I have a binary image with non closed curves of 1-pixel width on it. I want to grab this curves as a list of points (in proper order). I found bwboundaries function which tries to wrap all non-zero pixels and thus in this case returns duplicate points:
>> A = [0 0 0; 1 1 1; 0 0 0];
>> b = bwboundaries(A)
ans =
[5x2 double]
>> b{1}
ans =
2 1
2 2
2 3
2 2
2 1
bwtraceboundary do the same
>> bwtraceboundary(A, [2 1], 'E')
ans =
2 1
2 2
2 3
2 2
2 1
Is there any standard method to get matrix like [2 1; 2 2; 2 3] immediately?
It produces double entries because your region is only one pixel wide. I don't think there's a standard method that handles your special problem directly. However, you can simply use the unique() function to eliminate double entries of the result.
To keep the original order of the points, just do:
b = bwboundaries(A);
[dummy, ind] = unique(b{1}, 'rows', 'first');
contour = b{1}(sort(ind), :);
Related
I have the following code:
x = VarName3;
y = VarName4;
x = (x/6000)/60;
plot(x, y)
Where VarName3 and VarName4 are 3000x1. I would like to apply a median filter to this in MATLAB. However, the problem I am having is that, if I use medfilt1, then I can only enter a single array of variables as the first argument. And for medfilt2, I can only enter a matrix as the first argument. But the data looks very obscured if I convert x and y into a matrix.
The x is time and y is a list of integers. I'd like to be able to filter out spikes and dips. How do I go about doing this? I was thinking of just eliminating the erroneous data points by direct manipulation of the data file. But then, I don't really get the effect of a median filter.
I found a solution using sort.
Median is the center element, so you can sort three elements, and take the middle element as median.
sort function also returns the index of the previous syntaxes.
I used the index information for restoring the matching value of X.
Here is my code sample:
%X - simulates time.
X = [1 2 3 4 5 6 7 8 9 10];
%Y - simulates data
Y = [0 1 2 0 100 1 1 1 2 3];
%Create three vectors:
Y0 = [0, Y(1:end-1)]; %Left elements [0 0 1 2 0 2 1 1 1 2]
Y1 = Y; %Center elements [0 1 2 0 2 1 1 1 2 3]
Y2 = [Y(2:end), 0]; %Right elements [1 2 0 2 1 1 1 2 3 0]
%Concatenate Y0, Y1 and Y2.
YYY = [Y0; Y1; Y2];
%Sort YYY:
%sortedYYY(2, :) equals medfilt1(Y)
%I(2, :) equals the index: value 1 for Y0, 2 for Y1 and 3 for Y2.
[sortedYYY, I] = sort(YYY);
%Median is the center of sorted 3 elements.
medY = sortedYYY(2, :);
%Corrected X index of medY
medX = X + I(2, :) - 2;
%Protect X from exceeding original boundries.
medX = min(max(medX, min(X)), max(X));
Result:
medX =
1 2 2 3 6 7 7 8 9 9
>> medY
medY =
0 1 1 2 1 1 1 1 2 2
Use a sliding window on the data vector centred at a given time. The value of your filtered output at that time is the median value of the data in the sliding window. The size of the sliding window is an odd value, not necessarily fixed to 3.
Let z = [1 3 5 6] and by getting all the difference between each elements:
we get:
bsxfun(#minus, z', z)
ans =
0 -2 -4 -5
2 0 -2 -3
4 2 0 -1
5 3 1 0
I now want to order these values in ascending order and remove the duplicates. So:
sort(reshape(bsxfun(#minus, z', z),1,16))
ans =
Columns 1 through 13
-5 -4 -3 -2 -2 -1 0 0 0 0 1 2 2
Columns 14 through 16
3 4 5
C = unique(sort(reshape(bsxfun(#minus, z', z),1,16)))
C =
-5 -4 -3 -2 -1 0 1 2 3 4 5
But by looking at -5 in [-5 -4 -3 -2 -1 0 1 2 3 4 5],
how can I tell where -5 comes from. By reading myself the matrix,
0 -2 -4 -5
2 0 -2 -3
4 2 0 -1
5 3 1 0
I know it comes from z(1) - z(4), i.e. row 1 column 4.
