Ok, this might be a little dumb to ask but I'm really having a hard time understanding the image coordinates in Matlab.
So, in a mathematical equation, f(x,y) f is the image function where x and y are the coordinates of the image. For example, in matlab code, we can:
img = imread('autumn.tif');
img(1,4); %f(x,y)
where img(1,4) is equivalent to the function f(x,y). Now, in Matlab, there is an option to convert the cartesian coordinate (x,y) to polar coordinate (rho,theta) with cart2pol() function.
Now, here's where I don't understand. Is it possible to apply f(rho,theta) which is the polar coordinates instead of the cartesian coordinate in Matlab?
I tried doing something like:
img(2.14,1.5)
But I get the error message saying about array indexing is only supported with integers or logical values.
Could anyone clear up my understanding on this? Because I'm required to apply f(rho,theta) instead of the conventional f(x,y).
An image in Matlab is basically just an 2D array (if you consider just a greyscale image). Therefore you also need integer indices, just as for all other arrays, to access the pixels of the image.
% i,j integers, not doubles, floates, etc.
pixel = img(i,j);
The polar coordinates from yor last question (theta, rho) can therefore not be used to access the image array. That is also the exact reason for the error message. At least you'd need to round them or find some other way to use them as indices (e.g. convert them back to cartesian coords. would be best, due to matrix indexing)
Regarding your application: As far as I have found out, these polar coordinates are used as parameters for the Zernike polynomials. So why would you use them to access the image?
Related
I am using matlab's built in function called Procrustes to see the rotation translation and scale between two images. But, I am just using coordinates of the brightest points in the image and rotating these coordinates about the center of the image. Procrustes compares two matrices and gives you the rotation, translation, and scale. However, procrustes only works correctly if the matrices are in the same order for comparison.
I am given an image and a separate comparison coordinate matrix. The end goal is to find how much the image has been rotated, translated, and scaled compared to the coordinate matrix. I can just use Procrustes for this, but I need to correctly order the coordinates found from the image to match the order in the comparison coordinate matrix. My thought was to compare the distance between every possible combination of points in the coordinate matrix and compare it to the coordinates that I find in the picture. I just do not know how to write this code due to the fact if there is n coordinates, there will be n! possible combinations.
Just searching for the shortest distance is not so hard.
A = rand(1E4,2);
B = rand(1E4,2);
tic
idx = nan(1,1E4);
for ct = 1:size(A,1)
d = sum((A(ct,:)-B).^2,2);
idx(ct) = find(d==min(d));
end
toc
plot(A(1:10,1),A(1:10,2),'.r',B(idx(1:10),1),B(idx(1:10),2),'.b')
takes half a second on my PC.
The problems can start when two points in set A are matched to the same location in set B.
length(unique(idx))==length(idx)
This can be solved in several ways. The best (imho) is to determine a probability that point B matches with point A based on the distance (usually something that decreases exponentially), and solve for the most probable situation.
A simpler method (but more error prone) is to remove the matched point from set B.
edit: I decided to split this question into two parts, because it were really two questions: 1. how to make a polar surface plot in MATLAB (this question) and 2. how to put fit polar data points into a coarse (and non-polar) matrix
I have a matrix that contains certain grey values (values between zero and one). These points are stored in a rectangular matrix, but really the data points are acquired by rotating the detector. This means that I actually have polar coordinates (I know the polar coordinates for every single pixel in my starting matrix).
I want to make a polar plot of the data points. I have the example of this below.
Because MATLAB stores images as matrices, the polar coordinates I have do not exactly match the 'bins' of the matrix. Therefore, we currently use an interpolation algorithm to put the polar coordinates into a square matrix. However, this is extremely slow. I see two methods to solve this issue:
let MATLAB directly plot the data points as polar.
calculate once how to convert from the start matrix to the end matrix and let MATLAB do this through matrix multiplication.
Some basic information:
Input matrix size: 512×960
Current output matrix size: 1024×1024
I think there is built in function for polar plot in matlab.
Z = [2+3i 2 -1+4i 3-4i 5+2i -4-2i -2+3i -2 -3i 3i-2i];
polarplot(Z,'*')
this command plots:
plot polar
See this link:
http://www.mathworks.com/help/matlab/ref/polarplot.html
To plot in grayscale, use "pcolor" and specify colormap to "gray"
www.mathworks.com/help/matlab/ref/ pcolor.html
The question was solved (apart from a minor flaw), partially because K.M. Shihab Uddin pointed me in the right direction. Unfortunately, using surf means continuously really plotting the image in a figure, and this is slow as well.
