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I am trying to create a program in GNU Octave to draw a histogram showing the fundamental and harmonics of a modified sinewave (the output from an SCR dimmer, which consists of a sinewave which is at zero until part way through the wave).
I've been able to generate the waveform and perform FFT to get a set of Frequency vs Amplitude points, however I am not sure how to convert this data into bins suitable for generating a histogram.
Sample code and an image of what I'm after below - thanks for the help!
clear();
vrms = 120;
freq = 60;
nCycles = 2;
level = 25;
vpeak = sqrt(2) * vrms;
sampleinterval = 0.00001;
num_harmonics = 10
disp("Start");
% Draw the waveform
x = 0 : sampleinterval : nCycles * 1 / freq; % time in sampleinterval increments
dimmed_wave = [];
undimmed_wave = [];
for i = 1 : columns(x)
rad_value = x(i) * 2 * pi * freq;
off_time = mod(rad_value, pi);
on_time = pi*(100-level)/100;
if (off_time < on_time)
dimmed_wave = [dimmed_wave, 0]; % in the dimmed period, value is zero
else
dimmed_wave = [dimmed_wave, sin(rad_value)]; % when not dimmed, value = sine
endif
undimmed_wave = [undimmed_wave, sin(rad_value)];
endfor
y = dimmed_wave * vpeak; % calculate instantaneous voltage
undimmed = undimmed_wave * vpeak;
subplot(2,1,1)
plot(x*1000, y, '-', x*1000, undimmed, '--');
xlabel ("Time (ms)");
ylabel ("Voltage");
% Fourier Transform to determine harmonics
subplot(2,1,2)
N = length(dimmed_wave); % number of points
fft_vals = abs(fftshift(fft(dimmed_wave))); % perform fft
frequency = [ -(ceil((N-1)/2):-1:1) ,0 ,(1:floor((N-1)/2)) ] * 1 / (N *sampleinterval);
plot(frequency, fft_vals);
axis([0,400]);
xlabel ("Frequency");
ylabel ("Amplitude");
You know your base frequency (fundamental tone), let's call it F. 2*F is the second harmonic, 3*F the third, etc. You want to set histogram bin edges halfway between these: 1.5*F, 2.5*F, etc.
You have two periods in your input signal, therefore your (integer) base frequency is k=2 (the value at fft_vals[k+1], the first peak in your plot). The second harmonic is at k=4, the third one at k=6, etc.
So you would set your bins edges at k = 1:2:end.
In general, this would be k = nCycles/2:nCycles:end.
You can compute your bar graph according to our computed bin edges as follows:
fft_vals = abs(fft(dimmed_wave));
nHarmonics = 9;
edges = nCycles/2 + (0:nHarmonics)*nCycles;
H = cumsum(fft_vals);
H = diff(H(edges));
bar(1:nHarmonics,H);
I want to train svm on data set consisting of features p1, p2 , p3 . p1 is vector , p2 and p3 are integers on which i want to train . For e.g p1=[1,2,3], p2=4 , p3=5
X=[p1 , p2 , p3],but p1 itself is a vector, so X=[ [ 1 , 2 , 3 ], 4 , 5 ] and Y is output named label
but X can't take input in this form
clf.fit(X,Y)
It gives error of form below: meaning X cannot take in this form
array = np.array(array, dtype=dtype, order=order, copy=copy)
ValueError: setting an array element with a sequence.
You basically have two options:
Convert your data to regular format and run typical SVM kernel, in your case if p1 is always 3-element, just flatten representation thus [[1,2,3],4,5] becomes [1,2,3,4,5] and you are good to go.
Implement your own custom kernel function, that treats each part separately, since sum of two kernels is still a kernel, you can for example define K(x, y) = K([p1, p2, p3], [q1, q2, q3]) := K1(p1, q1) + K2([p2,p3], [q2,q3]). Now both K1 and K2 work on regular vectors, so you can define them in arbitrary manner and just use their sum as your "joint" kernel function. This approach is more complex, but gives you much freedom in how you define the way of dealing with your complex data.
