Matlab: How to bend line in image - matlab

Question

I have a image(png format) in hand. The lines that bound the ellipses (represent the nucleus) are over straight which are impractical. How could i extract the lines from the image and make them bent, and with the precondition that they still enclose the nucleus.
The following is the image:
After bending
EDIT: How can i translate the Dilation And Filter part in answer2 into Matlab language? I can't figure it out.

Answer 1

Ok, here is a way involving several randomization steps needed to get a "natural" non symmetrical appearance.
I am posting the actual code in Mathematica, just in case someone cares translating it to Matlab.
(* A preparatory step: get your image and clean it*)
i = Import#"http://i.stack.imgur.com/YENhB.png";
i1 = Image#Replace[ImageData[i], {0., 0., 0.} -> {1, 1, 1}, {2}];
i2 = ImageSubtract[i1, i];
i3 = Inpaint[i, i2]
(*Now reduce to a skeleton to get a somewhat random starting point.
The actual algorithm for this dilation does not matter, as far as we
get a random area slightly larger than the original elipses *)
id = Dilation[SkeletonTransform[
Dilation[SkeletonTransform#ColorNegate#Binarize#i3, 3]], 1]
(*Now the real random dilation loop*)
(*Init vars*)
p = Array[1 &, 70]; j = 1;
(*Store in w an image with a different color for each cluster, so we
can find edges between them*)
w = (w1 =
WatershedComponents[
GradientFilter[Binarize[id, .1], 1]]) /. {4 -> 0} // Colorize;
(*and loop ...*)
For[i = 1, i < 70, i++,
(*Select edges in w and dilate them with a random 3x3 kernel*)
ed = Dilation[EdgeDetect[w, 1], RandomInteger[{0, 1}, {3, 3}]];
(*The following is the core*)
p[[j++]] = w =
ImageFilter[ (* We apply a filter to the edges*)
(Switch[
Length[#1], (*Count the colors in a 3x3 neighborhood of each pixel*)
0, {{{0, 0, 0}, 0}}, (*If no colors, return bkg*)
1, #1, (*If one color, return it*)
_, {{{0, 0, 0}, 0}}])[[1, 1]] (*If more than one color, return bkg*)&#
Cases[Tally[Flatten[#1, 1]],
Except[{{0.`, 0.`, 0.`}, _}]] & (*But Don't count bkg pixels*),
w, 1,
Masking -> ed, (*apply only to edges*)
Interleaving -> True (*apply to all color chanels at once*)]
]
The result is:
Edit
For the Mathematica oriented reader, a functional code for the last loop could be easier (and shorter):
NestList[
ImageFilter[
If[Length[#1] == 1, #1[[1, 1]], {0, 0, 0}] &#
Cases[Tally[Flatten[#1, 1]], Except[{0.` {1, 1, 1}, _}]] & , #, 1,
Masking -> Dilation[EdgeDetect[#, 1], RandomInteger[{0, 1}, {3, 3}]],
Interleaving -> True ] &,
WatershedComponents#GradientFilter[Binarize[id,.1],1]/.{4-> 0}//Colorize,
5]

Answer 2

What you have as input is the Voronoi diagram. You can recalculate it using another distance function instead of the Euclidean one.
Here is an example in Mathematica using the Manhattan Distance (i3 is your input image without the lines):
ColorCombine[{Image[
WatershedComponents[
DistanceTransform[Binarize#i3,
DistanceFunction -> ManhattanDistance] ]], i3, i3}]
Edit
I am working with another algorithm (preliminary result). What do you think?

Answer 3

Here is what I came up with, it is not a direct translation of #belisarius code, but should be close enough..
%# read image (indexed image)
[I,map] = imread('http://i.stack.imgur.com/YENhB.png');
%# extract the blobs (binary image)
BW = (I==1);
%# skeletonization + dilation
BW = bwmorph(BW, 'skel', Inf);
BW = imdilate(BW, strel('square',2*1+1));
%# connected components
L = bwlabel(BW);
imshow(label2rgb(L))
%# filter 15x15 neighborhood
for i=1:13
L = nlfilter(L, [15 15], #myFilterFunc);
imshow( label2rgb(L) )
end
%# result
L(I==1) = 0; %# put blobs back
L(edge(L,'canny')) = 0; %# edges
imshow( label2rgb(L,#jet,[0 0 0]) )
myFilterFunc.m
function p = myFilterFunc(x)
if range(x(:)) == 0
p = x(1); %# if one color, return it
else
p = mode(x(x~=0)); %# else, return the most frequent color
end
end
The result:
and here is an animation of the process: