I have a MxNx3 matrix that represents an RGB image. I am trying to retrieve, for each pixel, the maximum among R, G and B. This would be made easy by using a for loop, which I do not wish to do for performance reasons.
How could I go about doing that? My idea is to use find and max in the following way and get an MxN matrix:
maxRGB = find(max(rgbImage(i, j, :)));
But I am not sure how I could eliminate i and j.
The max function allows to specify along which dimension the maximum value is determined. The standard value is the first dimension. In your case, you'll want to calculate the maximum along the third dimension of the array:
maxValue = max(rgbImage,[],3);
Which returns a matrix of size MxN containing the maximum value of each pixel.
For example, lets take a random 3x3 RGB image. Applying the max function as above yields
rgbImage = rand(3,3,3);
maxValue = max(rgbImage,[],3);
maxValue =
0.6948 0.7094 0.7655
0.6555 0.7547 0.7952
0.9502 0.3816 0.8235
These are the maximal values which were present in rgbImage at each pixel location. But, you don't know if this value was in the R, G or B pixel.
To find out, which color was maximal, you can use the second (optional) argument of max, which is the index of the found maximum:
[~,maxIndex] = max(rgbImage,[],3);
which in this small example was
maxIndex =
2 3 2
1 3 2
2 2 1
where 1 corresponds to R, 2 corresponds to G and 3 corresponds to B.
To find all pixels, in which the red component was the largest, you can use the find function (probably with 2 output arguments: row and column)
[xRed,yRed] = find(maxIndex == 1)
xRed =
2
3
yRed =
1
3
So for the pixels at (2,1) and at (3,3) the red component was the largest. This is exactly what the matrix maxIndex also shows us.
Related
Let us have a 4D matrix (tensor), output:
[X,Y,Z] = ndgrid(-50:55,-55:60,-50:60);
a = 1:4;
output = zeros([size(X),length(a)]);
Next, we determine the area inside the ellipsoid:
position = [0,0,0];
radius = [10,20,10];
test_func = #(X,Y,Z) ((X-position(1))/radius(1)).^2 ...
+ ((Y-position(2))/radius(2)).^2 ...
+ ((Z-position(3))/radius(3)).^2 <= 1;
condition = test_func(X,Y,Z);
I need to fill the matrix output inside the ellipsoid for the first 3 dimensions. But for the fourth dimension I need to fill a. I need to do something like this:
output(condition,:) = a;
But it does not work. How to do it? Any ideas please!
If I understand your question correctly, you have a 4D matrix where each temporal blob of pixels in 3D for each 4D slice is filled with a number... from 1 up to 4 where each number tells you which slice you're in.
You can cleverly use bsxfun and permute to help you accomplish this task:
output = bsxfun(#times, double(condition), permute(a, [1 4 3 2]));
This takes a bit of imagination to imagine how this works but it's quite simple. condition is a 3D array of logical values where each location in this 3D space is either 0 if it doesn't or 1 if it does belong to a point inside an ellipsoid. a is a row vector from 1 through 4 or however many elements you want this to end with. Let's call this N to be more general.
permute(a, [1 4 3 2]) shuffles the dimensions such that we create a 4D vector where we have 1 row, 1 column and 1 slice but we have 4 elements going into the fourth dimension.
By using bsxfun in this regard, it performs automatic broadcasting on two inputs where each dimension in the output array will match whichever of the two inputs had the largest value. The condition is that for each dimension independently, they should both match or one of them is a singleton dimension (i.e. 1).
Therefore for your particular example, condition will be 106 x 116 x 111 while the output of the permute operation will be 1 x 1 x 1 x N. condition is also technically 106 x 116 x 111 x 1 and using bsxfun, we would thus get an output array of size 106 x 116 x 111 x N. Performing the element-wise #times operation, the permuted vector a will thus broadcast itself over all dimensions where each 3D slice i will contain the value of i. The condition matrix will then duplicate itself over the fourth dimension so we have N copies of the condition matrix, and performing the element-wise multiply thus completes what you need. This is doable as the logical mask you created contains only 0s and 1s. By multiplying element-wise with this mask, only the values that are 1 will register a change. Specifically, if you multiply the values at these locations by any non-zero value, they will change to these non-zero values. Using this logic, you'd want to make these values a. It is important to note that I had to cast condition to double as bsxfun only allows two inputs of the same class / data type to be used.
