One can mark the boundary of a binary image by bwboundaries function of MATLAB.
What should be done for obtaining boundaries of all segments as a binary image?
I have segmented an image and want to know if there is a way to mark boundaries between each neighbouring segment without applying morphological operations on each segment.
I have added images to illustrate what i want to do. Actually i want to obtain a binary image that keeps pink boundary marker pixels between all segments. Thus, I can overlay them with original image by the help of imoverlay function of Steve Eddins.
Random colored labeling of segmentation result:
Roughly-marked pink boundaries between segments:
You can find the region boundaries using a range filter, which finds the intensity range within each pixel's neighborhood. This takes advantage of the fact that the label matrix only has non-zero range at the region boundaries.
im = imread('http://i.stack.imgur.com/qPiA3.png');
boundaries = rangefilt(im,ones(3)) > 0;
imoverlay(label2rgb(im),boundaries,[0 0 0]);
These edges are also two pixels wide. Actually, I think the edges have to be two pixels wide; otherwise the regions will "lose" pixels to the border non-uniformly.
Since erosion and dilation work on non-binary images as well, you can write
img = imread('http://i.stack.imgur.com/qPiA3.png');
ei = imerode(img,ones(3));
di = imdilate(img,ones(3));
boundaries = ei~=img | di~=img;
This results in a bw image that has a boundary at the edge of each colored region (thus, the boundary line will be two pixels wide).
Note that this will not return an ordered list of pixels as bwboundaries, but rather a logical mask like bwperim, which is what imoverlay needs as input.
As a round-about way, I thought of making use of edge function of MATLAB.
First, I need to apply something like a label2gray operation. labels is the segmentation output (first image provided in the question) in the code below.
grayLabels = mat2gray(255* double(labels) ./ double(max(labels(:)))); %label2gray
bw_boundaries = edge(grayLabels,0.001);
Related
The image above has been processed to remove its background and increase contrast with im2bw. I want to now identify and measure the two elongated black regions at the top and bottom centre of the image. This is the result:
If I use imfill(I,'holes'), one of them does not get identified.
I would also like to identify the boundaries, so that I can measure the area of these regions and find their respective "weighted centroid".
What I want to achieve is something that allows me to measure an angle between the orientation of the elongated black regions in different frames, as pictured in the sketch below (the red line indicates the position of the top black region in a previous frame).
In this answer, I'll be using DIPimage 3, an image analysis toolbox for MATLAB (disclosure: I'm an author). However, the filters applied are quite simple, it should be no problem implementing this using other toolboxes instead.
The original image is very noisy. Simply thresholding that image leads to a noisy binary image that is very difficult to work with. I'm suggesting you filter the original image to highlight the structures of interest first, before thresholding and measuring.
Because we're interested in detecting lines, we'll use the Laplace of Gaussian filter. It is important to tune the sigma parameter to match the width of the lines to be detected. After applying the Laplace filter, dark lines will appear bright, and bright lines will appear dark. The bright dot in the middle of the image will also be enhanced, but appear dark.
img = readim('https://i.stack.imgur.com/0LzF3m.png');
img = img{1}; % all three channels of PNG file are identical, take one
out = laplace(img,10);
This image is straight-forward to threshold.
out = out > 0.25;
Finally, we'll measure the orientation of these two lines as the angle under which the projection is largest.
msr = measure(out,[],'feret');
angle = msr.Feret(:,4)
Output (angle in radian, 0 is to the right, pi/2 is down):
angle =
-1.7575
-1.7714
I'm trying to detect seams in welding images for an autonomous welding process.
I want to find pixel positions of the detected line (the red line in the desired image) in the original image.
I used the following code and finally removed noise from the image to reach the result below.
clc,clear,clf;
im = imread('https://i.stack.imgur.com/UJcKA.png');
imshow(im);title('Original image'); pause(0.5);
sim = edge(im, 'sobel');
imshow(sim);title('after Sobel'); pause(0.5);
mask = im > 5;
se = strel('square', 5);
mask_s = imerode(mask, se);
mask(mask_s) = false;
mask = imdilate(mask, se);
sim(mask) = false;
imshow(sim);title('after mask');pause(0.5);
sim= medfilt2(sim);
imshow(sim);title('after noise removal')
Unfortunately there is nothing remaining in the image to find the seam perfectly.
