How to count circle objects in a bright image using MATLAB?
The input image is:
imfindcircles function can't find any circle in this image.
Based on well known image processing techniques, you can write your own processing tool:
img = imread('Mlj6r.jpg'); % read the image
imgGray = rgb2gray(img); % convert to grayscale
sigma = 1;
imgGray = imgaussfilt(imgGray, sigma); % filter the image (we will take derivatives, which are sensitive to noise)
imshow(imgGray) % show the image
[gx, gy] = gradient(double(imgGray)); % take the first derivative
[gxx, gxy] = gradient(gx); % take the second derivatives
[gxy, gyy] = gradient(gy); % take the second derivatives
k = 0.04; %0.04-0.15 (see wikipedia)
blob = (gxx.*gyy - gxy.*gxy - k*(gxx + gyy).^2); % Harris corner detector (high second derivatives in two perpendicular directions)
blob = blob .* (gxx < 0 & gyy < 0); % select the top of the corner (i.e. positive second derivative)
figure
imshow(blob) % show the blobs
blobThresshold = 1;
circles = imregionalmax(blob) & blob > blobThresshold; % find local maxima and apply a thresshold
figure
imshow(imgGray) % show the original image
hold on
[X, Y] = find(circles); % find the position of the circles
plot(Y, X, 'w.'); % plot the circle positions on top of the original figure
nCircles = length(X)
This code counts 2710 circles, which is probably a slight (but not so bad) overestimation.
The following figure shows the original image with the circle positions indicated as white dots. Some wrong detections are made at the border of the object. You can try to make some adjustments to the constants sigma, k and blobThresshold to obtain better results. In particular, higher k may be beneficial. See wikipedia, for more information about the Harris corner detector.
Related
I want to convert an image from Cartesian to Polar and to use it for opengl texture.
So I used matlab referring to the two articles below.
Link 1
Link 2
My code is exactly same with Link 2's anwser
% load image
img = imread('my_image.png');
% convert pixel coordinates from cartesian to polar
[h,w,~] = size(img);
[X,Y] = meshgrid((1:w)-floor(w/2), (1:h)-floor(h/2));
[theta,rho] = cart2pol(X, Y);
Z = zeros(size(theta));
% show pixel locations (subsample to get less dense points)
XX = X(1:8:end,1:4:end);
YY = Y(1:8:end,1:4:end);
tt = theta(1:8:end,1:4:end);
rr = rho(1:8:end,1:4:end);
subplot(121), scatter(XX(:),YY(:),3,'filled'), axis ij image
subplot(122), scatter(tt(:),rr(:),3,'filled'), axis ij square tight
% show images
figure
subplot(121), imshow(img), axis on
subplot(122), warp(theta, rho, Z, img), view(2), axis square
The result was exactly what I wanted, and I was very satisfied except for one thing. It's the area (red circled area) in the picture just below. Considering that the opposite side (blue circled area) is not, I think this part should also be filled. Because of this part is empty, so there is a problem when using it as a texture.
And I wonder how I can fill this part. Thank you.
(little difference from Link 2's answer code like degree<->radian and axis values. but i think it is not important.)
Those issues you show in your question happen because your algorithm is wrong.
What you did (push):
throw a grid on the source image
transform those points
try to plot these colored points and let MATLAB do some magic to make it look like a dense picture
Do it the other way around (pull):
throw a grid on the output
transform that backwards
sample the input at those points
The distinction is called "push" (into output) vs "pull" (from input). Only Pull gives proper results.
Very little MATLAB code is necessary. You just need pol2cart and interp2, and a meshgrid.
With interp2 you get to choose the interpolation (linear, cubic, ...). Nearest-neighbor interpolation leaves visible artefacts.
im = im2single(imread("PQFax.jpg"));
% center of polar map, manually picked
cx = 10 + 409/2;
cy = 7 + 413/2;
% output parameters
radius = 212;
dRho = 1;
dTheta = 2*pi / (2*pi * radius);
Thetas = pi/2 - (0:dTheta:2*pi);
Rhos = (0:dRho:radius);
% polar mesh
[Theta, Rho] = meshgrid(Thetas, Rhos);
% transform...
