Why this simple case of watershed segmentation fails?

Questions
1

The question has been posted on StackExchange. https://mathematica.stackexchange.com/questions/160304/why-this-simple-case-of-watershed-segmentation-fails.

I tried a simple experiment today with WatershedComponents. I took this image from: https://fr.mathworks.com/help/images/ref/watershed.html (readers should use the image from the link above and crop the image themselves, rather than using the image directly below)

mask.png
mask.png240×238 1.5 KB

then I binarized the image

bin = Binarize[img];

the distance transform of the image yields dist:

dist = DistanceTransform[bin]//ImageAdjust;

dist.png
dist.png335×332 7.57 KB

Now to determine the seeds:

seeds = MaxDetect[dist]; (* notice two nice seeds in the image *)

seeds.png
seeds.png335×332 100 Bytes

finally using WatershedComponents i get this:

WatershedComponents[bin, seeds] // Colorize

watershed.png
watershed.png335×332 794 Bytes

Note: This is clearly how they should not be segmented. In contrast please see the segmentation performed by Matlab (link mentioned above). I tried using different methods but could not get a proper segmentation. What am i doing wrong?

2

Try with applying the watershed segmentation directly to the ridge lines:

ridgelines = RidgeFilter[bin, 3] // ImageAdjust
wsc = WatershedComponents[ridgelines, seeds];
wsc // Colorize
HighlightImage[img, wsc // Image // Binarize // ColorNegate]

2131im0.jpeg
2131im0.jpeg360×124 6.7 KB

3

This follows an example in the documentation:

binImg = Binarize[img];

distImg = DistanceTransform[binImg] // ImageAdjust;

negDistImg = ColorNegate[distImg] // ImageAdjust;

ImageMultiply[binImg, Image[WatershedComponents[negDistImg], "Bit"]]

This works, with ‘img’ as the image.