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I have 2 greyscale images that i am trying to align using scalar scaling 1 , rotation matrix [2,2] and translation vector [2,1]. I can calculate image1's transformed coordinates as
y = s*R*x + t;
Below the resulting images are shown.
The first image is image1 before transformation,
the second image is image1 (red) with attempted interpolation using interp2 shown on top of image2 (green)
The third image is when i manually insert the pixel values from image1 into an empty array (that has the same size as image2) using the transformed coordinates.
From this we can see that the coordinate transformation must have been successful, as the images are aligned although not perfectly (which is to be expected since only 2 coordinates were used in calculating s, R and t) .
How come interp2 is not producing a result more similar to when i manually insert pixel values?
Below the code for doing this is included:
Interpolation code
function [transformed_image] = interpolate_image(im_r,im_t,s,R,t)
[m,n] = size(im_t);
% doesn't help if i use get_grid that the other function is using here
[~, grid_xr, grid_yr] = get_ipgrid(im_r);
[x_t, grid_xt, grid_yt] = get_ipgrid(im_t);
y = s*R*x_t + t;
yx = reshape(y(1,:), m,n);
yy = reshape(y(2,:), m,n);
transformed_image = interp2(grid_xr, grid_yr, im_r, yx, yy, 'nearest');
end
function [x, grid_x, grid_y] = get_ipgrid(image)
[m,n] = size(image);
[grid_x,grid_y] = meshgrid(1:n,1:m);
x = [reshape(grid_x, 1, []); reshape(grid_y, 1, [])]; % X is [2xM*N] coordinate pairs
end
The manual code
function [transformed_image] = transform_image(im_r,im_t,s,R,t)
[m,n] = size(im_t);
[x_t, grid_xt, grid_yt] = get_grid(im_t);
y = s*R*x_t + t;
ymat = reshape(y',m,n,2);
yx = ymat(:,:,1);
yy = ymat(:,:,2);
transformed_image = zeros(m,n);
for i = 1:m
for j = 1:n
% make sure coordinates are inside
if (yx(i,j) < m & yy(i,j) < n & yx(i,j) > 0.5 & yy(i,j) > 0.5)
transformed_image(round(yx(i,j)),round(yy(i,j))) = im_r(i,j);
end
end
end
end
function [x, grid_x, grid_y] = get_grid(image)
[m,n] = size(image);
[grid_y,grid_x] = meshgrid(1:n,1:m);
x = [grid_x(:) grid_y(:)]'; % X is [2xM*N] coordinate pairs
end
Can anyone see what i'm doing wrong with interp2? I feel like i have tried everything
Turns out i got interpolation all wrong.
In my question i calculate the coordinates of im1 in im2.
However the way interpolation works is that i need to calculate the coordinates of im2 in im1 such that i can map the image as shown below.
This means that i also calculated the wrong s,R and t since they were used to transform im1 -> im2, where as i needed im2 -> im1. (this is also called the inverse transform). Below is the manual code, that is basically the same as interp2 with nearest neighbour interpolation
function [transformed_image] = transform_image(im_r,im_t,s,R,t)
[m,n] = size(im_t);
[x_t, grid_xt, grid_yt] = get_grid(im_t);
y = s*R*x_t + t;
ymat = reshape(y',m,n,2);
yx = ymat(:,:,1);
yy = ymat(:,:,2);
transformed_image = zeros(m,n);
for i = 1:m
for j = 1:n
% make sure coordinates are inside
if (yx(i,j) < m & yy(i,j) < n & yx(i,j) > 0.5 & yy(i,j) > 0.5)
transformed_image(i,j) = im_r(round(yx(i,j)),round(yy(i,j)));
end
end
end
end
I track the motion of an object from a video file in MATLAB and save the locations from each frame in a numberOfFrames x 2 array.
I know the theoretical path or intended path. When recording the movie the camera is at some unknown angle in space. Therefore, the path is skewed. The only information I have is the scaling between the pixels and millimeters by using the object diameter.