Any help would be appreciated.
Download Original image.
You need to make your filter more robust to noise. This can be done by giving it a larger support:
filter = [ones(2,9);zeros(1,9);-ones(2,9)];
msk = imerode(im > 0, ones(11)); % only object pixels, discarding BG
fim =imfilter(im,filter);
robust = bwmorph((fim>0.75).*msk,'skel',inf); % get only strong pixels
The robust mask looks like:
As you can see, the seam line is well detected, we just need to pick it as the largest connected component:
st = regionprops(bwlabel(robust,8), 'Area', 'PixelList');
[ma mxi] = max([st.Area]); % select the region with the largest area
Now we can fit a polygon (2nd degree) to the seem:
pp=polyfit(st(mxi).PixelList(:,1), st(mxi).PixelList(:,2), 2);
And here it is over the image:
imshow(im, 'border','tight');hold on;
xx=1:size(im,2);plot(xx,polyval(pp,xx)+2,'r');
Note the +2 Y offset due to filter width.
PS,
You might find this thread relevant.
Shai gives a great answer, but I wanted to add a bit more context about why your noise filtering doesn't work.
Why median filtering doesn't work
Wikipedia suggests that median filtering removes noise while preserving edges, which is why you might have chosen to use it. However, in your case it will almost certainly not work, here's why:
Median filtering slides a window across the image. In each area, it replaces the central pixel with the median value from the surrounding window. medfilt2 uses a 3x3 window by default. Let's look at a 3x3 block near your line,
A 3x3 block around [212 157] looks like this
[0 0 0
1 1 1
0 0 0]
The median value is 0! So even though we're in the middle of a line segment, the pixel will be filtered out.
The alternative to median filtering
Shai's method for removing noise instead finds the largest connected group of pixels and ignores smaller groups of pixels. If you also wanted to remove these small groups from your image, Matlab provides a filter bwareaopen which removes small objects from binary images.
For example, if you replace your line
sim= medfilt2(sim);
with
sim= bwareaopen(sim, 4);
The result is much better
Alternative edge detectors
One last note, Shai uses a horizontal gradient filter to find horizontal edges in your image. It works great because your edge is horizontal. If you edge will not always be horizontal, you might want to use another edge detection method. In your original code, you use Sobel, but Matlab provides many options, all of which perform better if you tune their thresholds. As an example, in the following image, I've highlighted the pixels selected by your code (with bwareaopen modification) using four different edge detectors.
I have this image (8 bit, pseudo-colored, gray-scale):
And I want to create an intensity band of a specific measure around it's border.
I tried erosion and other mathematical operations, including filtering to achieve the desired band but the actual image intensity changes as soon as I use erosion to cut part of the border.
My code so far looks like:
clear all
clc
x=imread('8-BIT COPY OF EGFP001.tif');
imshow(x);
y = imerode(x,strel('disk',2));
y1=imerode(y,strel('disk',7));
z=y-y1;
figure
z(z<30)=0
imshow(z)
The main problem I am encountering using this is that it somewhat changes the intensity of the original images as follows:
So my question is, how do I create such a band across image border without changing any other attribute of the original image?
Going with what beaker was talking about and what you would like done, I would personally convert your image into binary where false represents the background and true represents the foreground. When you're done, you then erode this image using a good structuring element that preserves the roundness of the contours of your objects (disk in your example).
The output of this would be the interior of the large object that is in the image. What you can do is use this mask and set these locations in the image to black so that you can preserve the outer band. As such, try doing something like this:
%// Read in image (directly from StackOverflow) and pseudo-colour the image
[im,map] = imread('http://i.stack.imgur.com/OxFwB.png');
out = ind2rgb(im, map);
%// Threshold the grayscale version
im_b = im > 10;
%// Create structuring element that removes border
se = strel('disk',7);
%// Erode thresholded image to get final mask
erode_b = imerode(im_b, se);
%// Duplicate mask in 3D
mask_3D = cat(3, erode_b, erode_b, erode_b);
%// Find indices that are true and black out result
final = out;
final(mask_3D) = 0;
figure;
imshow(final);
Let's go through the code slowly. The first two lines take your PNG image, which contains a grayscale image and a colour map and we read both of these into MATLAB. Next, we use ind2rgb to convert the image into its pseudo-coloured version. Once we do this, we use the grayscale image and threshold the image so that we capture all of the object pixels. I threshold the image with a value of 10 to escape some quantization noise that is seen in the image. This binary image is what we will operate on to determine those pixels we want to set to 0 to get the outer border.
