The title isn't very accurate because I didn't know the specific terms to describe it.
I have a matrix of known dimensions width and height. This matrix contains every
integer from 0 to width*height-1 so for example:
width = 7
height = 4
0 1 2 3 4 5 6
7 8 9 10 11 12 13
14 15 16 17 18 19 20
21 22 23 24 25 26 27
n = 18
x = ?
y = ?
Now if I'm given the value n = 18 I want the program to set x = 4 and y = 2 .
What is the mathematical operation behind it?
It feels like it should be pretty easy but I can wrap my head around it.
I thought the answer was x = n % width and y = n / height but it's not working, unless I'm just implementing it the wrong way
SOLVED
I'll leave the post here in case someone needs it.
The answer was actually x = n % width and y = n / width and I feel kinda dumb. You can also use height instead of width but keep in mind that you'll need to swap the operations.
Related
So I have a rectilinear grid that can be described with 2 vectors. 1 for the x-coordinates of the cell centres and one for the y-coordinates. These are just points with spacing like x spacing is 50 scaled to 10 scaled to 20 (55..45..30..10,10,10..10,12..20,20,20) and y spacing is 60 scaled to 40 scaled to 60 (60,60,60,55..42,40,40,40..40,42..60,60) and the grid is made like this
e.g. x = 1 2 3, gridx = 1 2 3, y = 10 11 12, gridy = 10 10 10
1 2 3 11 11 11
1 2 3 12 12 12
so then cell centre 1 is 1,10 cc2 is 2,10 etc.
Now Im trying to formulate an algorithm to calculate the positions of the cell edges in the x and y direction. So like my first idea was to first get the first edge using x(1)-[x(2)-x(1)]/2, in the real case x(2)-x(1) is equal to 60 and x(1) = 16348.95 so celledge1 = x(1)-30 = 16318.95. Then after calculating the first one I go through a loop and calculate the rest like this:
for aa = 2:length(x)+1
celledge1(aa) = x(aa-1) + [x(aa-1)-celledge(aa-1)]
end
And I did the same for y. This however does not work and my y vector in the area where the edge spacing should be should be 40 is 35,45,35,45... approx.
Anyone have any idea why this doesnt work and can point me in the right direction. Cheers
Edit: Tried to find a solution using geometric alebra:
We are trying to find the points A,B,C,....H. From basic geometry we know:
c1 (centre 1) = [A+B]/2 and c2 = [B+C]/2 etc. etc.
So we have 7 equations and 8 variables. We also know the the first few distances between centres are equal (60,60,60,60) therefore the first segment is 60 too.
B - A = 60
So now we have 8 equations and 8 variables so I made this algorithm in Matlab:
edgex = zeros(length(DATA2.x)+1,1);
edgey = zeros(length(DATA2.y)+1,1);
edgex(1) = (DATA2.x(1)*2-diffx(1))/2;
edgey(1) = (DATA2.y(1)*2-diffy(1))/2;
for aa = 2:length(DATA2.x)+1
edgex(aa) = DATA2.x(aa-1)*2-edgex(aa-1);
end
for aa = 2:length(DATA2.y)+1
edgey(aa) = DATA2.y(aa-1)*2-edgey(aa-1);
end
And I still got the same answer as before with the y spacing going 35,45,35,45 where it should be 40,40,40... Could it be an accuracy error??
Edit: here are the numbers if ur interested and I did the same computation as above only in excel: http://www.filedropper.com/workoutedges
It seems you're just trying to interpolate your data. You can do this with the built-in interp1
x = [30 24 19 16 8 7 16 22 29 31];
xi = interp1(2:2:numel(x)*2, x, 1:(numel(x)*2+1), 'linear', 'extrap');
This just sets up the original data as the even-indexed elements and interpolates the odd indices, including extrapolation for the two end points.
Results:
xi =
Columns 1 through 11:
33.0000 30.0000 27.0000 24.0000 21.5000 19.0000 17.5000 16.0000 12.0000 8.0000 7.5000
Columns 12 through 21:
7.0000 11.5000 16.0000 19.0000 22.0000 25.5000 29.0000 30.0000 31.0000 32.0000
I have a m x n matrix and want to be able to calculate sums of arbitrary rectangular submatrices. This will happen several times for the given matrix. What data structure should I use?
For example I want to find sum of rectangle in matrix
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
Sum is 68.
What I'll do is accumulating it row by row:
1 2 3 4
6 8 10 12
15 18 21 24
28 32 36 40
And then, if I want to find sum of the matrix I just accumulate 28,32,36,40 = 136. Only four operation instead of 15.
If I want to find sum of second and third row, I just accumulate 15,18,21,24 and subtract 1, 2, 3, 4. = 6+8+10+12+15+18+21+24 = 68.
But in this case I can use another matrix, accumulating this one by columns:
1 3 6 10
5 11 18 26
9 19 30 42
13 27 42 58
and in this case I just sum 26 and 42 = 68. Only 2 operation instead of 8. For wider sub-matrix is is efficient to use second method and matrix, for higher - first one. Can I somehow split merge this to methods to one matrix?
So I just sum to corner and subtract another two?
You're nearly there with your method. The solution is to use a summed area table (aka Integral Image):
http://en.wikipedia.org/wiki/Summed_area_table
The key idea is you do one pass through your matrix and accumulate such that "the value at any point (x, y) in the summed area table is just the sum of all the pixels above and to the left of (x, y), inclusive.".
Then you can compute the sum inside any rectangle in constant time with four lookups.
Why can't you just add them using For loops?
int total = 0;
for(int i = startRow; i = endRow; i++)
{
for(int j = startColumn; j = endColumn; j++)
{
total += array[i][j];
}
}
Where your subarray ("rectangle") would go from startRow to endRow (width) and startColumn to endColumn (height).
I have the following problem:
An image is given and I am doing some blob detection. As a limit, lets say I have a max of 16 blobs and from each blob I calculate the centroid (x,y position).
If no distorion happends, these centroids are arranged in an equidistant 4x4 grid but they could be really much distorted.
The assumption is that they keep more or less the grid form but they could be really much warped.
I need to sort the blobs such that I know which one is the nearest left, right, up and down. So the best would be to write these blobs into a matrix.
If this is not enough, it could happen that I detect less then 16 and then I also need to sort them into a matrix.
Does anyone know how this could be efficiently solved in Matlab?
Thanks.
[update 1:]
I uploaded an image and the red numbers are the numbers which my blob detection algorithm assign each blob.
The resulting matrix should look like this with these numbers:
1 2 4 3
6 5 7 8
9 10 11 12
13 16 14 15
e.g. I start with blob 11 and the nearest right number is 12 and so on
[update 2:]
The posted solution looks quite nice. In reality it could happen, that one of the outer spots is missing or maybe two ... I know that this makes everything much more complicated and I just want to get a feeling if this is worth spending time.
These problems arise if you analyze a wavefront with a shack-hartmann wavefront sensor and you want to increase the dynamic range :-)
The spots could be really warped such that the dividing lines are not orthogonal any more.
Maybe someone knows a good literature for classification algorithms.
Best solution would be one, which could be implemented on a FPGA without to much effort but this is at this stage not so much important.
This will work as long as the blobs form a square and are relatively ordered:
Image:
Code:
bw = imread('blob.jpg');
bw = im2bw(bw);
rp = regionprops(bw,'Centroid');
% Must be a square
side = sqrt(length(rp));
centroids = vertcat(rp.Centroid);
centroid_labels = cellstr(num2str([1:length(rp)]'));
figure(1);
imshow(bw);
hold on;
text(centroids(:,1),centroids(:,2),centroid_labels,'Color','r','FontSize',60);
hold off;
% Find topleft element - minimum distance from origin
[~,topleft_idx] = min(sqrt(centroids(:,1).^2+centroids(:,2).^2));
% Find bottomright element - maximum distance from origin
[~,bottomright_idx] = max(sqrt(centroids(:,1).^2+centroids(:,2).^2));
% Find bottom left element - maximum normal distance from line formed by
% topleft and bottom right blob
A = centroids(bottomright_idx,2)-centroids(topleft_idx,2);