To visually see that this is correct, I'll show scatter plots of each blob where the colour of each blob would denote what label in a it belongs to:
close all;
N = 4;
clrs = 'rgbm';
figure;
for ii = 1 : N
blob = output(:,:,:,ii);
subplot(2,2,ii);
plot3(X(blob == ii), Y(blob == ii), Z(blob == ii), [clrs(ii) '.']);
end
We get:
Notice that the spatial extent of each ellipsoid is the same but what is different are the colours assigned to each blob. I've made it such that the values for the first blob, or those assigned to a = 1 are red, those that are assigned to a = 2 are assigned to green, a = 3 to blue and finally a = 4 to magenta.
If you absolutely want to be sure that the coordinates of each blob are equal across all blobs, you can use find in each 3D blob individually and ensure that the non-zero indices are all equal:
inds = arrayfun(#(x) find(output(:,:,:,x)), a, 'un', 0);
all_equal = isequal(inds{:});
The code finds in each blob the column major indices of all non-zero locations in 3D. To know whether or not we got it right, each 3D blob should all contain the same non-zero column major indices. The arrayfun call goes through each 3D blob and returns a cell array where each cell element is the column major indices for a particular blob. We then pipe this into isequal to ensure that all of these column major indices arrays are equal. We get:
>> all_equal
all_equal =
1
I have x,y pixel coordinates of multiple objects that have been tracked from an image (3744x5616). The coordinates are stored in a structure called objects, e.g.
objects(1).centre = [1868 1236]
The objects are each uniquely identified by a numerical code, e.g.
objects(i).code = 33
I want to be able to record each time any two objects come within a radius of 300 pixels each other. What would be the best way to check through if any objects are touching and then record the identity of both objects involved in the interaction, like object 33 interacts with object 34.
Thanks!
Best thing I can think of right now is a brute force approach. Simply check the distances from one object's centre with the rest of the other objects and manually check if the distances are < 300 pixels.
If you want this fast, we should probably do this without any toolboxes. You can intelligently do this with vanilla MATLAB using bsxfun. First, create separate arrays for the X and Y coordinates of each object:
points = reshape([objects.centre], 2, []);
X = points(1,:);
Y = points(2,:);
[objects.centre] accesses the individual coordinates of each centre field in your structure and unpacks them into a comma-separated list. I reshape this array so that it is 2 rows where the first row is the X coordinate and the second row is the Y coordinate. I extract out the rows and place them into separate arrays.
Next, create two difference matrices for each X and Y where the rows denote one unique coordinate and the columns denote another unique coordinate. The values inside this matrix are the differences between the point i at row i and point j at column j:
Xdiff = bsxfun(#minus, X.', X);
Ydiff = bsxfun(#minus, Y.', Y);
bsxfun stands for Binary Singleton EXpansion FUNction. If you're familiar with the repmat function, it essentially replicates matrices and vectors under the hood so that both inputs you're operating on have the same size. In this case, what I'm doing is specifying X or Y as both of the inputs. One is the transposed version of the other. By doing this bsxfun automatically broadcasts each input so that the inputs match in dimension. Specifically, the first input is a column vector of X and so this gets repeated and stacked horizontally for as many times as there are values in X.
Similarly this is done for the Y value. After you do this, you perform an element-wise subtraction for both outputs and you get the component wise subtraction between one point and another point for X and Y where the row gives you the first point, and the column gives you the second point. As a toy example, imagine we had X = [1 2 3]. Doing a bsxfun call using the above code gives:
>> Xdiff = bsxfun(#minus, [1 2 3].', [1 2 3])
Xdiff =
## | 1 2 3
----------------------
1 | 0 -1 -2
2 | 1 0 -1
3 | 2 1 0
There are some additional characters I placed in the output, but these are used solely for illustration and to give you a point of reference. By taking a row value from the ## column and subtracting from a column value from the ## row gives you the desired subtract. For example, the first row second column illustrates 1 - 2 = -1. The second row, third column illustrates 2 - 3 = -1. If you do this for both the X and Y points, you get the component-wise distances for one point against all of the other points in a symmetric matrix.
You'll notice that this is an anti-symmetric matrix where the diagonal is all 0 ... makes sense since the distance of one dimension of one point with respect to itself should be 0. The bottom left triangular portion of the matrix is the opposite sign of the right... because of the order of subtraction. If you subtracted point 1 with point 2, doing the opposite subtraction gives you the opposite sign. However, let's assume that the rows denote the first object and the columns denote the second object, so you'd want to concentrate on the lower half.