[Xq,Yq] = pol2cart(Theta, Rho);
% translate to sit on the circle's center
Xq = Xq + cx;
Yq = Yq + cy;
% sample image at those points
Ro = interp2(im(:,:,1), Xq,Yq, "cubic");
Go = interp2(im(:,:,2), Xq,Yq, "cubic");
Bo = interp2(im(:,:,3), Xq,Yq, "cubic");
Vo = cat(3, Ro, Go, Bo);
Vo = imrotate(Vo, 180);
imshow(Vo)
The other way around (get a "torus" from a "ribbon") is quite similar. Throw a meshgrid on the torus space, subtract center, transform from cartesian to polar, and use those to sample from the "ribbon" image into the "torus" image.
I'm more familiar with OpenCV than with MATLAB. Perhaps MATLAB has something like OpenCV's warpPolar(), or a generic remap(). In any case, the operation is trivial to do entirely "by hand" but there are enough supporting functions to take the heavy lifting off your hands (interp2, pol2cart, meshgrid).
1.- The white arcs tell that the used translation pol-cart introduces significant errors.
2.- Reversing the following script solves your question.
It's a script that goes from cart-pol without introducing errors or ignoring input data, which is what happens when such wide white arcs show up upon translation apparently correct.
clear all;clc;close all
clc,cla;
format long;
A=imread('shaffen dass.jpg');
[sz1 sz2 sz3]=size(A);
szx=sz2;szy=sz1;
A1=A(:,:,1);A2=A(:,:,2);A3=A(:,:,3); % working with binary maps or grey scale images this wouldn't be necessary
figure(1);imshow(A);
hold all;
Cx=floor(szx/2);Cy=floor(szy/2);
plot(Cx,Cy,'co'); % because observe image centre not centered
Rmin=80;Rmax=400; % radius search range for imfindcircles
[centers, radii]=imfindcircles(A,[Rmin Rmax],... % outer circle
'ObjectPolarity','dark','Sensitivity',0.9);
h=viscircles(centers,radii);
hold all; % inner circle
[centers2, radii2]=imfindcircles(A,[Rmin Rmax],...
'ObjectPolarity','bright');
h=viscircles(centers2,radii2);
% L=floor(.5*(radii+radii2)); % this is NOT the length X that should have the resulting XY morphed graph
L=floor(2*pi*radii); % expected length of the morphed graph
cx=floor(.5*(centers(1)+centers2(1))); % coordinates of averaged circle centres
cy=floor(.5*(centers(2)+centers2(2)));
plot(cx,cy,'r*'); % check avg centre circle is not aligned to figure centre
plot([cx 1],[cy 1],'r-.');
t=[45:360/L:404+1-360/L]; % if step=1 then we only get 360 points but need an amount of L points
% if angle step 1/L over minute waiting for for loop to finish
R=radii+5;x=R*sind(t)+cx;y=R*cosd(t)+cy; % build outer perimeter
hL1=plot(x,y,'m'); % axis equal;grid on;
% hold all;
% plot(hL1.XData,hL1.YData,'ro');
x_ref=hL1.XData;y_ref=hL1.YData;
% Sx=zeros(ceil(R),1);Sy=zeros(ceil(R),1);
Sx={};Sy={};
for k=1:1:numel(hL1.XData)
Lx=floor(linspace(x_ref(k),cx,ceil(R)));
Ly=floor(linspace(y_ref(k),cy,ceil(R)));
% plot(Lx,Ly,'go'); % check
% plot([cx x(k)],[cy y(k)],'r');
% L1=unique([Lx;Ly]','rows');
Sx=[Sx Lx'];Sy=[Sy Ly'];
end
sx=cell2mat(Sx);sy=cell2mat(Sy);
[s1 s2]=size(sx);
B1=uint8(zeros(s1,s2));
B2=uint8(zeros(s1,s2));
B3=uint8(zeros(s1,s2));
for n=1:1:s2
for k=1:1:s1
B1(k,n)=A1(sx(k,n),sy(k,n));
B2(k,n)=A2(sx(k,n),sy(k,n));
B3(k,n)=A3(sx(k,n),sy(k,n));
end
end
C=uint8(zeros(s1,s2,3));
C(:,:,1)=B1;
C(:,:,2)=B2;
C(:,:,3)=B3;
figure(2);imshow(C);
the resulting
3.- let me know if you'd like some assistance writing pol-cart from this script.