Also 2 comes from both z(3) - z(2) and z(2) - z(1), which comes from two cases. Without reading the originally matrix itself, how can we know that the 2 in [-5 -4 -3 -2 -1 0 1 2 3 4 5] is originally in row 3 column 2 and row 2 column 1 of the original matrix?
So by looking at each element in [-5 -4 -3 -2 -1 0 1 2 3 4 5], how do we know, for example, where -5 comes from in the original matrix index efficiently. I want to know as I need to do operation on ,e.g.,-5 and two indices that produce this: for example, for each difference, say -5, i do (-5)*1*6, as z(1)- z(6) = -5. But for 2, I need to do 2*(3*2+2*1) as z(3) - z(2) = 2, z(2) - z(1) = 2 which is not distinct.
Thinking hard, I think i should not reshape bsxfun(#minus, z', z) to array. I will also create two index array such that I can do operations like (-5)*1*6 stated above effectively. However, this is easier said than done and I also have to take care of nondistinct sources. Or should I do the desired operations first?
Use the third output from unique. And don't sort, unique will do that for you.
[sortedOutput,~,linearIndices] = unique(reshape(bsxfun(#minus, z', z),[1 16]))
You can reconstruct the result from bsxfun like so:
distances = reshape(sortedOutput(linearIndices),[4 4]);
If you want to know where a certain value appears, you write
targetValue = -5;
targetValueIdx = find(sortedOutput==targetValue);
linearIndexIntoDistances = find(targetValueIdx==linearIndices);
[row,col] = ind2sub([4 4],linearIndexIntoDistances);
Because linearIndices is 1 wherever the first value in sortedOutput appears in the original vector.
If you save the result of bsxfun in an intermediate variable:
distances=bsxfun(#minus, z', z)
Then you can look for the values of C in distances using find iteratively.
[rows,cols]=find(C(i)==distances)
This will give all rows and cols if the values are repeated. You just need to then use them for your equation.
You can use accumarray to collect all row and column indices that correspond to the same value in the matrix of differences:
z = [1 3 5 6]; % data vector
zd = bsxfun(#minus, z.', z); % matrix of differences
[C, ~, ind] = unique(zd); % unique values and indices
[rr, cc] = ndgrid(1:numel(z)); % template for row and col indices
f = #(x){x}; % anonymous function to collect row and col indices
row = accumarray(ind, rr(:), [], f); % group row indices according to ind
col = accumarray(ind, cc(:), [], f); % same for col indices
For example, C(6) is value 0, which appears four times in zd, at positions given by row{6} and col{6}:
>> row{6}.'
ans =
3 2 1 4
>> col{6}.'
ans =
3 2 1 4
As you see, the results are not guaranteed to be sorted. If you need to sort them in linear order:
rowcol = cellfun(#(r,c)sortrows([r c]), row, col, 'UniformOutput', false);
so now
>> rowcol{6}
ans =
1 1
2 2
3 3
4 4
I'm not sure I've followed exactly but some points to consider:
unique will sort the data for you by default so you don't need to call sort first
unique actually has three outputs and you can recover your original vector (i.e. with duplicates) using the third output so
[C,~,ic] = unique(reshape(bsxfun(#minus, z', z),1,16))
now you can get back to bsxfun(#minus, z', z),1,16) by calling
reshape(C(ic), numel(z), numel(z))
You might be more interested in the second output of unique which tells you what index each unique value was at in your 1-by-16 vector. It really depends on what you're trying to do though. But with this you could get a list of row column pairs to match your unique values:
[rows, cols] = ndgrid(1:4);
coords = [rows(:), cols(:)];
[C, ia] = unique(reshape(bsxfun(#minus, z', z),1,16));
coords_pairs = coords(ia,:)
which results in
coords_pairs =
1 4
1 3
2 4
2 3
3 4
4 4
4 3
3 2
4 2
3 1
4 1
I have a vector of x-values at which I would like to add vertical lines to a graph, say a row vector: vec = [1 2 3 4 5]
I know that you can add single vertical lines like this:
plot([1 1],[0 1])
(gives a vertical line at x=1 from y=0 to y=1).
