thresholding Algorithms,” CVGIP: Graphical Models and Image Processing, vol. 55, no. 6, pp. 532–537, Nov. 1993. doi:10.1006/cgip.1993.1040

t = find_threshold(MinimumError(), histogram, edges)

Under the assumption that the histogram is a mixture of two Gaussian distributions the threshold is chosen such that the expected misclassification error rate is minimised.

Output

Returns a real number t that specifies the threshold.

Arguments

The function arguments are described in more detail below.

histogram

An AbstractArray storing the frequency distribution.

edges

An AbstractRange specifying how the intervals for the frequency distribution are divided.

Example

Compute the threshold for the "cameraman" image in the TestImages package.

using TestImages, ImageContrastAdjustment, HistogramThresholding

img = testimage("cameraman")
edges, counts = build_histogram(img,256)
#=
  The `counts` array stores at index 0 the frequencies that were below the
  first bin edge. Since we are seeking a threshold over the interval
  partitioned by `edges` we need to discard the first bin in `counts`
  so that the dimensions of `edges` and `counts` match.
=#
t = find_threshold(MinimumError(), counts[1:end], edges)

References

1. J. Kittler and J. Illingworth, “Minimum error thresholding,” Pattern Recognition, vol. 19, no. 1, pp. 41–47, Jan. 1986. doi:10.1016/0031-3203(86)90030-0
2. Q.-Z. Ye and P.-E. Danielsson, “On minimum error thresholding and its implementations,” Pattern Recognition Letters, vol. 7, no. 4, pp. 201–206, Apr. 1988. doi:10.1016/0167-8655(88)90103-1

t = find_threshold(Moments(), histogram, edges)

The following rule determines the threshold: if one assigns all observations below the threshold to a value z₀ and all observations above the threshold to a value z₁, then the first three moments of the original histogram must match the moments of this specially constructed bilevel histogram.

Output

Returns a real number t that specifies the threshold.

Arguments

The function arguments are described in more detail below.

histogram

An AbstractArray storing the frequency distribution.

edges

An AbstractRange specifying how the intervals for the frequency distribution are divided.

Example

Compute the threshold for the "cameraman" image in the TestImages package.

using TestImages, ImageContrastAdjustment, HistogramThresholding

img = testimage("cameraman")
edges, counts = build_histogram(img,256)
#=
  The `counts` array stores at index 0 the frequencies that were below the
  first bin edge. Since we are seeking a threshold over the interval
  partitioned by `edges` we need to discard the first bin in `counts`
  so that the dimensions of `edges` and `counts` match.
=#
t = find_threshold(Moments(), counts[1:end], edges)

Reference

[1] W.-H. Tsai, “Moment-preserving thresolding: A new approach,” Computer Vision, Graphics, and Image Processing, vol. 29, no. 3, pp. 377–393, Mar. 1985. doi:10.1016/0734-189x(85)90133-1

t = find_threshold(UnimodalRosin(), histogram, edges)

Generates a threshold assuming a unimodal distribution using Rosin's algorithm.

Output

Returns t, a real number that specifies the threshold.

Details

This algorithm first selects the bin in the histogram with the highest frequency. The algorithm then searches from the location of the maximum bin to the last bin of the histogram for the first bin with a frequency of 0 (known as the minimum bin.). A line is then drawn that passes through both the maximum and minimum bins. The bin with the greatest orthogonal distance to the line is chosen as the threshold value.

Assumptions

This algorithm assumes that:

• The histogram is unimodal.
• There is always at least one bin that has a frequency of 0. If not, the algorithm will use the last bin as the minimum bin.
• If the histogram includes multiple bins with a frequency of 0, the algorithm will select the first zero bin as its minimum.
• If there are multiple bins with the greatest orthogonal distance, the leftmost bin is selected as the threshold.

Arguments

The function arguments are described in more detail below.

histogram

An AbstractArray storing the frequency distribution.

edges

An AbstractRange specifying how the intervals for the frequency distribution are divided.

Example

Compute the threshold for the "moonsurface" image in the TestImages package.

using TestImages, ImageContrastAdjustment, HistogramThresholding

img = testimage("moonsurface")
edges, counts = build_histogram(img,256)
#=
  The `counts` array stores at index 0 the frequencies that were below the
  first bin edge. Since we are seeking a threshold over the interval
  partitioned by `edges` we need to discard the first bin in `counts`
  so that the dimensions of `edges` and `counts` match.
=#
t = find_threshold(UnimodalRosin(), counts[1:end], edges)

Reference

1. P. L. Rosin, “Unimodal thresholding,” Pattern Recognition, vol. 34, no. 11, pp. 2083–2096, Nov. 2001.doi:10.1016/s0031-3203(00)00136-9