I have a 5000 *5000 sparse matrix with 4 different values. I want to visualise the nonzero elements with 4 different colors such that I can recognise the ratio of this values and the relationships between them,I use imagesc but I can not recognise very well among different values, especially the values with smaller ratio.I think if I use some symboles for each value , it works but I don't know how is it in Matlab. Any suggestion? The result of Dan code is in figure below.
You could reform the matrix to be a set of [X, Y, F] coordinates (re-using my answer from Resampling Matrix and restoring in one single Matrix):
Assuming your matrix is M
[X, Y] = meshgrid(1:size(M,1), 1:size(M,2));
Mf = M(:); %used again later, hence stored
V = [X(:), Y(:), Mf];
get rid of the zero elements
V(Mf == 0, :) = [];
At this point, if you have access to the statistics toolbox you can just go gscatter(V(:,1), V(:,2), V(:,3)) to get the correct plot otherwise continue with the following if you don't have the toolbox:
Find a list of the unique values in M
Vu = unique(V(:,3));
For each such value, plot the points as an xy scatter plot, note hold all makes sure the colour changes each time a new plot is added i.e. each new iteration of the loop
hold all;
for g = 1:length(Vu)
Vg = V(V(:,3)==Vu(g),:)
plot(Vg(:,1), Vg(:,2), '*');
a{g}=num2str(Vu(g));
end
legend(a);
Example M:
M = zeros(1000);
M(200,30) = 7;
M(100, 900) = 10;
M(150, 901) = 13;
M(600, 600) = 13;
Result:
Now i can answer the first part of the question. I suppose you need to do something like
sum(histc(A, unique(A)),2)
to count the number of unique values in the matrix.
temp = histc(A, unique(A)) "is a matrix of column histogram counts." So you get the counts of all values of unique(A) as they appear in A columns.
I'm doing stat = sum(temp,2) to get counts of all values of unique(A) in the whole matrix.
Then you can use the code proposed from #Dan to visualize the result.
hold all;
u=unique(A);
for i = 1:length(stat)
plot(u(i), stat(i)/max(stat), '*');
end
Please clarify what kind of relationship between the values do you mean?
Related
I have a matrix named figmat from which I obtain the following pcolor plot (Matlab-Version R 2016b).
Basically I only want to extract the bottom red high intensity line from this plot.
I thought of doing it in some way of extracting the maximum values from the matrix and creating some sort of mask on the main matrix. But I'm not understanding a possible way to achieve this. Can it be accomplished with the help of any edge/image detection algorithms?
I was trying something like this with the following code to create a mask
A=max(figmat);
figmat(figmat~=A)=0;
imagesc(figmat);
But this gives only the boundary of maximum values. I also need the entire red color band.
Okay, I assume that the red line is linear and its values can uniquely be separated from the rest of the picture. Let's generate some test data...
[x,y] = meshgrid(-5:.2:5, -5:.2:5);
n = size(x,1)*size(x,2);
z = -0.2*(y-(0.2*x+1)).^2 + 5 + randn(size(x))*0.1;
figure
surf(x,y,z);
This script generates a surface function. Its set of maximum values (x,y) can be described by a linear function y = 0.2*x+1. I added a bit of noise to it to make it a bit more realistic.
We now select all points where z is smaller than, let's say, 95 % of the maximum value. Therefore find can be used. Later, we want to use one-dimensional data, so we reshape everything.
thresh = min(min(z)) + (max(max(z))-min(min(z)))*0.95;
mask = reshape(z > thresh,1,n);
idx = find(mask>0);
xvec = reshape(x,1,n);
yvec = reshape(y,1,n);
xvec and yvec now contain the coordinates of all values > thresh.
The last step is to do some linear polynomial over all points.
pp = polyfit(xvec(idx),yvec(idx),1)
pp =
0.1946 1.0134
Obviously these are roughly the coefficients of y = 0.2*x+1 as it should be.
I do not know, if this also works with your data, since I made some assumptions. The threshold level must be chosen carefully. Maybe some preprocessing must be done to dynamically detect this level if you really want to process your images automatically. There might also be a simpler way to do it... but for me this one was straight forward without the need of any toolboxes.
By assuming:
There is only one band to extract.
It always has the maximum values.
It is linear.