Next, we declare a structuring element that is a disk of a radius of 7, then erode the mask. Once I'm done, I duplicate this mask in 3D so that it has the same number of channels as the pseudo-coloured image, then use the locations of the mask to set the values that are internal to the object to 0. The result would be the original image, but having the outer contours of all of the objects remain.
The result I get is:
I was working on my image processing problem with detecting coins.
I have some images like this one here:
and wanted to separate the falsely connected coins.
We already tried the watershed method as stated on the MATLAB-Homepage:
the-watershed-transform-strategies-for-image-segmentation.html
especially since the first example is exactly our problem.
But instead we get a somehow very messed up separation as you can see here:
We already extracted the area of the coin using the regionprops Extrema parameter and casting the watershed only on the needed area.
I'd appreciate any help with the problem or even another method of getting it separated.
If you have the Image Processing Toolbox, I can also suggest the Circular Hough Transform through imfindcircles. However, this requires at least version R2012a, so if you don't have it, this won't work.
For the sake of completeness, I'll assume you have it. This is a good method if you want to leave the image untouched. If you don't know what the Hough Transform is, it is a method for finding straight lines in an image. The circular Hough Transform is a special case that aims to find circles in the image.
The added advantage of the circular Hough Transform is that it is able to detect partial circles in an image. This means that those regions in your image that are connected, we can detect them as separate circles. How you'd call imfindcircles is in the following fashion:
[centers,radii] = imfindcircles(A, radiusRange);
A would be your binary image of objects, and radiusRange is a two-element array that specifies the minimum and maximum radii of the circles you want to detect in your image. The outputs are:
centers: A N x 2 array that tells you the (x,y) co-ordinates of each centre of a circle that is detected in the image - x being the column and y being the row.
radii: For each corresponding centre detected, this also gives the radius of each circle detected. This is a N x 1 array.
There are additional parameters to imfindcircles that you may find useful, such as the Sensitivity. A higher sensitivity means that it is able to detect circular shapes that are more non-uniform, such as what you are showing in your image. They aren't perfect circles, but they are round shapes. The default sensitivity is 0.85. I set it to 0.9 to get good results. Also, playing around with your image, I found that the radii ranged from 50 pixels to 150 pixels. Therefore, I did this:
im = im2bw(imread('http://dennlinger.bplaced.net/t06-4.jpg'));
[centers,radii] = imfindcircles(im, [50 150], 'Sensitivity', 0.9);
The first line of code reads in your image directly from StackOverflow. I also convert this to logical or true black and white as the image you uploaded is of type uint8. This image is stored in im. Next, we call imfindcircles in the method that we described.
Now, if we want to visualize the detected circles, simply use imshow to show your image, then use the viscircles to draw the circles in the image.
imshow(im);
viscircles(centers, radii, 'DrawBackgroundCircle', false);
viscircles by default draws the circles with a white background over the contour. I want to disable this because your image has white circles and I don't want to show false contouring. This is what I get with the above code:
Therefore, what you can take away from this is the centers and radii variables. centers will give you the centre of each detected circle while radii will tell you what the radii is for each circle.
Now, if you want to simulate what regionprops is doing, we can iterate through all of the detected circles and physically draw them onto a 2D map where each circle would be labeled by an ID number. As such, we can do something like this:
[X,Y] = meshgrid(1:size(im,2), 1:size(im,1));
IDs = zeros(size(im));
for idx = 1 : numel(radii)
r = radii(idx);
cen = centers(idx,:);
loc = (X - cen(1)).^2 + (Y - cen(2)).^2 <= r^2;
IDs(loc) = idx;
end
We first define a rectangular grid of points using meshgrid and initialize an IDs array of all zeroes that is the same size as the image. Next, for each pair of radii and centres for each circle, we define a circle that is centered at this point that extends out for the given radius. We then use these as locations into the IDs array and set it to a unique ID for that particular circle. The result of IDs will be that which resembles the output of bwlabel. As such, if you want to extract the locations of where the idx circle is, you would do:
cir = IDs == idx;
For demonstration purposes, this is what the IDs array looks like once we scale the IDs such that it fits within a [0-255] range for visibility:
imshow(IDs, []);
Therefore, each shaded circle of a different shade of gray denotes a unique circle that was detected with imfindcircles.