Regards
John BG
I have many medical images with dcm file format. There are circles in the photos (6 circles but the sixth is too small to see).
I want to calculate the radius of these circles very precisely. At least the radius of the first three or two circles I need. I use Hough transform for this. The results are not good for my purpose yet. How could I find these circles and their radius more precisely? The Images and my code are below.
clear,
close all,
imtool close all,
clc,
% I - raw image data
I = dicomread('193500.dcm');
% scale with [scale] = 1mm/Pixel
k = 253/1024;
% Wiener filter for noise reduction
I = wiener2(I,[6,6]);
% Optimizing the contrast
I = imadjust(I,[0.388 0.398]);
imshow(I)
% Check for circles
[centers, radii] = imfindcircles(I,[6 40],'ObjectPolarity','dark');
% representation of the circles
viscircles(centers, radii,'Color','b');
%
radii = sortrows(radii,'descend');
radii = k*radii;
radii(2:4)
Title changed from: Specific transformation/distortion of an image using checkerboard coordinates
I have two checkerboard images. One of them is slightly more distorted than the other. I think it's a type of "barrel" distortion. I'm trying to compute the radial distortion parameters (or generate camera parameters) in order to distort one of the images to look like the other so that the checkerboard corners will line up.
Here is the binary undistorted image with its corners plotted in blue o's and the reference coordinates of the corners that we need to distort the image to plotted in red o's.
Most of the distortion is happening around the edges and the corners. I believe this is a type of radial distortion. How do I find the radial distortion coefficients between the two sets of coordinates representing the checkerboard corners?
Link to Image A (undistorted): http://imgur.com/rg4PNvp
Link to Image B (distorted): http://imgur.com/a/BIvid
I need to transform the checkerboard from Image B to have its corners line up with the corners from image A.
I have tried modifying the MATLAB Camera Calibration app generated script (link). I changed the world points that would be used to estimate camera parameters to equal my world points (corners) from Image A. However, this wasn't successful. The code I tried is can be seen in this pastebin: https://pastebin.com/D0StCb0p I used the same image in the imageFileNames because estimateCameraParameters requires at least 2 sets of coordinates.
Code:
% Define images to process
imageFileNames = {'C:\Users\asavelyev\Pictures\checkerB.tif',...
'C:\Users\asavelyev\Pictures\checkerB.tif',...
};
% Detect checkerboards in images
[imagePoints, boardSize, imagesUsed] = detectCheckerboardPoints(imageFileNames);
imageFileNames = imageFileNames(imagesUsed);
% Read the first image to obtain image size
originalImage = imread(imageFileNames{1});
[mrows, ncols, ~] = size(originalImage);
% AS: change these worldPoints to points of RGB image...
% Generate world coordinates of the corners of the squares
worldPoints = detectCheckerboardPoints('C:\Users\asavelyev\Pictures\checkerA.tif');
% Calibrate the camera
[cameraParams, imagesUsed, estimationErrors] = estimateCameraParameters(imagePoints, worldPoints, ...
'EstimateSkew', false, 'EstimateTangentialDistortion', false, ...
'NumRadialDistortionCoefficients', 2, 'WorldUnits', 'millimeters', ...
'InitialIntrinsicMatrix', [], 'InitialRadialDistortion', [], ...
