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Global Black-and-White Thresholding

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Tools for performing global black-and-white thresholding on datasets in Microscopy Image Browser (MIB).

Overview

Global thresholding interface

The Global black-and-white thresholding tool in MIB applies various algorithms to segment images into binary (black-and-white) regions based on pixel intensity. This tool is accessible via Menu → Tools → Semi-automatic segmentation → Global thresholding and supports multiple thresholding methods, each suited to different image characteristics.

Demonstration

Global black and white thresholding in MIB

Algorithms for global black and white thresholding

CONCAVITY algorithm

Details
  • Suitable when images lack distinct objects and background, rendering MINIMUM and INTERMODES algorithms ineffective
  • Identifies a threshold at the histogram's shoulder using concavity analysis
  • Constructs the convex hull H of the histogram y
  • Finds local maxima of |H - y|
  • Sets threshold t to the value of j maximizing the balance measure bj = Aj(An - Aj)
  • Works well in many cases but may produce unusable thresholds in some scenarios

References and Acknowledgements

  • A. Rosenfeld and P. De La Torre, "Histogram concavity analysis as an aid in threshold selection," IEEE Trans. Systems Man Cybernet., vol. 13, pp. 231-235, 1983
  • Based on the HistThresh Toolbox by Antti Niemistö, Tampere University of Technology, Finland

ENTROPY algorithm

Details
  • A maximum entropy method that splits the histogram into two probability distributions: objects and background
  • Chooses threshold t to maximize the sum of entropies of these distributions
  • Defines partial sums:
    Ej = Σ(i=0 to j) yi · log(yi), for j = 0, ..., n
  • Sets t to the value of j maximizing:
    (Ej / Aj) - log(Aj) + ((En - Ej) / (An - Aj)) - log(An - Aj)

References and Acknowledgements

  • J. N. Kapur, P. K. Sahoo, and A. K. C. Wong, "A new method for gray-level picture thresholding using the entropy of the histogram," Comput. Vision Graphics Image Process., vol. 29, pp. 273-285, 1985
  • Based on the HistThresh Toolbox by Antti Niemistö, Tampere University of Technology, Finland

INTERMEANS ITER algorithm

Details
  • An iterative algorithm similar to OTSU but less computationally intensive
  • Starts with an initial guess for threshold t
  • Calculates means μt and νt for the two classes
  • Updates t = [(μt + νt) / 2] and recalculates μt and νt
  • Repeats until t stabilizes across iterations
  • Results may depend heavily on the initial t value
  • Use MEAN for comparable object and background areas; use INTERMODES for small objects relative to the background

References and Acknowledgements

  • T. Ridler and S. Calvard, "Picture thresholding using an iterative selection method," IEEE Trans. Systems Man Cybernet., vol. 8, pp. 630-632, 1978
  • H. J. Trussell, "Comments on ‘Picture thresholding using an iterative selection method’," IEEE Trans. Systems Man Cybernet., vol. 9, p. 311, 1979
  • Based on the HistThresh Toolbox by Antti Niemistö, Tampere University of Technology, Finland

INTERMODES algorithm

Details
  • An alternative to MINIMUM, assuming a bimodal histogram
  • Identifies two peaks (local maxima) yj and yk
  • Sets t = (j + k) / 2
  • Refines t = [(μt + νt) / 2] and recalculates μt and νt
  • Unsuitable for histograms with extremely unequal peaks

References and Acknowledgements

  • J. M. S. Prewitt and M. L. Mendelsohn, "The analysis of cell images," Ann. New York Acad. Sci., vol. 128, pp. 1035-1053, 1966
  • Based on the HistThresh Toolbox by Antti Niemistö, Tampere University of Technology, Finland

MEAN algorithm

Details
  • Similar to MEDIAN but uses the mean instead
  • Sets t to the integer part of the mean of all pixel values: t = Bn / An
  • Ignores histogram shape, often yielding suboptimal results

References and Acknowledgements

  • Based on the HistThresh Toolbox by Antti Niemistö, Tampere University of Technology, Finland

MEDIAN and PERCENTILE algorithms

Details
  • Assumes a known percentage of object pixels
  • Sets t to the highest gray-level mapping at least (100 - p)% of pixels to the object category
  • Not ideal if object area is unknown
  • Parametric issue resolved by setting p = 50, making t the median of pixel values