I can adopt my previous answer to this case as well, with few minor changes:
First, we get the distribution of the values in the matrix and look for a population in the top values, that can be distinguished from the smaller values. This is done by finding the maximum value x(i) on the histogram that:
Is a local maximum (its bin is higher than that of x(i+1) and x(i-1))
Has more values above it than within it (the sum of the height of bins x(i+1) to x(end) < the height of bin x):
This is how it is done:
[h,x] = histcounts(figmat); % get the distribution of intesities
d = diff(fliplr(h)); % The diffrence in bin height from large x to small x
band_min_ind = find(cumsum(d)>size(figmat,2) & d<0, 1); % 1st bin that fit the conditions
flp_val = fliplr(x); % the value of x from large to small
band_min = flp_val(band_min_ind); % the value of x that fit the conditions
Now we continue as before. Mask all the unwanted values, interpolate the linear line:
mA = figmat>band_min; % mask all values below the top value mode
[y1,x1] = find(mA,1); % find the first nonzero row
[y2,x2] = find(mA,1,'last'); % find the last nonzero row
m = (y1-y2)/(x1-x2); % the line slope
n = y1-m*x1; % the intercept
f_line = #(x) m.*x+n; % the line function
And if we plot it we can see the red line where the band for detection was:
Next, we can make this line thicker for a better representation of this line:
thick = max(sum(mA)); % mode thickness of the line
tmp = (1:thick)-ceil(thick/2); % helper vector for expanding
rows = bsxfun(#plus,tmp.',floor(f_line(1:size(A,2)))); % all the rows for each column
rows(rows<1) = 1; % make sure to not get out of range
rows(rows>size(A,1)) = size(A,1); % make sure to not get out of range
inds = sub2ind(size(A),rows,repmat(1:size(A,2),thick,1)); % convert to linear indecies
mA(inds) = true; % add the interpolation to the mask
result = figmat.*mA; % apply the mask on figmat
Finally, we can plot that result after masking, excluding the unwanted areas:
imagesc(result(any(result,2),:))
I calculated the distance between an image A1 and different images like image1,image2,image3 and image4 based on its hierarchicalCentroid. dist_1_1{ii} contains 4 values. I want to find the minimum value present in the dist_1_1{ii}.But I shows the value 1 and also i want to show the image which gives minimum value. Please help me. Thanks in advance
%% demo
clc,clear all,close all
plotFlag = 1;
depth = 6;
alef1 = im2bw(imread('C1.bmp')); %% Binary image
vec1 = hierarchicalCentroid(alef1,depth,plotFlag);
% subplot(1,3,1);
A=[];
vec2=[];
dist_1_1=[];
for ii=1:4
A{ii} = imread(['image' num2str(ii) '.bmp']);
% subplot(1,3,2);
vec2{ii} = hierarchicalCentroid(A{ii},depth,plotFlag);
%subplot(1,3,3);
%vec3 = hierarchicalCentroid(tav,depth,plotFlag);
% vec4=hierarchicalCentroid(A,depth,plotFlag);
% vec5=hierarchicalCentroid(A,depth,plotFlag);
dist_1_1{ii} = sum((vec1 - vec2{ii}) .^ 2);
[~,I] = min(dist_1_1{ii});
figure;
subplot(1,2,1);imshow(alef1);
subplot(1,2,2);imshow(A{I});
end
Considering that your images are named such as image1.png, image2.png,...
first, read and store the images in a cell
for ii=1:n
A{ii} = imread(['image' num2str(ii) '.png']);
end
Then compute the similarity between the image A1 and other images:
ind = computeSimilarity(A1,A); % here you compute the similarity and
(of course you would need a for-loop.)
After you have stored the values in the ind vector:
ind = [0.76,1.96,2.96];
Then find the index of a minimum value and choose the image accordingly
[~,I] = min(ind);
figure;
subplot(1,2,1);imshow(A1);
subplot(1,2,2);imshow(A{I});
What should be corrected in your code:
First of all, avoid using cell when it is not necessary and define it correctly when you using it. You cannot define a cell array like A=[]. You should do it like this: A=cell(2,3). For instance, for storing the vector of the descriptors you do not need a cell, just store them as a matrix, as I did.
Second of all when posting your code here, remove the unnecessary parts such as commented plots and commands.
And then, try to modify your code as follows, I might made some mistake about the dimensions, but you can get the main idea.
and also remember that you do not need to check each distance inside the loop. Calculate the vectors first and then find the distances in one step, as I did.
depth = 6;
alef1 = im2bw(imread('C1.bmp'));
vec1 = hierarchicalCentroid(alef1,depth,0);
A=cell(1,4);
vMatrix=zeros(4,length(vec1));
for ii=1:4
A{1,ii} = imread(['image' num2str(ii) '.bmp']);
vecMatrix(ii,:) = hierarchicalCentroid(A{1,ii},depth,0);
end
dist = sum((repmat(vec1,4,1) - vMatrix) .^ 2,2);
[~,I] = min(dist);
I am performing a whisker-tracking experiments. I have high-speed videos (500fps) of rats whisking against objects. In each such video I tracked the shape of the rat's snout and whiskers. Since tracking is noisy, the number of whiskers in each frame may be different (see 2 consecutive frames in attached image, notice the yellow false-positive whisker appearing in the left frame but not the right one).
