This is sample code for K means algorithm.
k = 5;
[Centroid,new_cluster]=kmeans_algorithm(inv_trans_img,k);
for i_loop = 1:k
cluster = zeros(size(inv_trans_img));
pos = find(new_cluster==i_loop);
cluster(pos) = new_cluster(pos);
figure; imshow(cluster,[]);title('K-means');
end
I need to get the final image from this K means algorithm and I need to pass that image for thresholding process.I did it like below.
tumour_image=cluster;
n = 512;
binarized_img = zeros(n,n);
sort_val = sort(tumour_image(:));
mid_val = ceil(length(sort_val)/2);
threshold = tumour_image(mid_val);
binarized_img(find(tumour_image>=threshold)) = 1;
binarized_img(find(tumour_image<threshold)) = 0;
imshow(binarized_img);title('binarized image');
But now the problem is,only a white image is coming as a result.How can i solve this out.
Your threshold should be:
threshold = sort_val(mid_val);
You need to get the median of the sorted values, not the center element of tumour_image.
As #NeilSlater mentions in the comments, the reason that you're getting an all-white image from your existing code is that you are, by chance, selecting a black pixel from the original image, so when you threshold, the entire image is greater than or equal to that pixel in value.
In the case of images in which the majority of the pixels are 0, this will still give you an all-white image as as result. One way around this, and the most analogous to what you're currently doing, is to take the median of the nonzero pixels.
mid_val = ceil((find(sort_val, 1)+length(sort_val))/2);
Alternatively, if you know which clusters you're interested in you can simply keep only those clusters.
binarized_image = tumour_image >= 3; % keep clusters 3 and above
Related
I'm trying to find the broken ligaments for these two photos. Because the patten it got I can use the conv2 function find the general broken areas. However, it is really hard for me think how to make it tell the exact broken ligaments. Can you guys give me some idea for how to find which ligaments are broken please?
Because I'm new to this website, I can not post more photos with 2-D convolution results.
Original Picture
Broken Picture
Make a region growing algorithm inside each perfect square.
Once you get that, calculate the area of that section.
Once you find this, calculate the remaining areas. The larger values will be the broken ligaments :)
img = imread('unbroke.jpg');
level = graythresh(rgb2gray(img));
BW = im2bw(rgb2gray(img),level);
BW2= imdilate(imerode(BW, ones(5)), ones(5));
BW3 = bwmorph(BW2,'remove');
figure, imshow(BW2), hold on[![enter image description here][1]][1]
[H,T,R] = hough(BW2);
P = houghpeaks(H,15,'threshold',ceil(0.3*max(H(:))));
x = T(P(:,2)); y = R(P(:,1));
lines = houghlines(BW2,T,R,P,'FillGap',5,'MinLength',7);
max_len = 0;
for k = 1:length(lines)
xy = [lines(k).point1; lines(k).point2];
plot(xy(:,1),xy(:,2),'LineWidth',2,'Color','green');
% Plot beginnings and ends of lines
plot(xy(1,1),xy(1,2),'x','LineWidth',2,'Color','yellow');
plot(xy(2,1),xy(2,2),'x','LineWidth',2,'Color','red');
% Determine the endpoints of the longest line segment
len = norm(lines(k).point1 - lines(k).point2);
if ( len > max_len)
max_len = len;
xy_long = xy;
end
end
lines from unbroken image
lines from broken image
Now, you know what the line segments are do some matching. Or else find pairs of segments that would be connected (same slope + same x/y intercept) within a threshold.
This may be an interesting way to do this too. I saved the second image only as 'image.jpg'.
I = imread('image.jpg');
J = imbinarize(rgb2gray(I)); % Threshold to get a BW image.
BW = bwpropfilt(~J, 'Area', [35001, 1013283]);
imshow(BW)
shows
For selecting the area thresholds easily, I used https://www.mathworks.com/help/images/calculate-region-properties-using-image-region-analyzer.html
If you don't have a recent MATLAB version where imbinarize or bwpropfilt doesn't exist, you can use equivalent thresholding functions, and regionprops to extract all objects within the area range.