Here is a simple example
#include <opencv2/ml.hpp>
using namespace cv::ml;
// Set up training data
int labels[4] = { -1, -1, 1, 1}; //Negative and Positive class
Mat labelsMat(4, 1, CV_32SC1, labels);
//training data inputs
float a1 = 1, a2 = 2; //negative
float b1 = 2, b2 = 1; //negative
float c1 = 3, c2 = 4; //positive
float d1 = 4, d2 = 3; //positive
float trainingData[4][2] = {{ a1, a2 },{ b1, b2 },{ c1, c2 },{ d1, d2 };
Mat trainingDataMat(20, 2, CV_32FC1, trainingData);
// Set up SVM's parameters
Ptr<SVM> svm = SVM::create();
svm->setType(SVM::C_SVC);
svm->setKernel(SVM::RBF);
svm->setC(10);
svm->setGamma(0.01);
svm->setTermCriteria(TermCriteria(TermCriteria::MAX_ITER, 500, 1e-6));
// Train the SVM with given parameters
Ptr<TrainData> td = TrainData::create(trainingDataMat, ROW_SAMPLE, labelsMat);
svm->train(td);
To test
float t1 = 2, t2 = 2;
float testing[1][2] = { { t1,t2 } };
Mat testData(1, 2, CV_32FC1, testing);
Mat results;
svm->predict(testData, results);
Mat vec[2];
results.copyTo(vec[0]);
for (int i = 0; i < 2; i++)
{
cout << vec[i] << endl;
}
My goal is to create program on octave that loads audio file (wav, flac), calculates its mfcc features and serve them as output. The problem is that I do not have much experience with octave and cannot get octave load the audio file and that is why I am not sure if the extraction algorithms is correct. Is there simple way of loading the file and getting its features?
You can run mfcc code from RASTAMAT in octave, you only need to fix few things, the fixed version is available for download here.
The changes are to properly set windows in powspec.m
WINDOW = hanning(winpts);
and to fix the bug in specgram function which is not compatible with Matlab.
Check out Octave functions for calculating MFCC at https://github.com/jagdish7908/mfcc-octave
For a detailed theory on steps to compute MFCC, refer http://practicalcryptography.com/miscellaneous/machine-learning/guide-mel-frequency-cepstral-coefficients-mfccs/
function frame = create_frames(y, Fs, Fsize, Fstep)
N = length(y);
% divide the signal into frames with overlap = framestep
samplesPerFrame = floor(Fs*Fsize);
samplesPerFramestep = floor(Fs*Fstep);
i = 1;
frame = [];
while(i <= N-samplesPerFrame)
frame = [frame y(i:(i+samplesPerFrame-1))];
i = i+samplesPerFramestep;
endwhile
return
endfunction
function ans = hz2mel(f)
ans = 1125*log(1+f/700);
return
endfunction
function ans = mel2hz(f)
ans = 700*(exp(f/1125) - 1);
return
endfunction
function bank = melbank(n, min, max, sr)
% n = number of banks
% min = min frequency in hertz
% max = max frequency in hertz
% convert the min and max freq in mel scale
NFFT = 512;
% figure out bin value of min and max freq
minBin = floor((NFFT)*min/(sr/2));
maxBin = floor((NFFT)*max/(sr/2));
% convert the min, max in mel scale
min_mel = hz2mel(min);
max_mel = hz2mel(max);
m = [min_mel:(max_mel-min_mel)/(n+2-1):max_mel];
%disp(m);
h = mel2hz(m);
% replace frequencies in h with thier respective bin values
fbin = floor((NFFT)*h/(sr/2));
%disp(h);
% create triangular melfilter vectors
H = zeros(NFFT,n);
for vect = 2:n+1
for k = minBin:maxBin
if k >= fbin(vect-1) && k <= fbin(vect)
H(k,vect) = (k-fbin(vect-1))/(fbin(vect)-fbin(vect-1));
elseif k >= fbin(vect) && k <= fbin(vect+1)
H(k,vect) = (fbin(vect+1) - k)/(fbin(vect+1)-fbin(vect));
endif
endfor
endfor
bank = H;
return
endfunction
clc;
clear all;
close all;
pkg load signal;
% record audio
Fs = 44100;
y = record(3,44100);
% OR %
% Load existing file
%[y, Fs] = wavread('../FILE_PATH/');
%y = y(44100:2*44100);
% create mel filterbanks
minFreq = 500; % minimum cutoff frequency in Hz
maxFreq = 10000; % maximum cutoff frequency in Hz
% melbank(number_of_banks, minFreq, mazFreq, sampling_rate)
foo = melbank(30,minFreq,maxFreq,Fs);
% create frames
frames = create_frames(y, Fs, 0.025, 0.010);
% calculate periodogram of each frame
NF = length(frames(1,:));
[P,F] = periodogram(frames(:,1),[], 1024, Fs);
% apply mel filters to the power spectra
P = foo.*P(1:512);
% sum the energy in each filter and take the logarithm
P = log(sum(P));
% take the DCT of the log filterbank energies
% discard the first coeff 'cause it'll be -Inf after taking log
L = length(P);
P = dct(P(2:L));
PXX = P;
for i = 2:NF
P = periodogram(frames(:,i),[], 1024, Fs);
% apply mel filters to the power spectra
P = foo.*P(1:512);
% sum the energy in each filter and take the logarithm
P = log(sum(P));
% take the DCT of the log filterbank energies
% discard the first coeff 'cause it'll be -Inf after taking log
P = dct(P(2:L));
% coeffients are stacked row wise for each frame
PXX = [PXX; P];
endfor
% stack the coeffients column wise
PXX = PXX';
plot(PXX);
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I was wondering if there is a way to determine if an image is blurry or not by analyzing the image data.
