What is the best method for finding impulse peaks (dirac delta) in a 2d matrix.
More specifically, I would like to find the harmonic frequencies of a given image and so I need to find impulse peaks in the image absolute value DFT.
I thought of using findpeaks but there's no 2d version. I also saw earlier posts regarding finding ordinary peaks using imdilate and/or imextendedmax but those find all the peaks in a 2d matrix whereas I am only interested in impulse peaks. I am sure DSP people have a common recipe for this...
Please Help,
Thanks
What you want to do is find peaks with high contrast. Thus, you need a way to identify local maxima, plus a way to measure the difference between the peak and the surrounding values. Thresholding on this difference will identify the impulse peaks for you.
Assuming your input signal is called signal
%# dilate to find, for every pixel, the maximum of its neighbors
dilationMask = ones(3);
dilationMask(5) = 0;
dilSignal = imdilate(signal, dilationMask);
%# find all peaks
%# peaks = signal > dilSignal;
%# find large peaks peaks by thresholding, i.e. you accept a peak only
%# if it's more than 'threshold' higher than its neighbors
peaks = (signal - dilSignal) > threshold;
peaks is a logical array with 1's wherever there is a good peak. You can use it to read peak heights from signal with signal(peaks), and to find coordinates using find(peaks).
This paper I wrote contains Matlab source code for fast local peak detection in 2D. It works similar to imregionalmax() in Mathworks Image Processing Toolbox but allows you to specify a local neighborhood radius: bigger radius -> sparser peaks.
Since you expect sparse impulses, the nonmaxsupp_scanline() function may be suitable for you.
The findpeaks algorithm is pretty trivial; if an element is bigger than both its neighbours, then it is a peak. Writing a 2D version of this should be pretty simple.
Related
I have a signal 's' of voice of which you can see an extract here:
I would like to plot the zero crossing points in the same graph. I have tried with the following code:
zci = #(v) find(v(:).*circshift(v(:), [-1 0]) <= 0); % Returns Zero-Crossing Indices Of Argument Vector
zx = zci(s);
figure
set(gcf,'color','w')
plot(t,s)
hold on
plot(t(zx),s(zx),'o')
But it does not interpole the points in which the sign change, so the result is:
However, I'd like that the highlighted points were as near as possible to zero.
I hope someone can help me. Thanks you for your responses in advanced.
Try this?
w = 1;
crossPts=[];
for k=1:(length(s)-1)
if (s(k)*s(k+1)<0)
crossPts(w) = (t(k)+t(k+1))/2;
w = w + 1;
end
end
figure
set(gcf,'color','w')
plot(t,s)
hold on
plot(t, s)
plot(crossPts, zeros(length(crossPts)), 'o')
Important questions: what is the highest frequency conponent of the signal you are measuring? Can you remeasure this signal? What is your sampling rate? What is this analysis for? (Schoolwork or scholarly research). You may have quite a bit of trouble measuring the zeros of this function with any significance or accurracy because it looks like your waveform has a frequency greater than half of your sampling rate (greater than your Nyquist frequency). Upsampling/interpolating your entire waveform will allow you to find the zeros much more precisely (but with no greater degree of accurracy) but this is a huge no-no in the scientific community. While my method may not look super pretty, it's the most accurate method that doesn't make unsafe assumptions. If you just want it to look pretty, I would recommend interp1 and using the 'Spline' method. You can interpolate the whole waveform and then use the above answer to find more accurate zeros.
Also, you could calculate the zeros on the interpolated waveform and then display it on the raw data.
A remotely possible solution to improve your data;
If you're measuring a human voice, why not try filtering at the range of human speech? This should be fine mathematically and could possibly improve your waveform.
I want to test under Matlab an algorithm for essential matrix estimation within ransac framework. The inputs are sift correspondances and several Ransac iterations are performed to select inliers from outliers (false correspondances).
I want to test the efficiency of the algorithm with different levels of noise.
should I only introduce mismatch to certain number of correspondances randomly? alternatively How to add noise to sift correspondances (formula)?
The simplest way is to take the set of key-points for all frames (the pixel coordinates of the features) and add Gaussian noise to their position for both x,y.
For example, if you have a matrix of key-points p of size nx2
noisy_p = p + sigma * randn(n,2);
where sigma is the standard deviation of noise you want to experiment with. Using a value of 1/2 or 1 gives typical noise you get on real-world images.
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.
I was studying for a signals & systems project and I have come across this code on high and low pass filters for an audio signal on the internet. Now I have tested this code and it works but I really don't understand how it is doing the low/high pass action.
The logic is that a sound is read into MATLAB by using the audioread or wavread function and the audio is stored as an nx2 matrix. The n depends on the sampling rate and the 2 columns are due to the 2 sterio channels.