However, the shades of gray are probably a bit ambiguous for certain coins as this blends into the background. Another way that we could visualize this is to apply a different colour map to the IDs array. We can try using the cool colour map, with the total number of colours to be the number of unique circles + 1 for the background. Therefore, we can do something like this:
cmap = cool(numel(radii) + 1);
RGB = ind2rgb(IDs, cmap);
imshow(RGB);
The above code will create a colour map such that each circle gets mapped to a unique colour in the cool colour map. The next line applies a mapping where each ID gets associated with a colour with ind2rgb and we finally show the image.
This is what we get:
Edit: the following solution is more adequate to scenarios where one does not require fitting the exact circumferences, although simple heuristics could be used to approximate the radii of the coins in the original image based on the centers found in the eroded one.
Assuming you have access to the Image Processing toolbox, try imerode on your original black and white image. It will apply an erosion morphological operator to your image. In fact, the Matlab webpage with the documentation of that function has an example strikingly similar to your problem/image and they use a disk structure.
Run the following code (based on the example linked above) assuming the image you submitted is called ima.jpg and is local to the code:
ima=imread('ima.jpg');
se = strel('disk',50);
eroded = imerode(ima,se);
imshow(eroded)
and you will see the image that follows as output. After you do this, you can use bwlabel to label the connected components and compute whatever properties you may want, for example, count the number of coins or detect their centers.
How do I separate the two connected circles in the image below, using MATLAB? I have tried using imerode, but this does not give good results. Eroding does not work, because in order to erode enough to separate the circles, the lines disappear or become mangled. In other starting pictures, a circle and a line overlap, so isolating the overlapping objects won't work either.
The image shows objects identified by bwboundaries, each object painted a different color. As you can see, the two light blue circles are joined, and I want to disjoin them, producing two separate circles. Thanks
I would recommend you use the Circular Hough Transform through imfindcircles. However, you need version 8 of the Image Processing Toolbox, which was available from version R2012a and onwards. If you don't have this, then unfortunately this won't work :(... but let's go with the assumption that you do have it. However, if you are using something older than R2012a, Dev-iL in his/her comment above linked to some code on MATLAB's File Exchange on an implementation of this, most likely created before the Circular Hough Transform was available: http://www.mathworks.com/matlabcentral/fileexchange/9168-detect-circles-with-various-radii-in-grayscale-image-via-hough-transform/
This is a special case of the Hough Transform where you are trying to find circles in your image rather than lines. The beauty with this is that you are able to find circles even when the circle is partially completed or overlapping.
I'm going to take the image that you provided above and do some post-processing on it. I'm going to convert the image to binary, and remove the border, which is white and contains the title. I'm also going to fill in any holes that result so that all of the objects are filled in with solid white. There is also some residual quantization noise after I do this step, so I'm going to a small opening with a 3 x 3 square element. After, I'm going to close the shapes with a 3 x 3 square element, as I see that there are noticeable gaps in the shapes. Therefore:
Therefore, directly reading in your image from where you've posted it:
im = imread('http://s29.postimg.org/spkab8oef/image.jpg'); %// Read in the image
im_gray = im2double(rgb2gray(im)); %// Convert to grayscale, then [0,1]
out = imclearborder(im_gray > 0.6); %// Threshold using 0.6, then clear the border
out = imfill(out, 'holes'); %// Fill in the holes
out = imopen(out, strel('square', 3));
out = imclose(out, strel('square', 3));
This is the image I get:
Now, apply the Circular Hough Transform. The general syntax for this is:
[centres, radii, metric] = imfindcircles(img, [start_radius, end_radius]);
img would be the binary image that contains your shapes, start_radius and end_radius would be the smallest and largest radius of the circles you want to find. The Circular Hough Transform is performed such that it will find any circles that are within this range (in pixels). The outputs are:
centres: Which returns the (x,y) positions of the centres of each circle detected
radii: The radius of each circle
metric: A measure of purity of the circle. Higher values mean that the shape is more probable to be a circle and vice-versa.