See example 1:
As an end result of tracking, I get, for each frame, a varying number of variable-length vectors; each vector corresponding to a single whisker. At this point I would like to match the whiskers between frames. I have tried using Matlab's sample align to do this, but it works only somewhat properly. Its results are attached below (in attached image showing basepoint of all whiskers over 227 frames).
See example 2:
I would like to run some algorithm to cluster the whiskers correctly, such that each whisker is recognized as itself and separated from other over the course of many frames. In other words, I would like each slightly sinusoidal trajectory in the second image to be recognized as one trajectory. Whatever sorting algorithm I use should take into account that whiskers may disappear and reappear between consecutive frames. Unfortunately, I'm all out of ideas...
Any help?
Once again, keep in mind that for each point in attached image 2, I have many data points, since this is only a plot of whisker basepoint, while in actuality I have data for the entire whisker length.
This is how I would deal with the problem. Assuming that data vectors of different size are in a cell type called dataVectors, and knowing the number of whiskers (nSignals), I would try to extend the data to a second dimension derived from the original data and then perform k-means on two dimensions.
So, first I would get the maximum size of the vectors in order to convert the data to a matrix and do NaN-padding.
maxSize = -Inf;
for k = 1:nSignals
if length(dataVectors{k}.data) > maxSize
maxSize = length(dataVectors{k}.data);
end
end
Now, I would make the data 2D by elevating it to power of two (or three, your choice). This is just a very simple transformation. But you could alternatively use kernel methods here and project each vector against the rest; however, I don't think this is necessary, and if your data is really big, it could be inefficient. For now, raising the data to the power of two should do the trick. The result is stored in a second dimension.
projDegree = 2;
projData = zeros(nSignals, maxSize, 2).*NaN;
for k = 1:nSignals
vecSize = length(dataVectors{k}.data);
projData(k, 1:vecSize, 1) = dataVectors{k}.data;
projData(k, 1:vecSize, 2) = dataVectors{k}.data.*projDegree;
end
projData = reshape(projData, [], 2);
Here, projData will have in row 1 and column 1, the original data of the first whisker (or signal as I call it here), and column 2 will have the new dimension. Let's suppose that you have 8 whiskers in total, then, projData will have the data of the first whisker in row 1, 9, 17, and so on. The data of the second whisker in row 2, 10, 18, and so forth. That is important if you want to work your way back to the original data. Also, you can try with different projDegrees but I doubt it will make a lot of difference.
Now we perform k-means on the 2D data; however, we provide the initial points instead of letting it determine them with k-means++. The initial points, as I propose here, are the first data point of each vector for each whisker. In this manner, k-means will depart from there and will move to clusters means accordingly. We save the results in idxK.
idxK = kmeans(projData,nSignals, 'Start', projData(1:nSignals, :));
And there you have it. The variable idxK will tell you which data point belongs to what cluster.
Below is a working example of my proposed solution. The first part is simply trying to produce data that looks like your data, you can skip it.
rng(9, 'twister')
nSignals = 8; % number of whiskers
n = 1000; % number of data points
allData = zeros(nSignals, n); % all the data will be stored here
% this loop will just generate some data that looks like yours
for k = 1:nSignals
x = sort(rand(1,n));
nPeriods = round(rand*9)+1; % the sin can have between 1-10 periods
nShiftAmount = round(randn*30); % shift between ~ -100 to +100
y = sin(x*2*pi*nPeriods) + (randn(1,n).*0.5);
y = y + nShiftAmount;
allData(k, :) = y;
end
nanIdx = round(rand(1, round(n*0.05)*nSignals).*((n*nSignals)-1))+1;
allData(nanIdx) = NaN; % about 5% of the data is now missing
figure(1);
for k = 1:nSignals
nanIdx = ~isnan(allData(k, :));
dataVectors{k}.data = allData(k, nanIdx);
plot(dataVectors{k}.data, 'kx'), hold on;
end
% determine the max size
maxSize = -Inf;
for k = 1:nSignals
if length(dataVectors{k}.data) > maxSize
maxSize = length(dataVectors{k}.data);
end
end
% making the data now into two dimensions and NaN pad
projDegree = 2;
projData = zeros(nSignals, maxSize, 2).*NaN;
for k = 1:nSignals
vecSize = length(dataVectors{k}.data);
projData(k, 1:vecSize, 1) = dataVectors{k}.data;
projData(k, 1:vecSize, 2) = dataVectors{k}.data.*projDegree;
end
projData = reshape(projData, [], 2);
figure(2); plot(projData(:,1), projData(:,2), 'kx');
% run k-means using the first points of all measure as the initial points
idxK = kmeans(projData,nSignals, 'Start', projData(1:nSignals, :));
figure(3);
liColors = [{'yx'},{'mx'},{'cx'},{'bx'},{'kx'},{'gx'},{'rx'},{'gd'}];
for k = 1:nSignals
plot(projData(idxK==k,1), projData(idxK==k,2), liColors{k}), hold on;
end
% plot results on original data
figure(4);
for k = 1:nSignals
plot(projData(idxK==k,1), liColors{k}), hold on;
end
Let me know if this helps.
