Grayscale image segmentation

Question

I am having trouble getting the correct grayscale image segmentation:

The fundamental truth, that is, what we would like for this segmentation to look like this:

What interests me most is the three components within the circle. Thus, as you can see, I would like to segment the top image into three components: two semicircles and a rectangle between them.

I tried various combinations of dilatation, erosion and reconstruction, as well as various clustering algorithms, including k-means, isodate and a mixture of Gaussian - all with varying degrees of success.

Any suggestions would be appreciated.

Edit: here is the best result I could get. This was obtained using the active loop to segment the circular ROI and then apply isodata clustering:

There are two problems with this:

• A white halo around the lower right cluster, belonging to the upper left cluster
• A gray halo around the upper and lower left clusters belonging to the central cluster.

Answer 1

Here's the starter ... use the Hough circular transform to find the circular part. To do this, I initially generated a local image .

im=rgb2gray(imread('Ly7C8.png')); imbw = thresholdLocally(im,[2 2]); % thresold localy with a 2x2 window % preparing to find the circle props = regionprops(imbw,'Area','PixelIdxList','MajorAxisLength','MinorAxisLength'); [~,indexOfMax] = max([props.Area]); approximateRadius = props(indexOfMax).MajorAxisLength/2; radius=round(approximateRadius);%-1:approximateRadius+1); %find the circle using Hough trans. h = circle_hough(edge(imbw), radius,'same'); [~,maxIndex] = max(h(:)); [i,j,k] = ind2sub(size(h), maxIndex); center.x = j; center.y = i; figure;imagesc(im);imellipse(gca,[center.x-radius center.y-radius 2*radius 2*radius]); title('Finding the circle using Hough Trans.'); 

select only what is inside the circle:

  [y,x] = meshgrid(1:size(im,2),1:size(im,1)); z = (xj).^2+(yi).^2; f = (z<=radius^2); im=im.*uint8(f); 

EDIT:

find a place to start the image threshold to segment it by looking at the histogram, finding the first local maxima and iterating from there until 2 separate segments are found using bwlabel:

  p=hist(im(im>0),1:255); p=smooth(p,5); [pks,locs] = findpeaks(p); bw=bwlabel(im>locs(1)); i=0; while numel(unique(bw))<3 bw=bwlabel(im>locs(1)+i); i=i+1; end imagesc(bw); 

The middle part can now be obtained by removing two marked parts from the circle, and the remaining part will be the middle part (+ part of the halo)

  bw2=(bw<1.*f); 

but after some median filtering we get something more reasonable

  bw2= medfilt2(medfilt2(bw2)); 

and together we get:

  imagesc(bw+3*bw2); 

The last part is the real “quick and dirty" one, I’m sure that with the help of already used tools you will get better results ...

Answer 2

You can also get an approximate result using the conversion of watersheds . This is the watershed in the inverted image → the watershed (255-I). Here is an example:

Another simple method is to perform morphological closure of the original image using the disk structuring element (you can perform multiscale closure for granulometry), and then get a full circle. After that, removing the circle and lightening the components.

 se = strel('disk',3); Iclo = imclose(I, se);% This closes open circular cells. Ithresh = Iclo>170;% one can locate this threshold automatically by histogram modes (if you know apriori your cell structure.) Icircle = bwareaopen(Ithresh, 50); %to remove small noise components in the bg 

 Ithresh2 = I>185; % This again needs a simple histogram.