Auto Threshold and Auto Local Threshold
Requires ImageJ 1.42m or later.
These two plugins binarise 8-bit images using various global (histogram-derived) and local (adaptive) thresholding methods.
Latest version
Auto_Threshold v1.14, date: 14/Apr/2011Auto_Local_Threshold v1.4, date: 2/November/2011
Installation
ImageJ: Copy the (Auto_Threshold.jar file) into the ImageJ/Plugins folder and either restart ImageJ or run the Help>Update Menus command.After this, two new commands should appear in Image>Adjust>Auto Threshold and Image>Adjust>Auto Local Threshold.
Fiji: this plugin is part of the Fiji distribution, there is no need to download.
Auto Threshold
Use
Method selects the algorithm to be applied (detailed below). The Ignore black and Ignore white options set the image histogram bins for [0] and [255] greylevels to 0 respectively. This may be useful if the digitised image has under- or over- exposed pixels.White object on black background sets to white the pixels with values above the threshold value (otherwise, it sets to white the values less or equal to the threshold).
Set Threshold instead of Threshold (single images) sets the thresholding LUT, without changing the pixel data. This works only for single images.
It you are processing a stack, two additional options are available: Stack can be used to process all the slices (the threshold of each slice will be computed separately). If this option is left unchecked, only the current slice will be processed. Use stack histogram first computes the histogram of the whole stack, then computes the threshold based on that histogram and finally binarises all the slices with that single value. Selecting this option also selects the Stack option above automatically.
Note that the thresholded phase is always shown as white [255].
Since versions 1.8 and 1.1 of the two plugins respectively, the threshold of the binarised image is also silently set to 255 (i.e. not shown in red), so the particle analyzer should be able to pick the white pixels for the analysis.
Important notes:
1. This plugin is accessed through the Image>Auto Threshold menu entry, however the thresholding methods were also partially implemented in ImageJ's thresholder applet accessible through the Image>Adjust>Threshold... menu entry. While the Auto Threshold plugin can use or ignore the extremes of the image histogram (Ignore black, Ignore white) the applet cannot: the 'default' method ignores the histogram extremes but the others methods do not. This means that applying the two commands to the same image can produce apparently different results. In essence, the Auto Threshold plugin, with the correct settings, can reproduce the results of the applet, but not the way round.
2. From version 1.12 the plugin supports thresholding of 16-bit images. Since the Auto Threshold plugin processes the full greyscale space, it can be slow when dealing with 16-bit images. Note that the ImageJ thresholder applet also processes 16-bit images, but in reality ImageJ first computes a histogram with 256 bins. Therefore, there might be differences in the results obtained on 16-bit images when using the applet and the true 16-bit results obtained with this plugin. Note that for speeding up, the histogram is bracketed to include only the range of bins that contain data (and avoid processing empty histogram bins at both extremes).
3. The result of 16 bit images and stacks (when processing all slices) is an 8 bit container showing the result in white [255] to comply with the concept of "binary image" (i.e. 8 bits with 0 and 255 values). However, for stacks where only 1 slice is thresholded, the result is still a 16 bit container with the thresholded phase shown as white [65535]. This is to keep the data untouched in the remaining slices. The "Try all" option retains the 16 bit format to show methods that might fail to obtain a threshold. Images and stacks that impossible to threshold remain unchanged.
4. The same image in 8 and 16 bits (without scaling) returns the same threshold value, however Li's method originally would return different values when the image data was offset (e.g. when adding a fixed value to all pixels). The current implementation avoids this offset-dependent problem.
5. The same image scaled by a fixed value (e.g. when multiplying all pixels by a fixed value) returns a similar threshold result (within 2 greyscale levels of the original unscaled image) for all methods except Huang, Li and Triangle due to the way these algorithms work.While the Auto Threshold plugin can use or ignore the extremes of the image histogram (Ignore black, Ignore white) the applet cannot: the 'default' method ignores the histogram extremes but the others methods do not. This means that applying the two plugins to the same image can produce apparently different results. In essence, the Auto Threshold plugin, with the correct settings, can reproduce the results of the applet, but not the way round.
Try all
Which method segments your data best? You can attempt to answer this question using the Try all option. This produces a montage with the results from all the methods, so one can explore how the different algorithms perform on an image or stack. If you use stacks, you will realise that sometimes it might not be a good idea to segment each slice separately rather than with a single threshold for all slices (try the mri-stack.tif from the sample images to understand this issue).
Original image
Try all methods.