B = centroids(topleft_idx,1)-centroids(bottomright_idx,1);
C = -B*centroids(topleft_idx,2)-A*centroids(topleft_idx,1);
[~,bottomleft_idx] = max(abs(A*centroids(:,1)+B*centroids(:,2)+C)/sqrt(A^2+B^2));
% Sort blobs based on distance from line formed by topleft and bottomleft
% blob
A = centroids(bottomleft_idx,2)-centroids(topleft_idx,2);
B = centroids(topleft_idx,1)-centroids(bottomleft_idx,1);
C = -B*centroids(topleft_idx,2)-A*centroids(topleft_idx,1);
[~,leftsort_idx] = sort(abs(A*centroids(:,1)+B*centroids(:,2)+C)/sqrt(A^2+B^2));
% Reorder centroids and redetermine bottomright_idx and bottomleft_idx
centroids = centroids(leftsort_idx,:);
bottomright_idx = find(leftsort_idx == bottomright_idx);
bottomleft_idx = find(leftsort_idx == bottomleft_idx);
% Sort blobs based on distance from line formed by bottomleft and
% bottomright blob
A = centroids(bottomright_idx,2)-centroids(bottomleft_idx,2);
B = centroids(bottomleft_idx,1)-centroids(bottomright_idx,1);
C = -B*centroids(bottomleft_idx,2)-A*centroids(bottomleft_idx,1);
[~,bottomsort_idx] = sort(abs(A*reshape(centroids(:,1),side,side)+B*reshape(centroids(:,2),side,side)+C)/sqrt(A^2+B^2),'descend');
disp(leftsort_idx(bsxfun(#plus,bottomsort_idx,0:side:side^2-1)));
Output:
2 12 13 20 25 31
4 11 15 19 26 32
1 7 14 21 27 33
3 8 16 22 28 34
6 9 17 24 29 35
5 10 18 23 30 36
Just curious, are you using this to automate camera calibration through a checkerboard or something?
UPDATE:
For skewed image
tform = maketform('affine',[1 0 0; .5 1 0; 0 0 1]);
bw = imtransform(bw,tform);
Output:
1 4 8 16 21 25
2 5 10 18 23 26
3 6 13 19 27 29
7 9 17 24 30 32
11 14 20 28 33 35
12 15 22 31 34 36
For rotated image:
bw = imrotate(bw,20);
Output:
1 4 10 17 22 25
2 5 12 18 24 28
3 6 14 21 26 31
7 9 16 23 30 32
8 13 19 27 33 35
11 15 20 29 34 36
I have something like the following:
a = [1 11; 2 16; 3 9; 4 13; 5 8; 6 14];
b = a;
n = length(a);
Sum = [];
for i=1:1:n,
Sum = b(i,2)+b(i+1:1:n,2)
end
b =
1 11
2 16
3 9
4 13
5 8
6 14
For the first iteration I am looking to find the first combination of values in the second column which are between 19 and 25.
Sum =
27
20
24
19
25
Since 20 is that first combination (Rows 1&3) -- I would like to remove that data at start a new matrix or signify that is the first combination (i.e. place a 1 next to in by creating a third column)
The next step would be to sum the values which are still in the matrix with row 2 value:
Sum =
29
24
30
Then 2&5 would be combined.
However, I would like to allow not only pairs to be combined but also several rows if possible.
Is there something I am overlooking that may simplify this problem?
I don't think you're going to simplify this very much. It's a variation on the knapsack problem, which is NP-hard. The best algorithm to use might depend on the size of your inputs.
I am in the process of building a function in MATLAB. As a part of it I have to calculate differences between elements in two matrices and sum them up.
Let me explain considering two matrices,
1 2 3 4 5 6
13 14 15 16 17 18
and
7 8 9 10 11 12
19 20 21 22 23 24
The calculations in the first row - only four elements in both matrices are considered at once (zero indicates padding):
(1-8)+(2-9)+(3-10)+(4-11): This replaces 1 in initial matrix.
(2-9)+(3-10)+(4-11)+(5-12): This replaces 2 in initial matrix.
(3-10)+(4-11)+(5-12)+(6-0): This replaces 3 in initial matrix.
(4-11)+(5-12)+(6-0)+(0-0): This replaces 4 in initial matrix. And so on
I am unable to decide how to code this in MATLAB. How do I do it?
I use the following equation.
Here i ranges from 1 to n(h), n(h), the number of distant pairs. It depends on the lag distance chosen. So if I choose a lag distance of 1, n(h) will be the number of elements - 1.
When I use a 7 X 7 window, considering the central value, n(h) = 4 - 1 = 3 which is the case here.
You may want to look at the circshfit() function:
a = [1 2 3 4; 9 10 11 12];
b = [5 6 7 8; 12 14 15 16];
for k = 1:3
b = circshift(b, [0 -1]);
b(:, end) = 0;
diff = sum(a - b, 2)
end