I want to calculate p-value of my image comparison with ground truth image (reference image). So I find that we can calculate it from sensitivity and specificity value. Is it possible? Could you show me formula that apply for two images? Or any function in matlab?
p-values only make sense when you can model the statistical distribution of data.
In order to compute the p-value, first compute the c.d.f.:
https://en.wikipedia.org/wiki/Cumulative_distribution_function
If you cannot compute a c.d.f. for your problem (I am not aware of how one could compute c.d.f.s for images, don't ask me about this!), you won't be able to compute a p-value either.
Related
I have a question about multivariate kernel density in matlab, which is my first time using it.
I have a 3-dimensional sample data (x, y, z in axes) and want to find a probability of being in a certain volume using kernel density estimation. So, I used the mvksdensity function in matlab and got the probability density (estimated function values) for the points I decided.
What I originally wanted to do was to (if I could fine the function) triple integral the multivariate function for a given volume. But the mvksdensity function only returns the density estimates and does not return the function. I thought there will be an easy way to compute the probability from the density, but I’m stuck. Does anyone have any useful information for this? Thanks in advance.
I thought about fitdist function to find the distribution, but it only works for univariate kernel distribution.
I also tried to use mvncdf, which is a function that returns the cdf of the multivariate normal distribution for the row of the sample data after setting the mean and the std. But then I have to calculate the probability for a given volume for every normal distribution in each data point and then add it, which will be inefficient for a large amount of data and I don't know if it's a correct way.
I can suggest the following Monte-Carlo approach. You find a master volume that contains the entire mass of the estimated probability density. This should be as small as possible for the sake of efficiency. Then you generate a large number of test points in the master volume, either on a grid or randomly according to a uniform distribution. The probability content of a specific volume V can be estimated by the sum of the density values of the test points in V over the sum of the density values of all test points. I am afraid, however, that in 3D you would need at least 1E6 test points, probably more. If you give me access to your sample, I would be pleased to try out my suggestion. It should also be fairly easy to work out an estimate of the standard error of the estimated probability content of V.
I want to evaluate the grid quality where all coordinates differ in the real case.
Signal is of a ECG signal where average life-time is 75 years.
My task is to evaluate its age at the moment of measurement, which is an inverse problem.
I think 2D approximation of the 3D case is hard (done here by Abo-Zahhad) with with 3-leads (2 on chest and one at left leg - MIT-BIT arrhythmia database):
where f is a piecewise continuous function in R^2, \epsilon is the error matrix and A is a 2D matrix.
Now, I evaluate the average grid distance in x-axis (time) and average grid distance in y-axis (energy).
I think this can be done by Matlab's Image Analysis toolbox.
However, I am not sure how complete the toolbox's approaches are.
I think a transform approach must be used in the setting of uneven and noncontinuous grids. One approach is exact linear time euclidean distance transforms of grid line sampled shapes by Joakim Lindblad et all.
The method presents a distance transform (DT) which assigns to each image point its smallest distance to a selected subset of image points.
This kind of approach is often a basis of algorithms for many methods in image analysis.
I tested unsuccessfully the case with bwdist (Distance transform of binary image) with chessboard (returns empty square matrix), cityblock, euclidean and quasi-euclidean where the last three options return full matrix.
Another pseudocode
% https://stackoverflow.com/a/29956008/54964
%// retrieve picture
imgRGB = imread('dummy.png');
%// detect lines
imgHSV = rgb2hsv(imgRGB);
BW = (imgHSV(:,:,3) < 1);
BW = imclose(imclose(BW, strel('line',40,0)), strel('line',10,90));
%// clear those masked pixels by setting them to background white color
imgRGB2 = imgRGB;
imgRGB2(repmat(BW,[1 1 3])) = 255;
%// show extracted signal
imshow(imgRGB2)
where I think the approach will not work here because the grids are not necessarily continuous and not necessary ideal.
pdist based on the Lumbreras' answer
In the real examples, all coordinates differ such that pdist hamming and jaccard are always 1 with real data.
The options euclidean, cytoblock, minkowski, chebychev, mahalanobis, cosine, correlation, and spearman offer some descriptions of the data.
However, these options make me now little sense in such full matrices.
I want to estimate how long the signal can live.
Sources
J. Müller, and S. Siltanen. Linear and nonlinear inverse problems with practical applications.
EIT with the D-bar method: discontinuous heart-and-lungs phantom. http://wiki.helsinki.fi/display/mathstatHenkilokunta/EIT+with+the+D-bar+method%3A+discontinuous+heart-and-lungs+phantom Visited 29-Feb 2016.
