Histogram equalization (HE) transforms an image such that the new image has a "linearized" cumulative distribution function (CDF) across the value range. Since the CDF of a Gaussian is never "linearized", the new histogram equalized from any arbitrary distribution can never be a Gaussian. This answers your first question.

It is possible that the identical segmentations are particular to your image. You need to try many more images before drawing a firm conclusion. Another possibility: since the max-entropy method is an iterated method, if the number of iteration is sufficiently large, the method may lead to identical segmentations even if the contrast has been greatly enlarged. This answers your second question.

The answer to your third question depends on a lot of factors. If the original image already has sufficiently large contrast, contrast enhancement may not change the segmentation. Instead, if the original image is very dark or bright, we may expect a different segmentation after contrast enhancement. The answer also depends on the contrast enhancement and the segmentation methods you used.

Histogram equalization (HE) transforms an image such that the new image has a "linearized" cumulative distribution function (CDF) across the value range. Since the CDF of a Gaussian is never "linearized", the new histogram equalized from any arbitrary distribution can never be a Gaussian. This answers your first question.

It is possible that the identical segmentations are particular to your image. You need to try many more images before drawing a firm conclusion. Another possibility: since the max-entropy method is an iterated method, if the number of iteration is sufficiently large, the method may lead to identical segmentations even if the contrast has been greatly enlarged. This answers your second question.

The answer to your third question depends on a lot of factors. If the original image already has sufficiently large contrast, contrast enhancement may not change the segmentation. Instead, if the original image is very dark or bright, we may expect a different segmentation after contrast enhancement. The answer also depends on the contrast enhancement and the segmentation methods you used.

Dear Adam Hughes,

The link provided below may help you.

http://core.kmi.open.ac.uk/download/pdf/11963495.pdf

Thank you both, this is so helpful!

Have a look at our publications in research gate (see also www.medinfo.cs.ucy.ac.cy):

1) C.P. Loizou, C. Theofanous, M. Pantziaris, and T. Kasparis, “Despeckle filtering software toolbox for ultrasound imaging of the common carotid artery”, Computer Methods and Programs in Biomedicine, no. 114, pp. 109-124, January 2014

2) C.P. Loizou, C.S. Pattichis, M. Pantzaris, T. Tyllis, and A.N. Nicolaides, "Quality Evaluation of Ultrasound Imaging in the Carotid Artery Based on Normalization and Speckle Reduction Filtering", Medical and Biological Engineering and Computing, vol. 44, issue 8, pp. 405-413, 2006.

3) C.P. Loizou, C.S. Pattichis, C.I. Christodoulou, R.S.H. Istepanian, M. Pantzaris, and A.N. Nicolaides, "Comparative Evaluation of Despeckle Filtering in Ultrasound Imaging of the Carotid Artery", IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol. 52, issue 10, pp. 1653-1669, 2005

contrast is a key factor that highly affect the performance of segmentation. you need to provide a natural contrast for the segmented image to get a more accurate segmentation process.

This is a timely question for me, as I have been trying to understand the same. So, this is not an answer as such, but just my observations until now.

I have been using contrast-stretching as a preprocessing step in my application, which achieves segmentation by marker-controlled watershed segmentation of the gradient magnitude of the image. The preprocessed image is also used to find the markers (using the regional minima transform).

1) Contrast-stretching does not change the marker image much, since the operation wouldn't really change the location of the regional minima.

2) Contrast-stretching does change the segmentation result. The change is not drastic (but this depends on the image) and is only present at small parts of the object boundaries. These are areas with low contrast in the original image. 

In general, the segments are better aligned with the actual objects in my image, if contrast-stretching is applied first. This makes sense as the gradient magnitude highlights the edges better when the contrast is higher.

A quick answer is that whether you are using histogram equalisation or its adaptive version you end up highlighting structures in your images. Moreover, they both equalise the histogram (flattened as a whole or flattened within a predefined window size)  of the original signal. The assumption of "Gaussianity" does not hold here as rightly said above in Xiaomeng Wu's post.

 The consistency you observed in the segmentation before and after effect could be unique to your data set. For instance, following the same procedure, I get different segmentation results when applied to mammography images.

Image segmentation is a long standing problem and pre-processing of images is a crucial step in this regard.

Hope that helps.

maybe I missed something in the questions or the above answers: you say that you did various contrast enhancements and found them to have no effect on the segmentation, correct? Well, typically when we do contrast stretch or histogram equalization, you are only changing the LUT, i.e. the display values, so that the image looks different on your screen, but you are not changing the actual pixel values that the segmentation is based on. If that is indeed the case here, then this is the reason why you see no change in the segmentation. If you were to create actual derivatives that highlight contrast, such as a PCA, your segmentation results would certainly be affected.

Norman,

The histogram equalization process invariably creates an output image made up of the remapped values (i.e., the LUT values). The pixels in this output image would be different from those in the original image. This output image is what the segmentation would be based on if you are using histogram equalization as a preprocessing step.

When considering what kind of contrast enhancement to use you should always take into account the type of noise you're dealing with in your images. Contrast enhancement will usually increase the effects of noise. Once you can model that type of noise you have to consider what types of segmentation algorithms are you using and what types of structures you expect to use it on. 

E.g. you can get away with increasing stochastic noise if your algorithm has a way to deal with such local effects (snakes, adaptive surfaces, etc. ).

This is a very valid question which is raised very often when some kind of pre-processing is applied to an image before further processing (i.e. segmentation) and this needs to be definitively further evaluated. I would like to further contribute to this discussion with some more comments. There are a number of studies that have been performed for evaluating different segmentation methods while different pre-processing schemes or techniques have been applied to the images. The methodology more or less is the one followed in a number of publications of ours where we have investigated the performance of the segmentation algorithms in a large number of images or videos. There we have utilised two different groups of metrics for the evaluation; the objective and the subjective evaluation metrics. The objective evaluation is usually done by expert observers in the field of study which may evaluate the images using some objective criteria and give scores i.e in the scale of 1 to 5 for each image/video. Then you have the subjective criteria, which may be quality evaluation metrics, texture features or others for evaluating the performance of the algorithm. You may also ask the observers to manually delineate structures and then compare those with the ones generated by the automated segmentation or filtering algorithms. Nevertheless, it has been shown and we now know for sure that pre-processing influences segmentation a lot. This influence can be measureable as explained above and can be negative or positive in terms of subjective or objective quality criteria. We have shown that despeckle filtering, increased the visual performance of the observers, the final outcome of the segmentation algorithm, and also favours compression thus minimising the cost for image transportation, retrieval and processing. For more information and results have a look on our publications (ultrasound image despeckle filtering, segmentation of the carotid artery, despeckle filtering toolbox).

Thanks Christos.

We recently submitted a preprint to PeerJ (if it gets accepted, I'll link it) and we came to the same conclusion: sometimes preprocessing aids in segmentation, sometimes not, and it depends on too many aspects of the workflow/images to make generalized conclusions.  I'm glad to hear this confirmed by other people, as I'd hate to say something that was wrong or disagreeable.

Good luck Adam in your submission. I just want to reiterate that it is very often the case that a preprocessing phase may comprise a compound image enhancements steps to make images digitally prepared for the final aimed task. The final aggregated effect is affected by the nature of the enhancement methods being deployed and their permutations.

Here is the preprint if anyone is interested:

https://peerj.com/preprints/671/

These results are particularly pertinent to the preprocessing section.