Now I would like to rotate the intended path, and move it around until it is overlaid on the tracked motion path.
I start with my theoretical path (Pth) then rotate it in 3-dimensions to "Pthr". After that I loop over each point in "M". And for each point in "M", I look for the closest point from "Pthr". Then, I repeat for the next point in "M". This probably has a problem of choosing the same point in "Pthr" for multiple points in "M".
I noticed this is sensitive to my initial guess and it gives terrible results.
Also, M is not a perfect path, since it is experimental measurements it is no where near perfect. measured vs. theoretical unrotated path
% M = [Mx,My], is location in x and y, from motion tracking.
% scale = 20; % pixels/mm, using the size of object
% I build the theoretical path (Pth) goes from to (0,0,0) to (0,3,0) to
% (3,3,0) to (3,0,0) to be approximately the same length as M
Pthup = linspace(0,3,num)';
Pthdwn = linspace(3,0,num)';
Pth0 = zeros(size(Pthup));
Pth3 = 3*ones(size(Pthup));
% Pth is approximately same length as M
Pth = scale*[Pth0 Pthup Pth0;Pthup Pth3 Pth0;Pth3 Pthdwn Pth0];
% using fmincon in matlab to minimize the sum of the square
lb = [145 0 -45 min(min(M)) min(min(M))]; %upper bound
ub = [180 90 45 max(max(M)) max(max(M))]; %lower bound
coro = [180 0 0 mean(Mx) mean(My)]; %initial guess
% initial guess (theta(x),theta(y),theta(z), shift in x, shift in y)
cnt = 0; er = 1;
while (abs(er)>0.1)
[const,fval] = fmincon(#(cor)findOrientation(cor,Pth,M),coro,[],[],[],[],lb,ub);
er = sum(const-coro);
coro = const;
cnt = 1+cnt;
if (cnt>50)
cnt = cnt;
break
end
end
%% function findOrientation keeps rotating Pth until it is closest to M
function [Eo] = findOrientation(cor,Pth,M)
% cor = [angle of rotations, center coordinate];(degrees, non-dimensiolaized in pixels)
% M = measured coordinates from movie in pixel
% coor: is output of the form [x-coordiante,y-coordinate, absolute distance from Center(i,:)]
% F = sum of least square, sum(coor(:,3))
%% Rotation of theoretical path about z,y,x and shifting in it in xy
thx = cor(1);
thy = cor(2);
thz = cor(3);
xy = cor([4:5]);
% T = [cosd(thn) -sind(thn);
% sind(thn) cosd(thn)]; %rotation matrix in 3D
Tz = [cosd(thz) -sind(thz) 0;
sind(thz) cosd(thz) 0;0 0 1]; %rotation matrix
Ty = [cosd(thy) 0 -sind(thy);0 1 0;
sind(thy) 0 cosd(thy)]; %rotation matrix
Tx = [1 0 0;0 cosd(thx) -sind(thx);
0 sind(thx) cosd(thx)]; %rotation matrix
Pthr = zeros(size(Pth));
for i = 1:size(Pth,1)
xp = Tz*Pth(i,:)';
xp = Ty*xp;
xp = Tx*xp;
Pthr(i,:) = xp.';
end
Pthr = Pthr(:,[1,2]); % omit third value because it is 2D
Pthr = Pthr + [cor([4:5])];
rin = sqrt(Pthr(:,1).^2+Pthr(:,2).^2); %theoretical radius
Centern = sqrt(M(:,1).^2 + M(:,2).^2);%measured radius
for i = 1:size(M,1) %loop over each point in tracked motion
sub = Pthr-M(i,:); %subtracting M(i,:) from all Pthr
for j = 1:length(sub)
dist(j,1) = norm(sub(j,:));% distance from M(i,:) to all ri
end
%index is based on the min absolute distance between Pthr and M(i,:). It chooses the closest Pthr to a specific M(i,:)
[mn, index] = min(dist);
erri = abs(rin(index)-Centern(i))./rin(index);
coor(i,:) = erri;
end
Eo = sum(coor);
I'm trying to write a MATLAB script that does the following:
Given: pixel coordinates(x,y) for a .jpg image
Goal: Check, within a 5 pixel radius of given coordinates, if there is a pixel of a certain value.