Now here is the code for the low pass;
[hootie,fs]=wavread('hootie.wav'); % loads Hootie
out=hootie;
for n=2:length(hootie)
out(n,1)=.9*out(n-1,1)+hootie(n,1); % left
out(n,2)=.9*out(n-1,2)+hootie(n,2); % right
end
And this is for the high pass;
out=hootie;
for n=2:length(hootie)
out(n,1)=hootie(n,1)-hootie(n-1,1); % left
out(n,2)=hootie(n,2)-hootie(n-1,2); % right
end
I would really like to know how this produces the filtering effect since this is making no sense to me yet it works. Also shouldn't there be any cutoff points in these filters ?
The frequency response for a filter can be roughly estimated using a pole-zero plot. How this works can be found on the internet, for example in this link. The filter can be for example be a so called Finite Impulse Response (FIR) filter, or an Infinite Impulse Response (IIR) filter. The FIR-filters properties is determined only from the input signal (no feedback, open loop), while the IIR-filter uses the previous signal output to control the current signal output (feedback loop or closed loop). The general equation can be written like,
a_0*y(n)+a_1*y(n-1)+... = b_0*x(n)+ b_1*x(n-1)+...
Applying the discrete fourier transform you may define a filter H(z) = X(z)/Y(Z) using the fact that it is possible to define a filter H(z) so that Y(Z)=H(Z)*X(Z). Note that I skip a lot of steps here to cut down this text to proper length.
The point of the discussion is that these discrete poles can be mapped in a pole-zero plot. The pole-zero plot for digital filters plots the poles and zeros in a diagram where the normalized frequencies, relative to the sampling frequencies are illustrated by the unit circle, where fs/2 is located at 180 degrees( eg. a frequency fs/8 will be defined as the polar coordinate (r, phi)=(1,pi/4) ). The "zeros" are then the nominator polynom A(z) and the poles are defined by the denominator polynom B(z). A frequency close to a zero will have an attenuation at that frequency. A frequency close to a pole will instead have a high amplifictation at that frequency instead. Further, frequencies far from a pole is attenuated and frequencies far from a zero is amplified.
For your highpass filter you have a polynom,
y(n)=x(n)-x(n-1),
for each channel. This is transformed and it is possble to create a filter,
H(z) = 1 - z^(-1)
For your lowpass filter the equation instead looks like this,
y(n) - y(n-1) = x(n),
which becomes the filter
H(z) = 1/( 1-0.9*z^(-1) ).
Placing these filters in the pole-zero plot you will have the zero in the highpass filter on the positive x-axis. This means that you will have high attenuation for low frequencies and high amplification for high frequencies. The pole in the lowpass filter will also be loccated on the positive x-axis and will thus amplify low frequencies and attenuate high frequencies.
This description is best illustrated with images, which is why I recommend you to follow my links. Good luck and please comment ask if anything is unclear.
I am looking at some FFT code in a matlab project and the FFT and inverse FFT is computed this way:
% Here image is a 2D image.
image_fft = fftshift(image,1);
image_fft = fftshift(image_fft,2);
image_fft = fft(image_fft,[],1);
image_fft = fft(image_fft,[],2);
image_fft = fftshift(image_fft,1);
image_fft = fftshift(image_fft,2);
% Some processing and then same sequence of fftshift, ifft and fftshift to move to
% time domain
I tried to find some information online but am having trouble wondering why the fftshift needs to be done before computing the FFT.
Another question I have is whether this is something really Matlab specific. For example, I am planning to port this code to C++ and use KISS FFT. Do I need to be vary of this?
The reason why people like to swap prior to the DFT is because it makes the center pixel of the image the one with zero-phase shift. It often makes algorithms that depend on phase easier to think about and implement. It is not matlab specific and if you want to port an exact version of the code to another language, you'll need to perform the quadswap beforehand too.
EDIT:
Let me give an example that I hope will clear things up. Let's say that our image is the sum of a bunch of sinc functions with varying locations throughout the image. In the frequency domain, each of these sinc functions is a rect function with the same amplitude but with a different linear phase component that determines the location of the sinc in the image domain. By swapping the image prior to taking the DFT, we make the linear phase component of the frequency domain representation of the center pixel be zero. Moreover, the linear phase components of the other sinc functions will now be a function of their distance from the center pixel. If we didn't swap the image beforehand, then the linear phase components of the rect functions would be a function of their distance from the pixel in the top-left of the image. This would be non-intutive and would involve the same kind of phase wrapping considerations that one sees with equating the frequencies in the range (pi,2pi) rad/sample with more the intuitive (-pi,0) rad/sample.
For images, it's better to use fft2. It's matlab's convention to arrange 2D ffts with the DC in the corners. Presumably because of the row/array conventions. fftshift allows for a more intuitive display of the FFT with the DC in the center.
I don't fully understand what the piece of code you copied is about, here is an example of fft and inverse fft of an image using matlab.
And a more detailed tutorial here.