I have a boolean map, thus an array made just with zeros and ones. It has dimension 512x512 and I need to resize it to 256x256.
If I use Matlab imresize, values will be re-scaled and I will not have anymore only 0 and 1 but also other values which I don't want.
How can I do this?
Thanks
Some possible approaches:
Discard even-indexed entries:
map_resize = map(1:2:end, 1:2:end);
Discard odd-indexed entries:
map_resize = map(2:2:end, 2:2:end);
For each 2×2 block compute the mean and then round to 0 or 1:
map = randi([0 1], 6, 6); % example input
sz = size(map);
map_resize = col2im(mean(im2col(map, [2 2], 'distinct'), 1), [1 1], sz/2) >= .5;
__ = imresize(___,method) specifies the interpolation method used.
By default, imresize uses bicubic interpolation.
if im not mistaken 'nearest' should work in this case.
https://www.mathworks.com/help/images/ref/imresize.html#inputarg_method
Related
I have some working code in matlab, and speed is vital. I have vectorized/optimized many parts of it, and the profiler now tells me that the most time is spent a short piece of code. For this,
I have some parameter sets for a multi-variate normal
distribution.
I then have to get the value from the corresponding PDF at some point
pos,
and multiply it by some other value stored in a vector.
I have produced a minimal working example below:
num_params = 1000;
prob_dist_params = repmat({ [1, 2], [10, 1; 1, 5] }, num_params, 1);
saved_nu = rand( num_params, 1 );
saved_pos = rand( num_params, 2 );
saved_total = 0;
tic()
for param_counter = 1:size(prob_dist_params)
% Evaluate the PDF at specified points
pdf_vals = mvnpdf( saved_pos(param_counter,:), prob_dist_params{param_counter,1}, prob_dist_params{param_counter, 2} );
saved_total = saved_total + saved_nu(param_counter)*pdf_vals;
end % End of looping over parameters
toc()
I am aware that prob_dist_params are all the same in this case, but in my code we have each element of this different depending on a few things upstream. I call this particular piece of code many tens of thousands of time in my full program, so am wondering if there is anything at all I can do to vectorize this loop, or failing that, speed it up at all? I do not know how to do so with the inclusion of a mvnpdf() function.
Yes you can, however, I don't think it will give you a huge performance boost. You will have to reshape your mu's and sigma's.
Checking the doc of mvnpdf(X,mu,sigma), you see that you will have to provide X and mu as n-by-d numeric matrix and sigma as d-by-d-by-n.
In your case, d is 2 and n is 1000. You have to split the cell array in two matrices, and reshape as follows:
prob_dist_mu = cell2mat(prob_dist_params(:,1));
prob_dist_sigma = cell2mat(permute(prob_dist_params(:,2),[3 2 1]));
With permute, I make the first dimension of the cell array the third dimension, so cell2mat will result in a 2-by-2-by-1000 matrix. Alternatively you can define them as follows,
prob_dist_mu = repmat([1 2], [num_params 1]);
prob_dist_sigma = repmat([10, 1; 1, 5], [1 1 num_params]);
Now call mvnpdf with
pdf_vals = mvnpdf(saved_pos, prob_dist_mu, prob_dist_sigma);
saved_total = saved_nu.'*pdf_vals; % simple dot product
For matrices with dimensions equal or less then 2 the command is:
For instance:
>> mat2str(ones(2,2))
ans =
[1 1;1 1]
However, as the help states, this does not work for higher dimensions:
>> mat2str(rand(2,2,2))
Error using mat2str (line 49)
Input matrix must be 2-D.
How to output matrices with higher dimensions than 2 with that is code compatible, without resorting to custom made for loops?
This isn't directly possible because there is no built-in character to represent concatenation in the third dimension (an analog to the comma and semicolon in 2D). One potential workaround for this would be to perform mat2str on all "slices" in the third dimension and wrap them in a call to cat which, when executed, would concatenate all of the 2D matrices in the third dimension to recreate your input matrix.