For example, let's say I'm given the coordinates (100,100), then I want to check the neighborhood of (100,100) within my image for any pixels that are black (0,0,0). So perhaps, pixel (103, 100) and (104,100) might have the value (0,0,0).
Current code:
x_coord = uint32(coord(:,1));
y_coord = uint32(coord(:,2));
count = 0;
for i = 1:length(x_coord)
%(img(x,y) returns pixel value at that (x,y)
%Note 0 = black. Indicating that, at that position, the image is just
% black
if img(x_coord(i),y_coord(i)) == 0
count = count + 1;
end
end
It currently only checks at an exact location. Not in a local neighborhood. How to could I extend this?
EDIT: Also note, as long as there as at least one pixel in the neighborhood with the value, I increment count. I'm not trying to enumerate how many pixels in the neighborhood have that value, just trying to find evidence of at least one pixel that has that value.
EDIT:
Even though I am unable to identify an error with the code, I am not able to get the exact results I want. Here is the code I am using.
val = 0; %pixel value to check
N = 50; % neighbourhood radius
%2D grid of coordinates surrounding center coordinate
[R, C] = ndgrid(1 : size(img, 1), 1 : size(img, 2));
for kk = 1 : size(coord, 1)
r = coord(kk, 1); c = coord(kk, 2); % Get pixel locations
% mask of valid locations within the neighbourhood (avoid boundary problems)
mask = (R - r).^2 + (C - c).^2 <= N*N;
pix = img(mask); % Get the valid pixels
valid = any(pix(:) ~= val);
% Add either 0 or 1 depending if we have found any matching pixels
if(valid == 1)
img = insertMarker(img, [r c], 'x', 'color', 'red', 'size', 10);
imwrite(img, images(i).name,'tiff');
end
count = count + valid;
end
An easier way to do this would be to use indexing to grab a neighbourhood, then to check to see if any of the pixels in the neighbourhood have the value that you're looking for, use any on a flattened version of this neighbourhood. The trick with grabbing the right neighbourhood is to first generate a 2D grid of coordinates that span the entire dimensions of your image, then simply use the equation of a circle with the centre of it being each coordinate you are looking at and determine those locations that satisfy the following equation:
(x - a)^2 + (y - b)^2 <= N^2
N is the radius of the observation window, (a, b) is a coordinate of interest while (x, y) is a coordinate in the image. Use meshgrid to generate the coordinates.
You would use the above equation to create a logical mask, index into your image to pull the locations that are valid within the mask and check how many pixels match the one you want. Another added benefit with the above approach is that you are not subject to any out of bounds errors. Because you are pre-generating the list of all valid coordinates in your image, generating the mask will confine you within the boundaries of the image so you never have to check for out of boundaries conditions.... even when you specify coordinates to search that are out of bounds.
Specifically, assuming your image is stored in img, you would do:
count = 0; % Remembers total count of pixels matching a value
val = 0; % Value to match
N = 50; % Radius of neighbourhood
% Generate 2D grid of coordinates
[x, y] = meshgrid(1 : size(img, 2), 1 : size(img, 1));
% For each coordinate to check...