So I have X and Y values both in separate matrices and greyscale values (in a matrix called C) for every X and Y combination.
I found out that pcolor is just surf with a viewpoint from the top. So I used the following code to plot my graph.
surf(X,Y,C*255)
view([0,0,500])
However, this gave me a completely black image. This is because surf (and pcolor) create 960 grid lines radially in my case. The solution is to use:
surf(X,Y,img2*255,'EdgeColor','none')
view([0,0,500])
Now I have an almost perfect image, like I had before. Only, of my 960 radial lines, one is left white, so I still have to solve that. However, I feel this is a technical detail of the function surf, and answering this part does not belong in this question.
The resulting image
Please forgive me for the naive question, I don't remember linear algebra at all.
To do that I use a matrix that is associated to an image to apply transformations,
The matrix of the image is a matrix, now I want to get the how much the matrix has been translated and scale.
It's OK when there are no rotations applied,
but rotation confuses things a lot.
Say your new matrix N = RTS, where R is a rotation, T is a translation, and S is a scaling. This means in order you scale, translate, then rotate. If you want to see the scaling and translation, left-multiply by R-inverse, which is the same as R's transpose. With respect to your original view, you will see a stretched and transformed matrix.
If instead N = TSR, you would have to right multiply by R inverse. Note: The two matrices N obtained by these operations will not in general be the same!
Alternatively you can change coordinate systems, but this is more involved as rotation and translation do not commute in general.
With a camera inside a cylinder I capture a image. I want to transform that image into a plane 2d. The image inside the cylinder have a lot of dots which forms a grid.
What I tried to do was estimating the transformation. With blob analysis I can detect the center of each point and obtain the coordinates in pixels. I save this in matrix called ImCilynder. After that i create a matrix with coordinates of that points in the plane with the name Im2d.
I calculate the transformation (H) solving the equation:
Imcilynder * H= Im2d;
H= matrix [9x1]
H=pinv(Imcilynder) * Im2d
But, when i'm doing the test with the same points, the result is completely random, so i'm doing something wrong.
Is there a better way to solve this? Can you help me?
Explaining better,
I'm trying to find the transformation which transforms the image above to this image:
So, to clarify, I want the projection of the points which i see in the first image to a plane. Basically i want o unwrap the cylinder.
After the calculation of the transformation matrix. I'm expecting to multiply the first image with the transformation matrix and obtain the points in the plane. Or to multiply the coordinates of the center of the black dots and obtain the coordinates of that dots in the plane. Is this possibly?
Thank you very much,
Afonso
Well, what do yo wish to have in a plane? the circles forming a grid? Because if this is the case you need to remove the radial distortion, these kind of models are represented by some parameters, are non-linear by the way. May be if you can find a very good algorithm, you are going to obtain something like this:
If this is not your idea, you need to apply an elastic transformation and this kind of transformation needs to use a kind of grid that is the model of the transformation and you need to propose your model of grid. If you want to do this automatically you need to resort to elastic registration algorithms and you can use a model like this one:
Any ways, this is not a trivial task, there are a lot of research about complex transformations of course if you want to automatically obtain the transformation. Otherwise you can use photoshop ;).
I have a 3d object which is free to rotate along x,y and z axis and it is then saved as a transform matrix. In a case where the sequence of rotation is not known and the object is rotated for more than 3 times (eg :-if i rotate the object x-60degress, y-30 degrees, z-45 degrees then again x->30 degrees), is it possible to extract the angles rotated from the transform matrix?.I know that it is possible to get angles if the sequence of rotation is known, but if I have only the final transform matrix with me and nothing else, is it possible to get the angles rotated(x,y,and z) from the transform matrix ?
Euler angle conversion is a pretty well known topic. Just normalize the matrix orientation vectors and then use something like this c source code.
The matrix is the current state of things it has no knowledge of what the transformation has been in the past. It does not know how the matrix was built. You can just take the matrix into and decompose it into any pieces you like, as long as:
The data do not overlap. For example:Two X turns after each other is indistinguishable form each other (no way to know if its 1 2 or three different rotations summed).
The sequence order is known
A decomposition can be built out of the data (for example scale can be measured)