'ImageSize', [mrows, ncols]);
% For example, you can use the calibration data to remove effects of lens distortion.
undistortedImage = undistortImage(originalImage, cameraParams);
This was solved by using this post from Mathematics StackOverflow: https://math.stackexchange.com/questions/302093/how-to-calculate-the-lens-distortion-coefficients-with-a-known-displacement-vect
Main issue I oversaw was the normalizion of the data points used in computing the K coefficients used in radial distortion.
Here is the MATLAB script I wrote for finding these coefficients:
% input images should be black and white checkerboards already thresholded into a binary image
% output image are the K coefficients used in radial distortion
function K = CalculateRadialDistortion(DistortedImg, UndistortedImg)
distortedCorners = detectCheckerboardPoints(DistortedImg);
undistortedCorners = detectCheckerboardPoints(UndistortedImg);
% normalize data
X1 = distortedCorners(:,1) - size(DistortedImg, 2)/2;
Y1 = distortedCorners(:,2) - size(DistortedImg, 1)/2;
X1p = undistortedCorners(:,1) - size(DistortedImg, 2)/2;
Y1p = undistortedCorners(:,2) - size(DistortedImg, 1)/2;
% X1p = (1+k1*r^2 + k2*r^4)X1 where r^2 = X1^2 + Y1^2
Rsq = X1.^2 + Y1.^2;
Rquad = Rsq.^2;
Rsqd = cat(1, Rsq, Rsq);
Rquadd = cat(1, Rquad, Rquad);
R = cat(2, Rsqd, Rquadd);
X1poX1 = X1p ./ X1;
X1poX1 = X1poX1 - 1;
Y1poY1 = Y1p ./ Y1;
Y1poY1 = Y1poY1 - 1;
X1Y1 = cat(1, X1poX1, Y1poY1);
K = linsolve(R, X1Y1);
end
I am making a script in Matlab that takes in an image of the rear of a car. After some image processing I would like to output the original image of the car with a rectangle around the license plate of the car. Here is what I have written so far:
origImg = imread('CAR_IMAGE.jpg');
I = imresize(origImg, [500, NaN]); % easier viewing and edge connecting
G = rgb2gray(I);
M = imgaussfilt(G); % blur to remove some noise
E = edge(M, 'Canny', 0.4);
% I can assume all letters are somewhat upright
RP = regionprops(E, 'PixelIdxList', 'BoundingBox');
W = vertcat(RP.BoundingBox); W = W(:,3); % get the widths of the BBs
H = vertcat(RP.BoundingBox); H = H(:,4); % get the heights of the BBs
FATTIES = W > H; % find the BBs that are more wide than tall
RP = RP(FATTIES);
E(vertcat(RP.PixelIdxList)) = false; % remove more wide than tall regions
D = imdilate(E, strel('disk', 1)); % dilate for easier viewing
figure();
imshowpair(I, D, 'montage'); % display original image and processed image
Here are some examples:
From here I am unsure how to isolate the letters of the license plate, particularly like in the second example above where each letter has a decreased area due to the perspective of the image. My first idea was to get the bounding box of all regions and keep only the regions where the perimeter to area ratio is "similar" but this resulted in removing the letters of the plate that were connected when I dilate the image like the K and V in the fourth example above.
I would appreciate some suggestions on how I should go about isolating these letters. No code is necessary, and any advice is appreciated.