Now, compute the distance, and make sure you set either the upper or lower triangular half to NaN because when computing the distance, the sign gets ignored. If you don't ignore this, we'd find duplicate objects that interact, so object 3 and object 1 would be a different interaction than object 1 and object 3. You obviously don't care about the order, so set either the upper or lower triangular half to NaN for the next step. Assuming Euclidean distance:
dists = sqrt(Xdiff.^2 + Ydiff.^2);
dists(tril(ones(numel(objects))==1)) = NaN;
The first line computes the Euclidean distance of all pairs of points and we use tril to extract the lower triangular portion of a matrix that consists of all logical 1. Extracting this matrix, we use this to set the lower half of the matrix to NaN. This allows us to skip entries we're not interested in. Note that I also set the diagonal to 0, because we're not interested in distances of one object to itself.
Now that you're finally here, search for those objects that are < 300 pixels:
[I,J] = find(dists < 300);
I and J are row/column pairs that determine which rows and columns in the matrix have values < 300, so in our case, each pair of I and J in the array gives you the object locations that are close to each other.
To finally figure out the right object codes, you can do:
codes = [[objects(I).code].' [objects(J).code].'];
This uses I and J to access the corresponding codes of those objects that were similar in a comma-separated list and places them side by side into a N x 2 matrix. As such, each row of codes gives you unique pairs of objects that satisfied the distance requirements.
For copying and pasting:
points = reshape([objects.centre], 2, []);
X = points(1,:);
Y = points(2,:);
Xdiff = bsxfun(#minus, X.', X);
Ydiff = bsxfun(#minus, Y.', Y);
dists = sqrt(Xdiff.^2 + Ydiff.^2);
dists(tril(ones(numel(objects))==1)) = NaN;
[I,J] = find(dists < 300);
codes = [[objects(I).code].' [objects(J).code].'];
Toy Example
Here's an example that we can use to verify if what we have is correct:
objects(1).centre = [1868 1236];
objects(2).centre = [2000 1000];
objects(3).centre = [1900 1300];
objects(4).centre = [3000 2000];
objects(1).code = 33;
objects(2).code = 34;
objects(3).code = 35;
objects(4).code = 99;
I initialized 4 objects with different centroids and different codes. Let's see what the dists array gives us after we compute it:
>> format long g
>> dists
dists =
NaN 270.407100498489 71.5541752799933 1365.69396278961
NaN NaN 316.227766016838 1414.2135623731
NaN NaN NaN 1303.84048104053
NaN NaN NaN NaN
I intentionally made the last point farther than any of the other three points to ensure that we can show cases where there are points not near other ones.
As you can see, points (1,2) and (1,3) are all near each other, which is what we get when we complete the rest of the code. This corresponds to objects 33, 34 and 35 with pairings of (33,34) and (33,35). Points with codes 34 and 35 I made slightly smaller, but they are still greater than the 300 pixel threshold, so they don't count either:
>> codes
codes =
33 34
33 35
Now, if you want to display this in a prettified format, perhaps use a for loop:
for vec = codes.'
fprintf('Object with code %d interacted with object with code %d\n', vec(1), vec(2));
end
This for loop is a bit tricky. It's a little known fact that for loops can also accept matrices and the index variable gives you one column of each matrix at a time from left to right. Therefore, I transposed the codes array so that each pair of unique codes becomes a column. I just access the first and second element of each column and print it out.
We get:
Object with code 33 interacted with object with code 34
Object with code 33 interacted with object with code 35
Definition:
A(i, j) = 1 is a midpoint of a cross if the elements
A(i-1, j) = 1
A(i+1, j) = 1
A(i, j+1) = 1
A(i, j-1) = 1.
Together the elements and the midpoint form a cross in a matrix A, where A is at least a 3-by-3 matrix and i, j ∈ ℕ\{0}.
Suppose the image above is the 8-by-8 matrix A with natural numbers 1, 2, 3 ... as elements. From this definition the matrix has a total of 3 crosses. The crosses have their midpoints on A(2,2), A(5, 4) and A(5, 5).
What I want to do is write a function that finds the number of crosses in the matrix A. I have an idea but I'm not sure it's the most optimal one. Here's the pseudocode for it:
ITERATE FROM row 2 TO row 7
ITERATE FROM column 1 TO column 8
IF current element contains 1
INCREMENT xcount by 1
IF xcount >= 3
CHECK IF counted 1:s is part of a cross
ELSE IF xcount IS NOT 0
SET xcount to 0
The idea is to iterate through every column from row 2 to row 7. If I find 3 consecutive 1:s on the same row I immediately check if the 1:s belongs to a cross. This should work, but imagine having a very large matrix A - how efficient would this code be in that situation? Couldn't this problem be solved using vector notation?