There is a function in Matlab defined as pdist which computes the pairwisedistance between all row elements in a matrix and enables you to choose the type of distance you want to use (Euclidean, cityblock, correlation). Are you after something like this? Not sure I understood your question!
cheers!
Simply, do not do it in the post-processing. Those artifacts of the body can be about about raster images, about the viewer and/or ... Do quality assurance in the signal generation/processing step.
It is much easier to evaluate the original signal than its views.
How can we calculate the percentage of similarities between two pattern of Histogram?
For example, I have a histogram of template which I called HistA, and I have another histogram which is HistB where I want to check the similarities percentage of HistB with HistA.
I tried check out some of method such as histogram equalization, histogram matching but none of them works with my problem.
As image below, I create a multiple histogram between HistA and HistB. The value of the frequencies were actually value from a 1D data.
I saw the pattern of HistA and HistB almost the same, so I want to know how to calculate the percentage of the similarities of this two histogram.
Measure Bhattacharya co-efficient between the two normalized histograms and as
where N is the number of bins in the histograms.
Note the normalization.
For more information, see Bhattacharya distance|Wikipedia or On a measure of divergence between two statistical populations defined by their probability distributions.
Can someone explain to me the correlation function corr2 in MATLAB? I know that it is for 2D comparing similarities of objects, but in the equation I have doubts what it is A and B (probably matrices for comparison), and also Amn and Bmn.
I'm not sure how MATLAB executes this function, because I have found in several cases that the correlation is not executed for the entire image (matrix) but instead it divides the image into blocks and then compares blocks of one picture with blocks of another picture.
In MATLAB's documentation, the corr2 equation is not put as referral point to the way the equation itself is calculated, like in other functions in MATLAB's documentation, such as referring to what book it is taken from and where it is explained.
The correlation coefficient is a number representing the similarity between 2 images in relation with their respective pixel intensity.
As you pointed out this function is used to calculate this coefficient:
Here A and B are the images you are comparing, whereas the subscript indices m and n refer to the pixel location in the image. Basically what Matab does is to compute, for every pixel location in both images, the difference between the intensity value at that pixel and the mean intensity of the whole image, denoted as a letter with a straightline over it.
As Kostya pointed out, typing edit corr2 in the command window will show you the code used by Matlab to compute the correlation coefficient. The formula is basically this:
a = a - mean2(a);
b = b - mean2(b);
r = sum(sum(a.*b))/sqrt(sum(sum(a.*a))*sum(sum(b.*b)));
where:
a is the input image and b is the image you wish to compare to a.
If we break down the formula, we see that a - mean2(a) and b-mean2(b) are the elements in the numerator of the above equation. mean2(a) is equivalent to mean(mean(a)) or mean(a(:)), that is the mean intensity of the whole image. This is only calculated once.
The 3rd line of code calculates the coefficient. Here sum(sum(a.*b)) calculates the double-sum present in the formula element-wise, that is considering each pixel location separately. Be aware that using sum(a) calculates the sum in every column individually, hence in order to get a single value you need to apply sum twice.
That's pretty much the same happening in the denominator, however calculations are performed on a-mean2(a)^2 and b-mean2(b)^2. You can see this a some kind of normalization process in which you consider the pixel intensity difference among each individual image.
As for your last comment, you can break down an image into small blocks and calculate the correlation coefficient on them; that might save some time for very large images but since everything is vectorized the calculation is quite fast. It might be useful in distributed processing I guess. Of course the correlation coefficient between 2 blocks of images is not necessarily identical to that of the whole image.
For the sake of curiosity you can look at this paper which highlights some caveats in using the correlation coefficient for image comparison.
Hope that makes things a bit clearer!
I was given this task, I am a noob and need some pointers to get started with centroid calculation in Matlab:
Instead of an image first I was asked to simulate a Gaussian distribution(2 dimensional), add noise(random noise) and plot the intensities, now the position of the centroid changes due to noise and I need to bring it back to its original position by
-clipping level to get rid of the noise, noise reduction by clipping or smoothing, sliding average (lpf) (averaging filter 3-5 samples ), calculating the means or using Convolution filter kernel - which does matrix operations which represent the 2-D images
Since you are a noob, even if we wrote down the answer verbatim you probably won't understand how it works. So instead I'll do what you asked, give you pointers and you'll have to read the related documentation :
a) to produce a 2-d Gaussian use meshgrid or ndgrid
b) to add noise to the image look into rand ,randn or randi, depending what exactly you need.
c) to plot the intensities use imagesc
d) to find the centroid there are several ways, try to further search SO, you'll find many discussions. Also you can check TMW File exchange for different implementations for that.