I tried to padarray more than 1000 images. However when I time my code, this specific line take the highest amount of time to complete
I=abs(padarray(I, [2, 2], 'replicate', 'both'));
Mainly because of the line 35 of the padarray algorithm (inside profiler): images\private\padarray_algo
b = a(aIdx{:});
Any way to improve the efficiency? Perhaps using another method? Thanks!
You can use repmat and matrix concatenation to get the same result:
r=#repmat;
pad=#(I,d)[r(I(1),d) r(I(1,:),d(1),1) r(I(1,end),d)
r(I(:,1),1,d(2)) I r(I(:,end),1,d(2))
r(I(end,1),d) r(I(end,:),d(1),1) r(I(end),d)];
Usage:
pad(I,[2 2])
If all images are of the same size you can create a matrix of linear indices of the image and apply padarray to it then use padded index array to pad images:
%create matrix of indices
Idx = reshape(1:numel(I),size(I));
%pad the index
Idx_padded = padarray(Idx, [2, 2], 'replicate', 'both');
%use the padded index to pad images
result = I(Idx_padded);
result2 = I2(Idx_padded);
Related
I have a 3D-matrix A, with size lets say 3x12x100. The first two dimensions define 3×12 matrices, the latter one is simply the linear index. I want a very simple operation on these 100 matrices. For all these matrices, i want them multiplied with its conjugate transpose. With a very simple for loop, i can create this:
data = data;
A = zeros(100, 12, 12);
for i=1:100
A(i, :, :) = data(:, :, i)'*data(:, :, i);
end
But i like clean code, so i dont really prefer this for-loop. I have done some searching and sometimes find something like mtimesx (which is a custom made MATLAB function from 2010). I think i am missing something very obvious (as usual), because this seems a fairly easy operation (its just an "element-wise" matrix multiplication).
The size of my actual matrix is 3x12x862400. My original script takes about 10 minutes or longer, a variant on what #FangQ posts fixes it in a matter of seconds. My new code is as following, note that it still is under construction and i still need to validate it:
data = rand(3, 12, 862400) + i*rand(3, 12, 862400)
data2 = conj(permute(data, [2 1 3])); % conjugate transpose each matrix
% my data matrix contains 862400 3x12 matrices with complex numbers
Ap = permute(data2, [2 1 4 3]);
Bp = permute(data, [1 4 2 3]);
M = Ap.*Bp;
M = sum(M, 1);
M = permute(M, [2 3 4 1]);
#Cris was right, you can find an example from this MatlabCentral post
https://www.mathworks.com/matlabcentral/answers/10161-3d-matrix-multiplication#answer_413531
I have 2D matrixs of dimensions 400 x 500,each of these matrixs show an image. my process contain 2 steps:
1) I have to partition these images (split matrix to equal sized sub-matrices)
2) I have to save each of these split in one matrix
first step is done and dimention of matrix change from 2D-->3D (the last index shows index of splits)
now for the step 2 I have 100 images and I want to have matrix with 4 dimensions which the last index show the number of images
sample : for accessing split 3 of image 40 : [:,:,3,40]
I already try to using permut and reshape but not successful
here is my code
nCol = 10;
nRow = 4;
K=dir(p);
Len=length(K);
for i=3:Len
x1=imread(strcat(p,'\',K(i).name));
[m,n,d1]=size(x1);
if d1==1
x=double(x1);
else
x=double(rgb2gray(x1));
end
x=imresize(x,NN);
%% determined width and height of divided matrix %%%%%%%%%%%%%%%%%%%%%%%%%%
m = size(x,1)/nRow;
n = size(x,2)/nCol;
T = permute(reshape(permute(reshape(x, size(x, 1), n, []), [2 1 3]), n, m, []), [2 1 3]);
Im=[Im T(:,:,:,i-2)];
end
any idea would be appreciated.
reshape picks elements in column major ordering so you might have to write convoluted code to get it to work. Rather than going the way of using permute and reshape to create 4D matrices and potentially running into an out of memory issue I would advice the use of mat2cell to split your matrix into a cell array because mat2cell splits a matrix like you would want to split an image.
Here I show an example with an image
RGB = imread('peppers.png');
x = rgb2gray(RGB); % x is a 384 x 512 matrix, we want to split in 3 rows and 2 columns
x2 = mat2cell(x,384*ones(3,1)/3,512*ones(2,1)/2); % 2D cell array, each cell holds a part of the image
imshow(x2{1,1}) % Top left part of the image
You could loop over all your images and create a 3D cell array where each layer in the array represents each image split into pieces. I would suggest to preallocate you array and assign the matrix in the correct layer within the loop rather than incrementally increasing the size of your matrix.
Also there seems to be an Image processing toolbox specific function to do what you are trying to : Check this : How to divide an image into blocks in MATLAB?
In MATLAB, I am looking for an efficient (and/or vectorized) way of filling a matrix by selecting from multiple matrices given a "selector matrix." For instance, given three source matrices
M1 = [0.1, 0.2; 0.3, 0.4]
M2 = [1, 2; 3, 4]
M3 = [10, 20; 30, 40]
and a matrix of indices
I = [1, 3; 1, 2]
I want to generate a new matrix M = [0.1, 20; 0.3, 4] by selecting the first entry from M1, second from M3, etc.