Any answer is very much appreciated. Thanks in advance!
Not near matlab at the moment, but this is what I'd do. Assuming A is binary (has only 0'a and 1's):
crs=[0 1 0 ; 1 1 1 ; 0 1 0]; % a minimal "cross" filter
C=conv2(A,crs./sum(crs(:)),'same'); % convolve A with it
[x y]=find(C>0.9); % find x,y positions of the crosses by looking
% for peak values of C
so you basically convolve with a "minimal" (normalized) cross (crs) and look for peaks using max. x and y are the coordinates of your cross positions. No need to use for loops, just the built in (and pretty fast) 2d convolution, and the max function.
The threshold condition C>0.9, is just to illustrate that there's need to be a threshold that is weighted by intensity of crs. In this case I have normalized crs in the colvolution line (crs/sum(crs(:))) so if A is a binary matrix as in the example, you find that the convolution of the minimal normalized cross will leave the value of the pixel where the cross is at 1, whereas other pixels will be less than 1 (that's why I arbitrarily chose 0.9) . So you can replace the threshold to C==1, if it's always a binary.
Another way to visulize the position of the cross is just to look at C.*(C==1). This will generate a matrix the size of A with 1s only where the crosses were...
EDIT:
For maximal speed, you may consider writing it as a one liner, for example:
[x y]=find(conv2(A,[0 1 0 ; 1 1 1 ; 0 1 0]./5,'same')==1);
Using bit masks:
ux = [false(size(A,1),1) (A(:,3:end) & A(:,2:end-1) & A(:,1:end-2)) false(size(A,1),1)]
uy = [false(1,size(A,2)); (A(3:end,:) & A(2:end-1,:) & A(1:end-2,:)); false(1, size(A,2))]
u = ux & uy
[x y] = find(u)
I have a matrix X that represents an image that was affected by noise. I also have a boolean matrix M that represents which pixels were affected by noise. What I want to do is to set every 'corrupted' pixel to the mean of its eight neighboring pixels.
Corrupted pixels are guaranteed to always be surrounded by uncorrupted ones, and also none of the pixels on the borders of the image are corrupted. What function can I used to write a vectorised version of this?
For your situation, this should perform quite fast
fixed = conv2 (image, [1 1 1; 1 0 1; 1 1 1]/8, "same")
# mask is a logical matrix for the corrupted pixels
image(mask) = fixed(mask)
Explanation: a mean filter is done with the conv2 function. To calculate the average of a pixel and its neighbors, the kernel used is ones (3) / 9 which means that 1/9 of each pixel value is used to calculate the new value. Since you don't want to count the center pixel in the average, you make its value 0 (in the kernel), and the others to 1/8.
This is probably not the most effective solution, but it should work.
N = size(M, 1);
target_ind = find(M);
offset = [-N-1, -N, -N+1, -1, 0, 1, N-1, N, N+1];
area_ind = bsxfun(#plus, offset, target_ind);
X(target_ind) = median(X(area_ind), 2);
Since all corrupted pixels are guaranteed to be surrounded by pixels, we can rather easily compute the linear indices of each corrupted pixel's neighbors. Here I've assumed that X is a grayscale image.
If I has more than one channel, then we could loop over each channel and add an offset to
target_ind and area_ind each time:
for i = 1:size(X, 3)
chan_offset = (i - 1)*size(X, 1)*size(X, 2) % Add the number of elements in previous channels to get indices in the current channel
X(target_ind + chan_offset) = median(X(area_ind + chan_offset), 2);
end
I have two matrices, one matrix with values ranging from 0-1, and another having only values of 0 and 1. I'm interested in calculating the distance only to those pixels equal to 1. In this case, I thought of making a new matrix that only contains the pixels with value 1 from the second object and then taking the distance to those. But, in this case, the dimensions will differ.
Note: The two matrices are originally of the same dimension. But, there are many cels not of interest (i.e; those having value 0)
How can I perform such distance calculation with objects of different dimensions?
Thanks.
If the positions of the pixels are not important to the calculation, then you can use logical indexing like so:
A = [0 1 0 0 1 1 0 0 1 1 1];
B = rand(size(A));
nonZeroInd = A == 1;
Anz = A(nonZeroInd);
Bnz = B(nonZeroInd);
dist = Bnz - Anz;
If you need the results in a matrix in the same positions as the original then you can do
C = zeros(size(A));
C(nonZeroInd) = dist;