M = reshape(1:8, [2 2 2]);
arrays = arrayfun(#(k)mat2str(M(:,:,k)), 1:size(M, 3), 'uni', 0);
result = ['cat(3', sprintf(', %s', arrays{:}), ')'];
result =
'cat(3, [1 3;2 4], [5 7;6 8])'
isequal(eval(result), M)
1
UPDATE
After thinking about this some more, a more elegant solution is to flatten the input matrix, run mat2str on that, and then in the string used to recreate the data, we utilize reshape combined with the original dimensions to provide a command which will recreate the data. This will work for any dimension of data.
result = sprintf('reshape(%s, %s);', mat2str(M(:)), mat2str(size(M)));
So for the following 4D input
M = randi([0 9], 1, 2, 3, 4);
result = sprintf('reshape(%s, %s);', mat2str(M(:)), mat2str(size(M)));
'reshape([6;9;4;6;5;2;6;1;7;2;1;7;2;1;6;2;2;8;3;1;1;3;8;5], [1 2 3 4]);'
Now if we reconstruct the data using this generated string, we can ensure that we get the correct data back.
Mnew = eval(result);
size(Mnew)
1 2 3 4
isequal(Mnew, M)
1
By specifying both the class and precision inputs to mat2str, we can even better approximate the input data including floating point numbers.
M = rand(1,2,3,4,5);
result = sprintf('reshape(%s, %s);', mat2str(M(:),64,'class'), mat2str(size(M)));
isequal(eval(result), M)
1
I have an image U, and when I want to convolve it with a box filter:
0 1 0
1 -4 1
0 1 0
I use imfilter function with a constant 2D array and there is no problem. But, when I have the following operation:
u(i,j) = v(i-1,j)^2 * u(i-1,j) + v(i+1,j)^2 * u(i+1,j) + v(i, j+1)^2 * u(i,j+1) + v(i,j-1)^2 * u(i,j-1)
(A simplified version of my filter). In other words, my filter to be used over image U is related to the pixel values of image V, but in the same location which the filter is applied. Is there a way to implement such an operation in MATLAB, WITHOUT using nested for loops for each pixel?
You can solve it using im2col and col2im as following:
% Filtering A using B
mA = randn(10, 10); mB = randn(10, 10);
mACol = im2col(mA, [3, 3], 'sliding'); mBCol = im2col(mB, [3, 3],
'sliding');
mAColFilt = sum(mACol .* (mBCol .^ 2));
mAFilt = col2im(mAColFilt, [3, 3], [10, 10]);
I skipped the to get the correct coefficients (In your case, zero few of them and raise to the power of 2 the rest, I only raised all to the power of 2).
Pay attention that the filtered image is smaller (Bounadries of the filter).
You should pad it as required.
How does one create a vector that is composed of a random sampling of two other vectors?
For example
Vector 1 [1, 3, 4, 7], Vector 2 [2, 5, 6, 8]
Random Vector [random draw from vector 1 or 2 (value 1 or 2), random draw from vector 1 or 2 (value 3 or 5)... etc]
Finally, how can one ask matlab to repeat this process n times to draw a distribution of results?
Thank you,
There are many ways you could do this. One possibility is:
tmp=round(rand(size(vector1)))
res = tmp.*vector1 + (1-tmp).*vector2
To get one mixed sample, you may use the idea of the following code snippet (not the optimal one, but maybe clear enough):
a = [1, 3, 4, 7];
b = [2, 5, 6, 8];
selector = randn(size(a));
sample = a.*(selector>0) + b.*(selector<=0);
For n samples put the above code in a for loop:
for k=1:n
% Sample code (without initial "samplee" assignments)
% Here do stuff with the sample
end;
More generally, if X is a matrix and for each row you want to take a sample from a column chosen at random, you can do this with a loop:
y = zeros(size(X,1),1);
for ii = 1:size(X,1)
y(ii) = X(ii,ceil(rand*size(X,2)));
end
You can avoid the loop using clever indexing via sub2ind:
idx_n = ceil(rand(size(X,1),1)*size(X,2));
idx = sub2ind(size(X),(1:size(X,1))',idx_n);
y = X(idx);
If I understand your question, you are choosing two random numbers. First you decide whether to select vector 1 or vector 2; next you pick an element from the chosen vector.