In the implementation of downsampling by a factor of 2 to the image, the downsampled image is gray. What should I do in order to add all of the color components to the downsampling implementation so that it will be a color image?
I = imread('lena.gif','gif');
[j k] = size(I)
x_new = j./2;
y_new = k./2;
x_scale = j./x_new;
y_scale = k./y_new;
M = zeros(x_new,y_new);
for count1 = 1:x_new
for count2 = 1:y_new
M(count1,count2) = I(count1.*x_scale,count2.*y_scale);
end
end
figure,imshow(I);
title('Original Image');
M = uint8(M);
figure,imshow(M);
title('Downsample');
GIF images are what are known as indexed images. This means that what you read in with imread are values that are indices to a colour map. Each index generates a unique colour for you, and that's how GIF images are stored. They choose from a predefined set of colours, and each pixel in the GIF image comes from one of the colours in the colour map.
You first need to convert the image into RGB, and you do that with ind2rgb. However, you need to read in the colour map first with the two-output version of imread. You also will want to convert the images to uint8 as good practice with im2uint8:
[X,map] = imread('lena.gif');
I = im2uint8(ind2rgb(X,map));
What you need to do next is what #NKN suggested. You must apply the algorithm to all channels.
As such, simply make an output matrix that has three channels, and apply the algorithm to each plane independently. If I can make a suggestion, when accessing pixels this way after you downsample, make sure you floor or round the image coordinates so you're not inadvertently specifying locations that aren't defined - things like (13.8, 25.5) for example. Image pixel locations are integer, so you need to make sure the coordinates are integer too.
[X,map] = imread('lena.gif');
I = im2uint8(ind2rgb(X,map));
j = size(I,1); %// Change
k = size(I,2);
x_new = j./2;
y_new = k./2;
x_scale = j./x_new;
y_scale = k./y_new;
M = zeros(x_new,y_new,size(I,3)); %// Change
for jj = 1 : size(I,3) %// Change
for count1 = 1:x_new
for count2 = 1:y_new
M(count1,count2,jj) = I(floor(count1.*x_scale),floor(count2.*y_scale),jj); %// Change
end
end
end
figure,imshow(I);
title('Original Image');
M = uint8(M);
figure,imshow(M);
title('Downsample');
To test this, I'm using the mandrill dataset that's part of MATLAB. It is an indexed image with an associated colour map. These are coincidentally stored in X and map respectfully:
load mandrill;
I = im2uint8(ind2rgb(X,map));
Running the modified code, I get these two figures:
When you read the original image it contains 3 layers, R-G-B (as suggested by #rayryeng:
[X,map] = imread('lena.gif');
I = ind2rgb(X,map);
size(I)
ans =
768 1024 3
You should perform the down-sampling process on all the layers:
The code you provided does not down-sample. A simple downsampling example is as follows:
imshow(I(1:2:end,1:2:end,:))
So some background. I was tasked to write a matlab program to count the number yeast cells inside visible-light microscopic images. To do that I think the first step will be cell segmentation. Before I got the real experiment image set, I developed an algorithm use a test image set utilizing watershed. Which looks like this:
The first step of watershed is generating a BW mask for the cells. Then I would generate a bwdist image with imposed local minimums generated from the BW mask. With that I can generate the watershed easily.
As you can see my algorithm rely on the successful generation of BW mask. Because I need to generate the bwdist image and markers from it. Originally, I generate the BW mask following the following steps:
generate the Local standard deviation of image sdImage = stdfilt(grayImage, ones(9))
Use BW thresholding to generate the initial BW mask binaryImage = sdImage < 8;
use imclearborder to clear the background. Use some other code to add the cells on the border back.
Background finished. Here is my problem
But today I received the new real data sets. The image resolution is much smaller and the light condition is different from the test image set. The color depth is also much smaller. These make my algorithm useless. Here is it:
Using stdfilt failed to generate a good clean images. Instead it generate stuff like this (Note: I have adjusted parameters for the stdfilt function and the BW threshold value, following is the best result I can get) :
As you can see there are light pixels in the center of the cells that not necessary darker than the membrane. Which lead the bw thresholding generate stuff like this:
The new bw image after bw thresholding have either incomplete membrane or segmented cell centers and make them unsuitable to the other steps.