So I continued to work despite not receiving any answers here on SO and managed to get a working version through trial and error. All of the following code comes after the code in my original question and all plots below are from the first example image above. First, I found the variance for every single pixel row of the image and plotted them like so:
V = var(D, 0, 2);
X = 1:length(V);
figure();
hold on;
scatter(X, V);
I then fit a very high order polynomial to this scatter plot and saved the values where the slope of the polynomial was zero and the variance value was very low (i.e. the dark row of pixels immediately before or after a row with some white):
P = polyfit(X', V, 25);
PV = polyval(P, X);
Z = X(find(PV < 0.03 & abs(gradient(PV)) < 0.0001));
plot(X, PV); % red curve on plot
scatter(Z, zeros(1,length(Z))); % orange circles on x-axis
I then calculate the integral of the polynomial between any consecutive Z values (my dark rows), and save the two Z values between which the integral is the largest, which I mark with lines on the plot:
MAX_INTEG = -1;
MIN_ROW = -1;
MAX_ROW = -1;
for i = 1:(length(Z)-1)
TEMP_MIN = Z(i);
TEMP_MAX = Z(i+1);
Q = polyint(P);
TEMP_INTEG = diff(polyval(Q, [TEMP_MIN, TEMP_MAX]));
if (TEMP_INTEG > MAX_INTEG)
MAX_INTEG = TEMP_INTEG;
MIN_ROW = TEMP_MIN;
MAX_ROW = TEMP_MAX;
end
end
line([MIN_ROW, MIN_ROW], [-0.1, max(V)+0.1]);
line([MAX_ROW, MAX_ROW], [-0.1, max(V)+0.1]);
hold off;
Since the X-values of these lines correspond row numbers in the original image, I can crop my image between MIN_ROW and MAX_ROW:
I repeat the above steps now for the columns of pixels, crop, and remove any excess black rows of columns to result in the identified plate:
I then perform 2D cross correlation between this cropped image and the edged image D using Matlab's xcorr2 to locate the plate in the original image. After finding the location I just draw a rectangle around the discovered plate like so:
I have for example the following image and a corresponding mask.
I would like to weight the pixels inside the white circle with a Gaussian, g = #(x,y,xc,yc) exp(-( ((x-xc)^2)/0.5 + ((y-yc)^2)/0.5 ));, placed in the centroid (xc,yc) of the mask. x, y are the coordinates of the corresponding pixels. Could you please someone suggest a way to do that without using for loops?
Thanks.
By "weighting" pixels inside the ellipse, I assume you mean multiply elementwise by a 2D gaussian. If so, here's the code:
% Read images
img = imread('img.jpg');
img = im2double(rgb2gray(img));
mask = imread('mask.jpg');
mask = im2double(rgb2gray(mask)) > 0.9; % JPG Compression resulted in some noise
% Gaussian function
g = #(x,y,xc,yc) exp(-(((x-xc).^2)/500+((y-yc).^2)./200)); % Should be modified to allow variances as parameters
% Use rp to get centroid and mask
rp_mask = regionprops(mask,'Centroid','BoundingBox','Image');
% Form coordinates
centroid = round(rp_mask.Centroid);
[coord_x coord_y] = meshgrid(ceil(rp_mask.BoundingBox(1)):ceil(rp_mask.BoundingBox(1))+rp_mask.BoundingBox(3)-1, ...
ceil(rp_mask.BoundingBox(2)):ceil(rp_mask.BoundingBox(2))+rp_mask.BoundingBox(4)-1);
% Get Gaussian Mask
gaussian_mask = g(coord_x,coord_y,centroid(1),centroid(2));
gaussian_mask(~rp_mask.Image) = 1; % Set values outside ROI to 1, this negates weighting outside ROI
% Apply Gaussian - Can use temp variables to make this shorter
img_g = img;
img_g(ceil(rp_mask.BoundingBox(2)):ceil(rp_mask.BoundingBox(2))+rp_mask.BoundingBox(4)-1, ...
ceil(rp_mask.BoundingBox(1)):ceil(rp_mask.BoundingBox(1))+rp_mask.BoundingBox(3)-1) = ...
img(ceil(rp_mask.BoundingBox(2)):ceil(rp_mask.BoundingBox(2))+rp_mask.BoundingBox(4)-1, ...
ceil(rp_mask.BoundingBox(1)):ceil(rp_mask.BoundingBox(1))+rp_mask.BoundingBox(3)-1) .* gaussian;
% Show
figure, imshow(img_g,[]);
The result:
If you instead want to perform some filtering within that roi, there's a function called roifilt2 which will allow you to filter the image within that region as well:
img_filt = roifilt2(fspecial('gaussian',[21 21],10),img,mask);
figure, imshow(img_filt,[]);
The result: