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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

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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