I can definitely do it in a nested loop, going through each entry and filling in the value, but I am sure there is a more efficient way.
What if M1, M2, M3 and M are all 3D matrices (RGB images)? Each entry of I tells us from which matrix we should take a 3-vector. Say, if I(1, 3) = 3, then we know entries indexed by (1, 3, :) of M should be M3(1, 3, :).
A way of doing this, without changing the way you store your variable is to use masks. If you have a few matrices, it is doing the job avoiding a for loop. You won't be able to fully vectorize without going through the cat function, or using cells.
M = zeros(size(M1));
Itmp = repmat(I==1,[1 1 size(M1,3)]); M(Itmp) = M1(Itmp);
Itmp = repmat(I==2,[1 1 size(M1,3)]); M(Itmp) = M2(Itmp);
Itmp = repmat(I==3,[1 1 size(M1,3)]); M(Itmp) = M3(Itmp);
I think the best way to approach this is to stack dimensions (ie have a matrix with values that are each of your indvidiual matricies). Unfortunately MATLAB doesn't really support array level indexing so what ends up happening is you end up using linear indexing to convert your values through the subs2ind command. I believe you can use the code below.
M1 = [0.1, 0.2; 0.3, 0.4]
M2 = [1, 2; 3, 4]
M3 = [10, 20; 30, 40]
metamatrix=cat(3,M1,M2,M3)
%Create a 3 dimenssional or however many dimension matrix by concatenating
%lower order matricies
I=[1,1,1;1,2,3;2,1,1;2,2,2]
M=reshape(metamatrix(sub2ind(size(metamatrix),I(:,1),I(:,2),I(:,3))),size(metamatrix(:,:,1)))
With a more complex (3 dimensional case), you would have to extend the code for higher dimensions.
One way of doing this could be to generate a 4D matrix with you images. It has the cost of increasing the amount of memory, or at least, change you memory scheme.
Mcat = cat(4, M1, M2, M3);
Then you can use the function sub2ind to get a vectorized Matrix creation.
% get the index for the basic Image matrix
I = repmat(I,[1 1 3]); % repeat the index for for RGB images
Itmp = sub2ind(size(I),reshape(1:numel(I),size(I)));
% update so that indices reach the I(x) value element on the 4th dim of Mcat.
Itmp = Itmp + (I-1)*numel(I);
% get the matrix
M = Mcat(Itmp);
I haven't tested it properly, but it should work.
I would like to compute the weighted maxima of a vector in Matlab. For weighted maxima I intend the following:
Given a vector of 2*N+1 weights W={w[-N], w[-N+1] .. w[0] .. w[N]} and given an input sequence A, weighted maxima is a vector M where m[i]=max(w[-N]*a[i-N], w[-N+1]*a[i-N+1], ... w[N]*a[i+N])
So for example given a vector A= [1, 4, 12, 2, 4] and weights W=[0.5, 1, 0.5], the weighted maxima would be M=[2, 6, 12, 6, 4].
This can be done using ordfilt2, but ordfilt2 uses weights as additive rather then multiplicative.
I am actually working on 4D matrixes, but any 1D solution would work as the 4D weight matrix is separable.
My current solution is to generate shifted copies of the input array A, weight them according to the shift and maximize all the arrays. Shift is performed using circshift and is the bottleneck in the process. generating shifted matrixes "manually" trough indexing turned out to be even slower.
Can you suggest any more efficient solution?
EDIT: For a positive A, M=exp(ordfilt2(log(A), length(W), ones(size(W)), log(W))) does the job, but still takes longer than the circshift solution above. I am still looking for more efficient solutions.
>> B = padarray(A, [0 floor(numel(W)/2)], 0); % Pad A with zeros
>> B = bsxfun(#times, B(bsxfun(#plus, 1:numel(B)-numel(W)+1, (0:numel(W)-1)')), W(:)); % Apply the weights
>> M = max(B) % Compute the local maxima
M =
2 6 12 6 4
Suppose I have 4 letters and I want to arrange them in 3 places (repetition allowed), so I would have 43=64 possible permutations. How can I compute and print them?
Simplifying Amro's answer, you could use this:
%// Sample data
x = 'ABCD'; %// Set of possible letters
K = 3; %// Length of each permutation
%// Create all possible permutations (with repetition) of letters stored in x
C = cell(K, 1); %// Preallocate a cell array
[C{:}] = ndgrid(x); %// Create K grids of values
y = cellfun(#(x){x(:)}, C); %// Convert grids to column vectors
y = [y{:}]; %// Obtain all permutations
Matrix y should store the permutations you're after.
How about the function N_PERMUTE_K from the File Exchange?
An intuitive one-liner:
unique(nchoosek(repmat('ABCD', 1,4), 3), 'rows')
Although nice-looking, it's slow and inefficient. Don't use it for large data sets.
Pseudocode solution:
Generate the (base ten) numbers 0 to 63.
Change them to base 4, which only has the digits 0, 1, 2, and 3.
Convert numbers to letters.
The actual Matlab code is left as an exercise for the student.