But when I try something like
vec = [1 2 3 4 5];
lowLine = [0 0 0 0 0];
highLine = [1 1 1 1 1];
plot([vec vec],[lowLine highLine])
It does not give the required result, instead it gives a z-shape. Where am I going wrong?
In order to plot several lines in a single plot, you need to use the fact that MATLAB's plot function handles matrices as inputs, and that it sees each column of the inputs as different plots :
If X and Y are both matrices, then they must have equal size. The plot
function plots columns of Y versus columns of X.
Thus, in order to get the expected result, you need to write :
vec = [1 2 3 4 5];
lowLine = [0 0 0 0 0];
highLine = [1 1 1 1 1];
plot([vec;vec],[lowLine;highLine])
Result :
I have a Matrix of size M by N in which each row has some zero entries. I want to create M row vectors such that each of the vector contains the non zero elements of each row. For example if I have the following Matrix
A=[0 0 0 5;0 0 4 6;0 1 2 3;9 10 2 3]
I want four different row vectors of the following form
[5]
[4 6]
[1 2 3]
[9 10 2 3]
This can be done with accumarray using an anonymous function as fourth input argument. To make sure that the results are in the same order as in A, the grouping values used as first input should be sorted. This requires using (a linearized version of) A transposed as second input.
ind = repmat((1:size(A,2)).',1,size(A,2)).';
B = A.';
result = accumarray(ind(:), B(:), [], #(x){nonzeros(x).'});
With A = [0 0 0 5; 0 0 4 6; 0 1 2 3; 9 10 2 3]; this gives
result{1} =
5
result{2} =
4 6
result{3} =
1 2 3
result{4} =
9 10 2 3
Since Matlab doesn't support non-rectangular double arrays, you'll want to settle on a cell array. One quick way to get the desired output is to combine arrayfun with logical indexing:
nonZeroVectors = arrayfun(#(k) A(k,A(k,:)~=0),1:size(A,1),'UniformOutput',false);
I used the ('UniformOutput',false) name-value pair for the reasons indicated in the documentation (I'll note that the pair ('uni',0) also works, but I prefer verbosity). This input produces a cell array with the entries
>> nonZerosVectors{:}
ans =
5
ans =
4 6
ans =
1 2 3
ans =
9 10 2 3
I want to compare every row of a matrix with its every other row, element by element wise, using MATLAB. If two of the entries match, the result will be stored as 1, and if they don't match, it will be 0. This will give a symmetric matrix consisting of 0s and 1s.
For example, let A = [4 6 7 9 5; 2 6 9 9 1]
Then, the result expected is [1 1 1 1 1; 0 1 0 1 0; 0 1 0 1 0; 1 1 1 1 1]
The code I am using is (for a 1000*1000 random matrix):
A = randi(50,1000,1000);
B = zeros(1000000,1000);
D = zeros(1000000,1);
c=0;
for i=1:1000
for k=1:1000
for j=1:1000
if A(i,j)==A(k,j)
B(k+c,j)=1;
else
B(k+c,j)=0;
end
end
end
c=c+1000;
end
for l=1:1000000
D(l)=0;
for m=1:1000
D(l)=D(l)+(B(l,m)/(1000));
end
end
E=reshape(D,1000,1000);
This goes out of memory. Could anyone please suggest a solution or a more efficient code?
you can try row by row comparison directly as taking a complete row array and comparing with the other row array.
For example,
let
A = [4 6 7 9 5; 2 6 9 9 1];
nA = length(A(:,1));
finalMat = [];
for i = 1:nA
matRow = ones(nA,1)*A(i,:); % create a matrix size of A consists of same row elements
finalMat = [finalMat;matRow == A];
end
see if it is okay for you application.
You can use permute to align dimensions apprpriately and then bsxfun for the comparisons:
reshape(bsxfun(#eq, permute(A, [1 3 2]), permute(A, [3 1 2])), [], size(A,2))