I've been performing a 2D mode filter on an RGB image by running medfilt2 independently on the R,G and B channels. However, splitting the RGB channels like this gives artifacts in the colouring. Is there a way to perform the 2D median filter while keeping RGB values 'together'?
Or, I could explain this more abstractly: Imagine I had a 2D matrix, where each value contained a pair of index coordinates (i.e. a cell matrix of 2X1 vectors). How would I go about performing a median filter on this?
Here's how I can do an independent mode filter (giving the artifacts):
r = colfilt(r0,[5 5],'sliding',#mode);
g = colfilt(g0,[5 5],'sliding',#mode);
b = colfilt(b0,[5 5],'sliding',#mode);
However colfilt won't work on a cell matrix.
Another approach could be to somehow combine my RGB channels into a single number and thus create a standard 2D matrix. Not sure how to implement this, though...
Any ideas?
Thanks for your help.
Cheers,
Hugh
EDIT:
OK, so problem solved. Here's how I did it.
I adapted my question so that I'm no longer dealing with (RGB) vectors, but (UV) vectors. Still essentially the same problem, except that my vectors are 2D not 3D.
So firstly I load the individual U and V channels, arrange them each into a 1D list, then combine them, so I essentially have a list of vectors. Then I reduce it to just those which are unique. Then, I assign each pixel in my matrix the value of the index of that unique vector. After this I can do the mode filter. Then I basically do the reverse, in that I go through the filtered image pixelwise, and read the value at each pixel (i.e. an index in my list), and find the unique vector associated with that index and insert it at that pixel.
% Create index list
img_u = img_iuv(:,:,2);
img_v = img_iuv(:,:,3);
coordlist = unique(cat(2,img_u(:),img_v(:)),'rows');
% Create a 2D matrix of indices
img_idx = zeros(size(img_iuv,1),size(img_iuv,2),2);
for y = 1:length(Y)
for x = 1:length(X)
coords = squeeze(img_iuv(x,y,2:3))';
[~,idx] = ismember(coords,coordlist,'rows');
img_idx(x,y) = idx;
end
end
% Apply the mode filter
img_idx = colfilt(img_idx,[n,n],'sliding',#mode);
% Re-construct the original image using the filtered data
for y = 1:length(Y)
for x = 1:length(X)
idx = img_idx(x,y);
try
coords = coordlist(idx,:);
end
img_iuv(x,y,2:3) = coords(:);
end
end
Not pretty but it gets the job done. I suppose this approach would also work for RGB images, or other similar situations.
Cheers,
Hugh
I don't see how you can define the median of a vector variable. You probably need to reduce the R,G,B components to a single value and then compunte the median on that value. Why not use the intensity level as that single value? You could do it easily with rgb2gray.
I have a 2D grid (G= 250x250) and just about 100 points of this is known and the rest is unknown (NaN). I want to resize this matrix. My problem is that imresize cannot do it for me in MATLAB, because it deletes the known values for me and just gives a NaN matrix.
Anyone know about a method that can do it for me? A suggestion is to use an interpolation method (e.g. by using inverse distance weighting), but I am not sure whether it works or not or even is there any better method?
G = NaN(250,250);
a = ceil(rand(1,50)*250*250);
b = ceil(rand(1,50)*250*250);
G (a) = 1; G (b) = 0;
How about this:
% find the non-NaN entries in G
idx = ~isnan(G);
% find their corresponding row/column indices
[i,j] = find(idx);
% resize your matrix as desired, i.e. scale the row/column indices
i = ceil(i*100/250);
j = ceil(j*100/250);
% write the old non-NaN entries to Gnew using accumarray
% you have to set the correct size of Gnew explicitly
% maximum value is chosen if many entries share the same scaled i/j indices
% NaNs are used as the fill
Gnew = accumarray([i, j], G(idx), [100 100], #max, NaN);
You can also choose a different accumulation function for accumarray if max is not suitable for you. And you can change the fill value from NaN to something else if it is not what you need.