References and Acknowledgements

  • W. Doyle, "Operation useful for similarity-invariant pattern recognition," J. Assoc. Comput. Mach., vol. 9, pp. 259-267, 1962
  • Based on the HistThresh Toolbox by Antti Niemistö, Tampere University of Technology, Finland

MINERROR algorithm

Details
  • Similar to OTSU, treating the histogram as a probability density function of a mixture population
  • Assumes a Gaussian mixture model with normal distributions for objects and background, allowing different means and variances
  • Defines statistics:
    pt = At / An, qt = (An - At) / An
    σt² = (Ct / At) - μt², τt² = ((Cn - Ct) / (An - At)) - νt²
  • Sets t to minimize:
    pj log(σj / pj) + qj log(τj / qj)

References and Acknowledgements

  • J. Kittler and J. Illingworth, "Minimum error thresholding," Pattern Recognition, vol. 19, pp. 41-47, 1986
  • Based on the HistThresh Toolbox by Antti Niemistö, Tampere University of Technology, Finland

MINERROR ITER algorithm

Details
  • An iterative, less intensive version of MINERROR
  • Initializes t using MEAN
  • Solves:
    x² (1/σ² - 1/τ²) - 2x (μ/σ² + ν/τ²) + (μ²/σ² - ν²/τ² + log(σ²q² / τ²p²)) = 0
  • Sets t = (w1 + √(w1² - w0w2)) / w0, where w0, w1, and w2 are the equation terms
  • Recalculates and repeats until convergence
  • Fails if the quadratic equation lacks a real solution

References and Acknowledgements

  • J. Kittler and J. Illingworth, "Minimum error thresholding," Pattern Recognition, vol. 19, pp. 41-47, 1986
  • Based on the HistThresh Toolbox by Antti Niemistö, Tampere University of Technology, Finland

MINIMUM algorithm

Details
  • Assumes a bimodal histogram
  • Smooths the histogram with a three-point mean filter until only two local maxima remain
  • Chooses t where yt-1 > yt < yt+1
  • Unsuitable for histograms with unequal peaks or broad, flat valleys

References and Acknowledgements

  • J. M. S. Prewitt and M. L. Mendelsohn, "The analysis of cell images," Ann. New York Acad. Sci., vol. 128, pp. 1035-1053, 1966
  • Based on the HistThresh Toolbox by Antti Niemistö, Tampere University of Technology, Finland

MOMENTS algorithm

Details
  • Sets t to preserve the first three moments of the gray-level image in the binary result
  • Calculates t where At / An is closest to x0:
    x0 = ½ - (Bn/An + x2/2) / √(x2² - 4x1)
    x1 = (BnDn - Cn²) / (AnCn - Bn²), x2 = (BnCn - AnDn) / (AnCn - Bn²), Dn = Σ(i=0 to n) i²yi

References and Acknowledgements

  • W. Tsai, "Moment-preserving thresholding: a new approach," Comput. Vision Graphics Image Process., vol. 29, pp. 377-393, 1985
  • Based on the HistThresh Toolbox by Antti Niemistö, Tampere University of Technology, Finland

OTSU algorithm

Details
  • Implements MATLAB’s Otsu algorithm via graythresh
  • Calculates an optimal threshold t to minimize intra-class variance

References and Acknowledgements

  • N. Otsu, "A Threshold Selection Method from Gray-Level Histograms," IEEE Transactions on Systems, Man, and Cybernetics, vol. 9, no. 1, pp. 62-66, 1979

Programming tips

This tool supports batch scripting for automation.

Example of usage

Define parameters in a structure, using field names from widget tooltips (some are optional), and start the controller:

BatchOpt.colChannel = 2;         % define color channel for thresholding
BatchOpt.Mode = '3D, Stack';     % mode to use
BatchOpt.Method = 'Otsu';        % thresholding algorithm
BatchOpt.Destination = 'selection'; % [optional] destination layer, 'mask' or 'selection'
BatchOpt.t = [1 1];              % [optional] time points, [t1, t2]
BatchOpt.z = [10 20];            % [optional] slices, [z1, z2]
BatchOpt.x = [10 120];           % [optional] part of the image, [x1, x2]
BatchOpt.Orientation = 4;        % [optional] dataset orientation
obj.startController('mibHistThresController', [], BatchOpt); % start thresholding

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