When processing stacks with many slices, the montages can become very
large (~13 times the original stack size) and one risks running out of
ram. A popup window will appear (when stacks have more than 25 slices)
to confirm whether the procedure should display the stack montages.
Select No to compute the threshold values and display
these in the log window.
Default
This is the original method of auto thresholding available in ImageJ which is a variation of the IsoData algorithm (see below). In this plugin the Default option should return the same values as the Image>Adjust>Threshold>Auto, when selecting Ignore black and Ignore white. While ImageJ tries to guess which pixels belong to the object and which to the background, this can be overridden and force segmentation of the desired phase with the White objects on black background option. The code in ImageJ that implements this function is the getAutoThreshold() method in the ImageProcessor class. The IsoData method is also known as iterative intermeans.Huang
Implements Huang's fuzzy thresholding method. This uses Shannon's entropy function (one can also use Yager's entropy function)- Huang L-K, Wang M-J J. (1995) Image Thresholding by Minimizing the Measures of Fuzziness, Pattern Recognition, 28(1): 41-51.
Intermodes
This assumes a bimodal histogram. The histogram is iteratively smoothed using a running average of size 3, until there are only two local maxima: j and k. The threshold t is then computed as (j+k)/2. Images with histograms having extremely unequal peaks or a broad and flat valley are unsuitable for this method.- Prewitt JMS, Mendelsohn ML. (1966) The analysis of cell images, in Annals of the New York Academy of Sciences, vol. 128, pp. 1035-1053.
IsoData
Iterative procedure based on the isodata algorithm of:- Ridler TW, Calvard S. (1978) Picture thresholding using an iterative selection method, IEEE Trans. System, Man and Cybernetics, SMC-8: 630-632.
The procedure divides the image into objects and background by taking an initial threshold,then the averages of the pixels at or below the threshold and pixels above are computed. The averages of those two values are computed, the threshold is incremented and the process is repeated until the threshold is larger than the composite average. That is, threshold = (average background + average objects)/2.
A description of the method, posted to sci.image.processing on 1996/06/24 by Tim Morris:
Subject: Re: Thresholding method?
The algorithm implemented in NIH Image sets the threshold as
that grey value, G, for which the average of the averages of
the grey values below and above G is equal to G. It does this
by initialising G to the lowest sensible value and iterating:
L = the average grey value of pixels with intensities <=G
H = the average grey value of pixels with intensities > G
is G = (L + H)/2?
yes: exit
no: increment G and repeat
Li
Implements Li's Minimum Cross Entropy thresholding method based on the iterative version (Ref. 2) of the algorithm.- Li CH, Lee CK. (1993) Minimum Cross Entropy Thresholding, Pattern Recognition, 26(4): 617-625.
- Li CH, Tam PKS. (1998) An Iterative Algorithm for Minimum Cross Entropy Thresholding, Pattern Recognition Letters, 18(8): 771-776.
- Sezgin M, Sankur B. (2004) Survey over Image Thresholding Techniques and Quantitative Performance Evaluation, Journal of Electronic Imaging, 13(1): 146-165. http://citeseer.ist.psu.edu/sezgin04survey.html
MaxEntropy
Implements Kapur-Sahoo-Wong (Maximum Entropy) thresholding method:- Kapur JN, Sahoo PK, Wong AKC. (1985) A New Method for Gray-Level Picture Thresholding Using the Entropy of the Histogram, Graphical Models and Image Processing, 29(3): 273-285.
Mean
Uses the mean of grey levels as the trhreshold. It is used by some other methods as a first guess threshold.- Glasbey, CA (1993), "An analysis of histogram-based thresholding algorithms", CVGIP: Graphical Models and Image Processing 55: 532-537.
MinError(I)
An iterative implementation of Kittler and Illingworth's Minimum Error thresholding. This version seems to be converge more often than the original implementation. Nevertheless, sometimes the algorithm does not converge to a solution. In that case a warning is reported to the log window and the result defaults to the initial estimate of the threshold which is computed using the Mean method.- Kittler, J & Illingworth, J (1986), "Minimum error thresholding", Pattern Recognition 19: 41-47
Minimum
Similarly to the Intermodes method, this assumes a bimodal histogram. The histogram is iteratively smoothed using a running average of size 3, until there are only two local maxima. Threshold t is such that yt-1 > yt <= yt+1.Images with histograms having extremely unequal peaks or a broad and flat valley are unsuitable for this method.