I searched for circles having a radius between 30 and 60 pixels. Therefore:
[centres, radii, metric] = imfindcircles(out, [30, 60]);
We can then demonstrate the detected circles, as well as the radii by a combination of plot and viscircles. Therefore:
imshow(out);
hold on;
plot(centres(:,1), centres(:,2), 'r*'); %// Plot centres
viscircles(centres, radii, 'EdgeColor', 'b'); %// Plot circles - Make edge blue
Here's the result:
As you can see, even with the overlapping circles towards the top, the Circular Hough Transform was able to detect two distinct circles in that shape.
Edit - November 16th, 2014
You wish to ensure that the objects are separated before you do bwboundaries. This is a bit tricky to do. The only way I can see you do this is if you don't even use bwboundaries at all and do this yourself. I'm assuming you'll want to analyze each shape's properties by themselves after all of this, so what I suggest you do is iterate through every circle you have, then place each circle on a new blank image, do a regionprops call on that shape, then append it to a separate array. You can also keep track of all of the circles by having a separate array that adds the circles one at a time to this array.
Once you've finished with all of the circles, you'll have a structure array that contains all of the measured properties for all of the measured circles you have found. You would use the array that contains only the circles from above, then use these and remove them from the original image so you get just the lines. You'd then call one more regionprops on this image to get the information for the lines and append this to your final structure array.
Here's the first part of the procedure I outlined above:
num_circles = numel(radii); %// Get number of circles
struct_reg = []; %// Save the shape analysis per circle / line here
%// For creating our circle in the temporary image
[X,Y] = meshgrid(1:size(out,2), 1:size(out,1));
%// Storing all of our circles in this image
circles_img = false(size(out));
for idx = 1 : num_circles %// For each circle we have...
%// Place our circle inside a temporary image
r = radii(idx);
cx = centres(idx,1); cy = centres(idx,2);
tmp = (X - cx).^2 + (Y - cy).^2 <= r^2;
% // Save in master circle image
circles_img(tmp) = true;
%// Do regionprops on this image and save
struct_reg = [struct_reg; regionprops(tmp)];
end
The above code may be a bit hard to swallow, but let's go through it slowly. I first figure out how many circles we have, which is simply looking at how many radii we have detected. I keep a separate array called struct_reg that will append a regionprops struct for each circle and line we have in our image. I use meshgrid to determine the (X,Y) co-ordinates with respect to the image containing our shapes so that I can draw one circle onto a blank image at each iteration. To do this, you simply need to find the Euclidean distance with respect to the centre of each circle, and set the pixels to true only if that location has its distance less than r. After doing this operation, you will have created only one circle and filtered all of them out. You would then use regionprops on this circle, add it to our circles_img array, which will only contain the circles, then continue with the rest of the circles.
At this point, we will have saved all of our circles. This is what circles_img looks like so far:
You'll notice that the circles drawn are clean, but the actual circles in the original image are a bit jagged. If we tried to remove the circles with this clean image, you will get some residual pixels along the border and you won't completely remove the circles themselves. To illustrate what I mean, this is what your image looks like if I tried to remove the circles with circles_img by itself:
... not good, right?
If you want to completely remove the circles, then do a morphological reconstruction through imreconstruct where you can use this image as the seed image, and specify the original image to be what we're working on. The job of morphological reconstruction is essentially a flood fill. You specify seed pixels, and an image you want to work on, and the job of imreconstruct is from these seeds, flood fill with white until we reach the boundaries of the objects that the seed pixels resided in. Therefore:
out_circles = imreconstruct(circles_img, out);
Therefore, we get this for our final reconstructed circles image:
Great! Now, use this and remove the circles from the original image. Once you do this, run regionprops again on this final image and append to your struct_reg variable. Obviously, save a copy of the original image before doing this:
out_copy = out;
out_copy(out_circles) = false;
struct_reg = [struct_reg; regionprops(out_copy)];
Just for sake of argument, this is what the image looks like with the circles removed:
Now, we have analyzed all of our shapes. Bear in mind I did the full regionprops call because I don't know exactly what you want in your analysis... so I just decided to give you everything.
Hope this helps!
erosion is the way to go. You should probably use a larger structuring element.
How about
1 erode
2 detect your objects
3 dilate each object for itself using the same structuring element