I only start image processing recently and have no idea how should I proceed. If you have an idea please help me! Thanks!
For your convience, I have attached a link from dropbox for a subset of the images
I think there's a fundamental problem in your approach. Your algorithm uses stdfilt in order to binarize the image. But what that essentially means is you're assuming there is there is low "texture" in the background and within the cell. This works for your first image. However, in your second image there is a "texture" within the cell, so this assumption is broken.
I think a stronger assumption is that there is a "ring" around each cell (valid for both images you posted). So I took the approach of detecting this ring instead.
So my approach is essentially:
Detect these rings (I use a 'log' filter and then binarize based on positive values. However, this results in a lot of "chatter"
Try to remove some of the "chatter" initially by filtering out very small and very large regions
Now, fill in these rings. However, there is still some "chatter" and filled regions between cells left
Again, remove small and large regions, but since the cells are filled, increase the bounds for what is acceptable.
There are still some bad regions, most of the bad areas are going to be regions between cells. Regions between cells are detectable by observing the curvature around the boundary of the region. They "bend inwards" a lot, which is expressed mathematically as a large portion of the boundary having a negative curvature. Also, to remove the rest of the "chatter", these regions will have a large standard deviation in the curvature of their boundary, so remove boundaries with a large standard deviation as well.
Overall, the most difficult part will be removing regions between cells and the "chatter" without removing the actual cells.
Anyway, here's the code (note there are a lot of heuristics and also it's very rough and based on code from older projects, homeworks, and stackoverflow answers so it's definitely far from finished):
cell = im2double(imread('cell1.png'));
if (size(cell,3) == 3)
cell = rgb2gray(cell);
end
figure(1), subplot(3,2,1)
imshow(cell,[]);
% Detect edges
hw = 5;
cell_filt = imfilter(cell, fspecial('log',2*hw+1,1));
subplot(3,2,2)
imshow(cell_filt,[]);
% First remove hw and filter out noncell hws
mask = cell_filt > 0;
hw = 5;
mask = mask(hw:end-hw-1,hw:end-hw-1);
subplot(3,2,3)
imshow(mask,[]);
rp = regionprops(mask, 'PixelIdxList', 'Area');
rp = rp(vertcat(rp.Area) > 50 & vertcat(rp.Area) < 2000);
mask(:) = false;
mask(vertcat(rp.PixelIdxList)) = true;
subplot(3,2,4)
imshow(mask,[]);
% Now fill objects
mask1 = true(size(mask) + hw);
mask1(hw+1:end, hw+1:end) = mask;
mask1 = imfill(mask1,'holes');
mask1 = mask1(hw+1:end, hw+1:end);
mask2 = true(size(mask) + hw);
mask2(hw+1:end, 1:end-hw) = mask;
mask2 = imfill(mask2,'holes');
mask2 = mask2(hw+1:end, 1:end-hw);
mask3 = true(size(mask) + hw);
mask3(1:end-hw, 1:end-hw) = mask;
mask3 = imfill(mask3,'holes');
mask3 = mask3(1:end-hw, 1:end-hw);
mask4 = true(size(mask) + hw);
mask4(1:end-hw, hw+1:end) = mask;
mask4 = imfill(mask4,'holes');
mask4 = mask4(1:end-hw, hw+1:end);
mask = mask1 | mask2 | mask3 | mask4;
% Filter out large and small regions again
rp = regionprops(mask, 'PixelIdxList', 'Area');
rp = rp(vertcat(rp.Area) > 100 & vertcat(rp.Area) < 5000);
mask(:) = false;
mask(vertcat(rp.PixelIdxList)) = true;
subplot(3,2,5)
imshow(mask);
% Filter out regions with lots of positive concavity
% Get boundaries
[B,L] = bwboundaries(mask);
% Cycle over boundarys
for i = 1:length(B)
b = B{i};
% Filter boundary - use circular convolution
b(:,1) = cconv(b(:,1),fspecial('gaussian',[1 7],1)',size(b,1));