- Prewitt JMS, Mendelsohn ML. (1966) The analysis of cell images, in Annals of the New York Academy of Sciences, vol. 128, pp. 1035-1053.
Moments
Tsai's method attempts to preserve the moments of the original image in the thresholded result.- Tsai W. (1985) Moment-preserving thresholding: a new approach, Computer Vision, Graphics, and Image Processing, vol. 29, pp. 377-393.
Otsu
Otsu's threshold clustering algorithm searches for the threshold that minimizes the intra-class variance, defined as a weighted sum of variances of the two classes- Otsu N. (1979) A threshold selection method from gray-level histograms, IEEE Trans. Sys., Man., Cyber. 9: 62-66. doi:10.1109/TSMC.1979.4310076.
Percentile
Assumes a fraction of foreground pixels to be 0.5.- Doyle W. (1962) Operation useful for similarity-invariant pattern recognition, Journal of the Association for Computing Machinery, vol. 9,pp. 259-267.
RenyiEntropy
Similar to the MaxEntropy method, but using Renyi's entropy instead.- Kapur JN, Sahoo PK, Wong AKC. (1985) A New Method for Gray-Level Picture Thresholding Using the Entropy of the Histogram, Graphical Models and Image Processing, 29(3): 273-285.
Shanbhag
- Shanhbag A.G. (1994) "Utilization of Information Measure as a Means of Image Thresholding" Graphical Models and Image Processing, 56(5): 414-419.
Triangle
This is an implementation of the Triangle method:- Zack, G. W., Rogers, W. E. and Latt, S. A., 1977, Automatic Measurement of Sister Chromatid Exchange Frequency, Journal of Histochemistry and Cytochemistry 25 (7), pp. 741-753.
The Triangle algorithm, being a geometric method, cannot tell whether the data is skewed to one side or another, but assumes a maximum peak towards one end of the histogram and one end towards the other. This causes a problem in the absence of information of the type of image to be processed, or when the maximum is not towards one of the histogram extremes (resulting in two possible threshold regions between that max and the extremes). Here the algorithm was extended to to find out to which side of the max peak the data goes the furthest, and search for the threshold within the largest range.
Yen
Implements Yen's thresholding method from:- Yen JC, Chang FJ, Chang S. (1995) A New Criterion for Automatic Multilevel Thresholding, IEEE Trans. on Image Processing, 4(3): 370-378
- Sezgin M. and Sankur B. (2004) "Survey over Image Thresholding Techniques and Quantitative Performance Evaluation" Journal of Electronic Imaging, 13(1): 146-165 http://citeseer.ist.psu.edu/sezgin04survey.html
Auto Local Threshold
Use
Method selects the algorithm to be applied (detailed below).The radius sets the radius of the local domain over which the threshold will be computed, White object on black background sets to white the pixels with values above the threshold value (otherwise, it sets to white the values less or equal to the threshold). Special parameters 1 and 2 set specific values for each method. Those are detailed below for each method. It you are processing a stack, one additional options is available: Stack can be used to process all the slices.
Try all
Which method segments your data best? You can attempt to answer this question using the Try all option. This produces a montage with results from all the methods, so one can explore how the different algorithms perform on an image or stack.
Original image
Try all methods.
When processing stacks with many slices, the montages can become
very
large (several times the original stack size) and one risks running out
of ram. A popup window will appear (when stacks have more than 25
slices) to confirm whether the procedure should display the stack
montages.
Bernsen
Implements Bernsen's thresholding method. Note that this implementation uses circular windows instead of rectangular in the original.Parameter 1: is the contrast threshold. The default value is 15. Any number different than 0 will change the value.
Parameter 2: not used, ignored.
The method uses a user-provided contrast threshold. If the local contrast (max-min within the radius of the pixel) is above or equal to the contrast threshold, the threshold is set at the local midgrey value (the mean of the minimum and maximum grey values in the local window). If the local contrast is below the contrast threshold, the neighbourhood is considered to consist only of one class and the pixel is set to object or background depending on the value of the midgrey.
if ( local_contrast <= contrast_threshold )
pixel = ( mid_gray >= 128 ) ? object : background
else
pixel = (pixel >= mid_gray ) ? object : background
- Bernsen, J (1986), "Dynamic Thresholding of Grey-Level Images", Proc. of the 8th Int. Conf. on Pattern Recognition
- Sezgin, M and Sankur, B (2004), "Survey over Image Thresholding Techniques and Quantitative Performance Evaluation", Journal of Electronic Imaging 13(1): 146-165