for kk = 1 : size(coord, 1)
a = coord(kk, 1); b = coord(kk, 2); % Get the pixel locations
mask = (x - a).^2 + (y - b).^2 <= N*N; % Get a mask of valid locations
% within the neighbourhood
pix = img(mask); % Get the valid pixels
count = count + any(pix(:) == val); % Add either 0 or 1 depending if
% we have found any matching pixels
end
The proposed solution:
fc = repmat(-5:5,11,1);
I = (fc.^2+fc'.^2)<=25;
fc_x = fc(I);
fc_y = fc'; fc_y = fc_y(I);
for i = 1:length(x_coord)
x_toCheck = fc_x + x_coord(i);
y_toCheck = fc_y + y_coord(i);
I = x_toCheck>0 & x_toCheck<=yourImageWidth;
I = I.*(y_toCheck>0 & y_toCheck<=yourImageHeight);
x_toCheck = x_toCheck(logical(I));
y_toCheck = y_toCheck(logical(I));
count = sum(img(x_toCheck(:),y_toCheck(:)) == 0);
end
If your img function can only check one pixel at a time, just add a for loop:
for i = 1:length(x_coord)
x_toCheck = fc_x + x_coord(i);
y_toCheck = fc_y + y_coord(i);
I = x_toCheck>0 & x_toCheck<=yourImageWidth;
I = I.*(y_toCheck>0 & y_toCheck<=yourImageHeight);
x_toCheck = x_toCheck(logical(I));
y_toCheck = y_toCheck(logical(I));
for j = 1:length(x_toCheck)
count = count + (img(x_toCheck(j),y_toCheck(j)) == 0);
end
end
Step-by-step:
You first need to get all the coordinates within 5 pixels range of the given coordinate.
We start by building a square of 11 pixels in length/width.
fc = repmat(-5:5,11,1);
fc_x = fc;
fc_y = fc';
plot(fc_x,fc_y,'.');
We now need to build a filter to get rid of those points outside the 5-pixel radius.
I = (fc.^2+fc'.^2)<=25;
Apply the filter, so we can get a circle of 5-pixel radius.
fc_x = fc_x(I);
fc_y = fc_y(I);
Next translate the centre of the circle to the given coordinate:
x_toCheck = fc_x + x_coord(i);
y_toCheck = fc_y + y_coord(i);
You need to check whether part of the circle is outside the range of your image:
I = x_toCheck>0 & x_toCheck<=yourImageWidth;
I = I.*(y_toCheck>0 & y_toCheck<=yourImageHeight);
x_toCheck = x_toCheck(logical(I));
y_toCheck = y_toCheck(logical(I));
Finally count the pixels:
count = sum(img(x_toCheck,y_toCheck) == 0);
I have lena image in Matlab. First I need to find the centroid C, and then divide the image into equal number of parts. I can calculate the centroid of the image but from that how can I divide the image into equal number of parts as shown below. Please anyone help me.
Thanks
Using poly2mask to create binary sectors and using the resulting sectors for indexing
Code:
im = imread('peppers.png');
r = 300;
out1 = ones(max(size(im,1),r*2)+2,max(size(im,2),r*2)+2,3).*255;
xoffset = floor((size(out1,2)-size(im,2))/2);
yoffset = floor((size(out1,1)-size(im,1))/2);
out1(yoffset:yoffset+size(im,1)-1,xoffset:xoffset+size(im,2)-1,:) = im(:,:,:);
im = out1;
cy = floor(size(im,1)/2);
cx = floor(size(im,2)/2);
figure;
imshow(uint8(im));
hold on
pos = [cx-r+1 cy-r+1 r*2 r*2];
rectangle('Position',pos,'Curvature',[1 1]);
x1 = [-r, 0, -r*cosd(45), -r*cosd(45); r, 0, r*cosd(45), r*cosd(45)]+cx+1;
y1 = [0, -r, -r*sind(45), r*sind(45); 0, r, r*sind(45), -r*sind(45)]+cy+1;
plot(x1,y1);
hold off
figure;
for i = 0:45:315
t = linspace(-i,-i-45,128);
x = [cx, cx+r*cosd(t), cx];
y = [cy, cy+r*sind(t), cy];
