# Global black-and-white thresholding

Perform global black-and-white thresholding of the dataset.

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A demonstration of the global black-and-white thresholding is available in the following video:

https://youtu.be/mzfgxLvkGTI

## Contents

## CONCAVITY algorithm

- If the image does not have distinct objects and background, the MINIMUM and INTERMODES algorithms are not suitable.
- A good threshold may be found at the shoulder of the histogram.
- The shoulder location can be found based on the concavity of the histogram.
- Construct the convex hull H of the histogram y.
- Find the local maxima of
`H - y`. - Set
`t`to the value of`j`at which the balance measure`bj = Aj(An - Aj)`is maximized - The algorithm seems to work well in many cases, but in some cases it gives thresholds that are clearly unusable

**Reference** 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

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

## ENTROPY algorithm

- One of several maximum entropy algorithms
- Divides the histogram of the image into two probability distributions, one representing the objects and one representing the background
- Choose t such that the sum of the entropies of these probability distributions is maximized
- Define the partial sums:

- Set t to the value of j at which an equiation below is maximized

**Reference**

- 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.

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

## INTERMEANS ITER algorithm

- An iterative algorithm that gives similar results as the OTSU algorithm
- Computationally less intensive than OTSU
- The algorithm starts with an initial guess for
`t` - Define the means μt and νt of the two classes
- Set
`t = [(μt + νt)/2]`and recalculate μt and νt. - Repeat until
`t`has the same value in two consecutive iterations - The obtained t may strongly depend on its initial value
- If the objects and background occupy comparable areas, use MEAN
- If the objects are small compared to the background, use INTERMODES.

**References**

- 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.

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

## INTERMODES algorithm

- An alternative to MINIMUM
- Assumes a bimodal histogram
- Find the two peaks (local maxima)
`yj`and`yk` - Set
`t`to`(j + k)/2` - Set
`t = [(μt + νt)/2]`and recalculate μt and νt. - Still unsuitable for images that have a histogram with extremely unequal peaks

**Reference**

- J. M. S. Prewitt and M. L. Mendelsohn, The analysis of cell images, in Ann. New York Acad. Sci., vol. 128, pp. 1035-1053, 1966

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

## MEAN algorithm

- Similar to the MEDIAN algorithm
- Instead of median, set
`t`such that it is the integer part of the mean of all pixel values - With the partial sum notation,
`t = Bn/An` - Does not take into account histogram shape, so obviously the results are suboptimal

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

## MEDIAN and PERCENTILE algorithms

- Assumes that the percentage of object pixels is known
- Set
`t`to the highest gray-level which maps at least`(100 - p)%`of the pixels into the object category - Not suitable if the object area is not know
- Problem: the algorithm is parametric
- Solution: set
`p = 50`so that`t`is the median of the distribution of pixel values

**Reference**

- W. Doyle, Operation useful for similarity-invariant pattern recognition, J. Assoc. Comput. Mach, vol. 9, pp. 259-267, 1962

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

## MINERROR algorithm

- Similar to the OTSU algorithm
- Views the histogram as an estimate of the probability density function of the mixture population (objects and background)
- Assumes a Gaussian mixture model, that is,
**A)**the pixels in the two categories come from a normal distribution and**B)**the normal distributions may have different means as well as variances - Define the following statistics:

- Set
`t`to the value of`j`at which is minumized

**Reference**

- J. Kittler and J. Illingworth, Minimum error thresholding, Pattern Recognition, vol. 19, pp. 41-47, 1986

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

## MINERROR ITER algorithm

- The iterative version of the MINERROR algorithm is computationally less intensive
- Find initial value for
`t`using MEAN - The integer part of the larger solution provides a new value
`t`:

- Let w0, w1 and w2 denote the three terms
- Set
- Recalculate all the terms using the new value of
`t`and re-derive`t` - Repeat until convergence
- This minimizes the number of misclassi?cations between the two normal distributions with the given means, variances, and proportions
- The algorithm fails to converge if the quadratic equation does not have a real solution

**Reference**

- J. Kittler and J. Illingworth, Minimum error thresholding, Pattern Recognition, vol. 19, pp. 41-47, 1986

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

## MINIMUM algorithm

- Assumes a bimodal histogram
- The histogram needs to be smoothed (using the three-point mean filter) iteratively until the histogram has only two local maxima
- Choose
`t`such that`yt - 1 > yt ? yt + 1` - Unsuitable for images that have a histogram with extremely unequal peaks or a broad and flat valley

**Reference**

- J. M. S. Prewitt and M. L. Mendelsohn, The analysis of cell images, in Ann. New York Acad. Sci., vol. 128, pp. 1035-1053, 1966

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

## MOMENTS algorithm

- Choose
`t`such that the binary image has the same ?rst three moments as the gray-level image - his is achieved by setting
`t`such that`At/An`is the value of the fraction nearest to`x0`, where

**Reference**

- W. Tsai, Moment-preserving thresholding: a new approach, Comput. Vision Graphics Image Process., vol. 29, pp. 377-393, 1985

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

## OTSU algorithm

- MATLAB implementation of the Otsu algorithm
- The
`t`value is calculated using`graythresh`

**Reference**

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

## Programming tips

This function is compatible with the batch scripting.

- Define parameters as a structure, where the names of the fields can be checked from the tooltips of the widgets
- Some of the parameters are optional
- use mibController.startController function, where the 3rd input is the defined structure with parameters

For example,

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, [z1, z2] BatchOpt.Orientation = 4; % [optional], dataset orientation obj.startController('mibHistThresController', [], BatchOpt); % start the thresholding

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