b(:,2) = cconv(b(:,2),fspecial('gaussian',[1 7],1)',size(b,1));
% Find curvature
curv_vec = zeros(size(b,1),1);
for j = 1:size(b,1)
p_b = b(mod(j-2,size(b,1))+1,:); % p_b = point before
p_m = b(mod(j,size(b,1))+1,:); % p_m = point middle
p_a = b(mod(j+2,size(b,1))+1,:); % p_a = point after
dx_ds = p_a(1)-p_m(1); % First derivative
dy_ds = p_a(2)-p_m(2); % First derivative
ddx_ds = p_a(1)-2*p_m(1)+p_b(1); % Second derivative
ddy_ds = p_a(2)-2*p_m(2)+p_b(2); % Second derivative
curv_vec(j+1) = dx_ds*ddy_ds-dy_ds*ddx_ds;
end
if (sum(curv_vec > 0)/length(curv_vec) > 0.4 || std(curv_vec) > 2.0)
L(L == i) = 0;
end
end
mask = L ~= 0;
subplot(3,2,6)
imshow(mask,[])
Output1:
Output2:
If I have an image, in which there is a page of text shot on a uniform background, how can I auto detect the boundaries between the paper and the background?
An example of the image I want to detect is shown below. The images that I will be dealing with consist of a single page on a uniform background and they can be rotated at any angle.
One simple method would be to threshold the image by some known value once you convert the image to grayscale. The problem with that approach is that we are applying a global threshold and so some of the paper at the bottom of the image will be lost if you make the threshold too high. If you make the threshold too low, then you'll certainly get the paper, but you'll include a lot of the background pixels too and it will probably be difficult to remove those pixels with post-processing.
One thing I can suggest is to use an adaptive threshold algorithm. An algorithm that has worked for me in the past is the Bradley-Roth adaptive thresholding algorithm. You can read up about it here on a post I commented on a while back:
Bradley Adaptive Thresholding -- Confused (questions)
However, if you want the gist of it, an integral image of the grayscale version of the image is taken first. The integral image is important because it allows you to calculate the sum of pixels within a window in O(1) complexity. However, the calculation of the integral image is usually O(n^2), but you only have to do that once. With the integral image, you scan neighbourhoods of pixels of size s x s and you check to see if the average intensity is less than t% of the actual average within this s x s window then this is pixel classified as the background. If it's larger, then it's classified as being part of the foreground. This is adaptive because the thresholding is done using local pixel neighbourhoods rather than using a global threshold.
I've coded an implementation of the Bradley-Roth algorithm here for you. The default parameters for the algorithm are s being 1/8th of the width of the image and t being 15%. Therefore, you can just call it this way to invoke the default parameters:
out = adaptiveThreshold(im);
im is the input image and out is a binary image that denotes what belongs to foreground (logical true) or background (logical false). You can play around with the second and third input parameters: s being the size of the thresholding window and t the percentage we talked about above and can call the function like so:
out = adaptiveThreshold(im, s, t);
Therefore, the code for the algorithm looks like this:
function [out] = adaptiveThreshold(im, s, t)
%// Error checking of the input
%// Default value for s is 1/8th the width of the image
%// Must make sure that this is a whole number
if nargin <= 1, s = round(size(im,2) / 8); end
%// Default value for t is 15
%// t is used to determine whether the current pixel is t% lower than the
%// average in the particular neighbourhood
if nargin <= 2, t = 15; end
%// Too few or too many arguments?