The following code takes advantage of the fact that vector1 and vector2 are the same length:
N = 1000;
sampleMatrix = [vector1 vector2];
M = numel(sampleMatrix);
randIndex = ceil(rand(1,N)*M); % N random numbers from 1 to M
randomNumbers = sampleMatrix(randIndex); % sample N times from the matrix
You can then display the result with, for instance
figure; hist(randomNumbers); % draw a histogram of numbers drawn
When vector1 and vector2 have different elements, you run into a problem. If you concatenate them, you will end up picking elements from the longer vector more often. One way around this is to create random samplings from both arrays, then choose between them:
M1 = numel(vector1);
M2 = numel(vector2);
r1 = ceil(rand(1,N)*M1);
r2 = ceil(rand(1,N)*M2);
randMat = [vector1(r1(:)) vector2(r2(:))]; % two columns, now pick one or the other
randPick = ceil(rand(1,N)*2);
randomNumbers = [randMat(randPick==1, 1); randMat(randPick==2, 2)];
On re-reading, maybe you just want to pick "element 1 from either 1 or 2", then "element 2 from either 1 or 2", etc for all the elements of the vector. In that case, do
N=numel(vector1);
randPick = ceil(rand(1,N)*2);
randMat=[vector1(:) vector2(:)];
randomNumbers = [randMat(randPick==1, 1); randMat(randPick==2, 2)];
This problem can be solved using the function datasample.
Combine both vectors into one and apply the function. I like this approach more than the handcrafted versions in the other answers. It gives you much more flexibility in choosing what you actually want, while being a one-liner.
I have a solution to creating a vector for just one element of a matrix:
[dx,dy] = gradient(Im);
orient11 = [(-dx(1,1)) (dy(1,1)) 0];
where
size(orient11) =
0 0 0
ie for the first element of orient, namely orient11, is a vector. How do I do this for all the other elements, so I have orient12, orient13....orientnn. I know I need a for loop, however what object do I store the vectors into from the for loop? I have discovered I can't create a matrix of vectors.
Thanks in advance.
You can try building an N-by-N-by-3 matrix, but it won't be so convenient to manipulate. This is because extracting a vector from this matrix would yield a 1-by-1-by-3 vector, which you would need to reshape. Definitely not fun.
Instead, I suggest that you build an N-by-N cell array of 1-by-3 vectors, like so:
[dx, dy] = gradient(Im);
vec = #(i)[-dx(i), dy(i), 0];
orient = arrayfun(vec, reshape(1:numel(dx), size(dx)), 'UniformOutput', 0);
To access a vector, use the curly braces. For example, the vector at the (1, 2) position would be:
orient12 = orient{1, 2};
Hope it helps!
v = -2:0.2:2;
[x,y] = meshgrid(v);
z = x .* exp(-x.^2 - y.^2);
[px,py] = gradient(z,.2,.2);
orient11 = [(-px(1,1)) (py(1,1)) 0]; % based off of your concatination there.
size(orient11)
I then get:
ans =
1 3
If you're looking to just grab the first column of data from the gradients you have and want to just stack zeros with them, you can do this:
orient11 = [(-px(:,1)) (py(:,1)) zeros(size(px,1),1)];
Instead of a for loop.
Update:
Orient = zeros(size(px,1),3,size(px,2));
for n = 1:size(px,1)
Orient(:,:,n) = [(-px(:,n)) (py(:,n)) zeros(size(px,1),1)];
end
The layout of Orient is now your -px, py, 0 in layers. Each layer represents the column from the initial data. So if you wanted to get access to row 4 column 14, you would call Orient(4,:,14).
Hope that makes sense and helps!