bw = poly2mask( x, y, size(im,1),size(im,2));
bw = repmat(bw,1,1,3);
out = ones(size(im,1),size(im,2),size(im,3)).*155;
out(bw) = im(bw);
subplot(2,4,(i/45)+1); imshow(uint8(out));
end;
Results:
Original Image
Partitions drawn over Original Image
Segments of the image
Update
for getting pixel values of the lines, by using Bresenham function from here
figure;
bw1 = zeros(size(im,1),size(im,2));
outmat = zeros(size(bw1));
[X,Y] = bresenham(cx+1-r,cy+1,cx+1+r,cy+1);
ind = sub2ind(size(outmat), Y, X);
outmat(ind) = 1;
[X,Y] = bresenham(cx+1,cy+1-r,cx+1,cy+1+r);
ind = sub2ind(size(outmat), Y, X);
outmat(ind) = 1;
[X,Y] = bresenham(cx+1-r*cosd(45),cy+1-r*sind(45),cx+1+r*cosd(45),cy+1+r*sind(45));
ind = sub2ind(size(outmat), Y, X);
outmat(ind) = 1;
[X,Y] = bresenham(cx+1-r*cosd(45),cy+1+r*sind(45),cx+1+r*cosd(45),cy+1-r*sind(45));
ind = sub2ind(size(outmat), Y, X);
outmat(ind) = 1;
se = strel('disk',5); %// change the '5' value to affect thickness of the line
outmat = imdilate(outmat,se);
outmat = repmat(boolean(outmat),1,1,3);
outmat1 = zeros(size(outmat));
outmat1(outmat) = im(outmat);
imshow(uint8(outmat1));
Pixel values under each lines
Check the following code. I just did it for a grayscale image. You can now change it to a color image as well. Check and pls confirm this is what you wanted.
clear all;
i = rgb2gray(imread('hestain.png'));
imshow(i);
cr = floor(size(i,1)/2);
cl = floor(size(i,2)/2);
r = min(cr, cl);
a = 90;
r1 = cr;
c1 = size(i,2);
v1=[c1 r1]-[cl cr];
i2 = zeros(size(i,1),size(i,2),ceil(360/a));
for ri = 1:size(i,1)
for ci = 1:size(i,2)
v2=[ci ri]-[cl cr];
a2 = mod(-atan2(v1(1)*v2(2)-v1(2)*v2(1), v1*v2'), 2*pi) * 180/pi;
d2 = pdist([ci ri; cl cr],'euclidean');
if d2<=r
if ceil(a2/a)==0
a2 =1;
end
i2(ri,ci,ceil(a2/a)) = i(ri,ci);
end
end
end
figure;
for i=1:360/a
subplot(2,180/a,i);
imshow(mat2gray(i2(:,:,i)));
end
Sample output:
I have a section of code that calculates the percent of pixels in a binary grid with value == 1 using a 50x50 sliding window:
f = #(x) numel(x(x==1))/numel(x);
I2 = nlfilter(buffer,[50 50],f);
I have heard that imfilter is a more efficient way to make focal calculations and, as such, hope to do some benchmarking. What is the imfilter() equivalent of the above nlfilter() function?
The complete code with sample data is attached
% Generate a grid of 0's to begin with.
m = zeros(400, 400, 'uint8');
% Generate 100 random "trees".
numRandom = 100;
linearIndices = randi(numel(m), 1, numRandom);
% Assign a radius value of 1-12 to each tree
m(linearIndices) = randi(12, [numel(linearIndices) 1]);
buffer = false(size(m));
for radius =1:12 % update to actual range
im_r = m==radius;
se = strel('disk',radius);
im_rb = imfilter(im_r, double(se.getnhood()));
buffer = buffer | im_rb;
end
% The imfilter approach
% The nlfilter approach
f = #(x) numel(x(x==1))/numel(x);
I2 = nlfilter(buffer,[50 50],f);
imshowpair(buffer,I2, 'montage')
For binary images (only 0s and 1s), what you have done is simple summation in a sliding window. Thus, the average filter of imfilter can be adopted here as:
h = fspecial( 'average', 50 );
I2 = imfilter( double( buffer ), h );