if nargin == 0, error('Too few arguments'); end
if nargin >= 4, error('Too many arguments'); end
%// Convert to grayscale if necessary then cast to double to ensure no
%// saturation
if size(im, 3) == 3
im = double(rgb2gray(im));
elseif size(im, 3) == 1
im = double(im);
else
error('Incompatible image: Must be a colour or grayscale image');
end
%// Compute integral image
intImage = cumsum(cumsum(im, 2), 1);
%// Define grid of points
[rows, cols] = size(im);
[X,Y] = meshgrid(1:cols, 1:rows);
%// Ensure s is even so that we are able to index the image properly
s = s + mod(s,2);
%// Access the four corners of each neighbourhood
x1 = X - s/2; x2 = X + s/2;
y1 = Y - s/2; y2 = Y + s/2;
%// Ensure no co-ordinates are out of bounds
x1(x1 < 1) = 1;
x2(x2 > cols) = cols;
y1(y1 < 1) = 1;
y2(y2 > rows) = rows;
%// Count how many pixels there are in each neighbourhood
count = (x2 - x1) .* (y2 - y1);
%// Compute row and column co-ordinates to access each corner of the
%// neighbourhood for the integral image
f1_x = x2; f1_y = y2;
f2_x = x2; f2_y = y1 - 1; f2_y(f2_y < 1) = 1;
f3_x = x1 - 1; f3_x(f3_x < 1) = 1; f3_y = y2;
f4_x = f3_x; f4_y = f2_y;
%// Compute 1D linear indices for each of the corners
ind_f1 = sub2ind([rows cols], f1_y, f1_x);
ind_f2 = sub2ind([rows cols], f2_y, f2_x);
ind_f3 = sub2ind([rows cols], f3_y, f3_x);
ind_f4 = sub2ind([rows cols], f4_y, f4_x);
%// Calculate the areas for each of the neighbourhoods
sums = intImage(ind_f1) - intImage(ind_f2) - intImage(ind_f3) + ...
intImage(ind_f4);
%// Determine whether the summed area surpasses a threshold
%// Set this output to 0 if it doesn't
locs = (im .* count) <= (sums * (100 - t) / 100);
out = true(size(im));
out(locs) = false;
end
When I use your image and I set s = 500 and t = 5, here's the code and this is the image I get:
im = imread('http://i.stack.imgur.com/MEcaz.jpg');
out = adaptiveThreshold(im, 500, 5);
imshow(out);
You can see that there are some spurious white pixels at the bottom white of the image, and there are some holes we need to fill in inside the paper. As such, let's use some morphology and declare a structuring element that's a 15 x 15 square, perform an opening to remove the noisy pixels, then fill in the holes when we're done:
se = strel('square', 15);
out = imopen(out, se);
out = imfill(out, 'holes');
imshow(out);
This is what I get after all of that:
Not bad eh? Now if you really want to see what the image looks like with the paper segmented, we can use this mask and multiply it with the original image. This way, any pixels that belong to the paper are kept while those that belong to the background go away:
out_colour = bsxfun(#times, im, uint8(out));
imshow(out_colour);
We get this:
You'll have to play around with the parameters until it works for you, but the above parameters were the ones I used to get it working for the particular page you showed us. Image processing is all about trial and error, and putting processing steps in the right sequence until you get something good enough for your purposes.
Happy image filtering!
Hi I am trying to get the boundary orientation of an image from the image gradient or canny edge detector as in equation 11 of http://www.cs.swan.ac.uk/~csjason/papers/xxmm-pami2008.pdf
I currently have:
clear all
Img = imread('littlecircle.png');
Img = Img(:,:,1);
Img = double(Img);
w = size(Img,1); % width size
h = size(Img,2); % height size
[Ix,Iy] = gradient(Img); %gradient of image
i=1; %iteration for magnetic field loop
b=0; %initialize b to zero
% Magnetic Field
for pxRow = 1:h % fixed pixel row
for pxCol = 1:w % fixed pixel column
for r = 1:h % row of distant pixel
for c = 1:w % column of distant pixel
O(c,r) = [-Iy(c,r),Ix(c,r)]; % O(x) = (-1).^lambda(-Iy(x),Ix(x)) --ERROR HERE
end
end
B(i) = {O}; % filling a cell array with results. read below
i = i+1;
end
end
However I am getting a subscript indices mismatch when storing into O(c,r). Why is this? and also if anyone thinks there is a better way to do this from the paper then I would love to here it. Thanks.
You could do the canny + orientation detection in one step, by modifying matlab's canny edge detection code or modify an alternative like this. Canny works by determining the orientation on each step, so you could modify the canny code to also return an orientation map for each pixel.