Another very simple way to estimate the sharpness of an image is to use a Laplace (or LoG) filter and simply pick the maximum value. Using a robust measure like a 99.9% quantile is probably better if you expect noise (i.e. picking the Nth-highest contrast instead of the highest contrast.) If you expect varying image brightness, you should also include a preprocessing step to normalize image brightness/contrast (e.g. histogram equalization).
I've implemented Simon's suggestion and this one in Mathematica, and tried it on a few test images:
The first test blurs the test images using a Gaussian filter with a varying kernel size, then calculates the FFT of the blurred image and takes the average of the 90% highest frequencies:
testFft[img_] := Table[
(
blurred = GaussianFilter[img, r];
fft = Fourier[ImageData[blurred]];
{w, h} = Dimensions[fft];
windowSize = Round[w/2.1];
Mean[Flatten[(Abs[
fft[[w/2 - windowSize ;; w/2 + windowSize,
h/2 - windowSize ;; h/2 + windowSize]]])]]
), {r, 0, 10, 0.5}]
Result in a logarithmic plot:
The 5 lines represent the 5 test images, the X axis represents the Gaussian filter radius. The graphs are decreasing, so the FFT is a good measure for sharpness.
This is the code for the "highest LoG" blurriness estimator: It simply applies an LoG filter and returns the brightest pixel in the filter result:
testLaplacian[img_] := Table[
(
blurred = GaussianFilter[img, r];
Max[Flatten[ImageData[LaplacianGaussianFilter[blurred, 1]]]];
), {r, 0, 10, 0.5}]
Result in a logarithmic plot:
The spread for the un-blurred images is a little better here (2.5 vs 3.3), mainly because this method only uses the strongest contrast in the image, while the FFT is essentially a mean over the whole image. The functions are also decreasing faster, so it might be easier to set a "blurry" threshold.
Yes, it is. Compute the Fast Fourier Transform and analyse the result. The Fourier transform tells you which frequencies are present in the image. If there is a low amount of high frequencies, then the image is blurry.
Defining the terms 'low' and 'high' is up to you.
Edit:
As stated in the comments, if you want a single float representing the blurryness of a given image, you have to work out a suitable metric.
nikie's answer provide such a metric. Convolve the image with a Laplacian kernel:
1
1 -4 1
1
And use a robust maximum metric on the output to get a number which you can use for thresholding. Try to avoid smoothing too much the images before computing the Laplacian, because you will only find out that a smoothed image is indeed blurry :-).
During some work with an auto-focus lens, I came across this very useful set of algorithms for detecting image focus. It's implemented in MATLAB, but most of the functions are quite easy to port to OpenCV with filter2D.
It's basically a survey implementation of many focus measurement algorithms. If you want to read the original papers, references to the authors of the algorithms are provided in the code. The 2012 paper by Pertuz, et al. Analysis of focus measure operators for shape from focus (SFF) gives a great review of all of these measure as well as their performance (both in terms of speed and accuracy as applied to SFF).
EDIT: Added MATLAB code just in case the link dies.
function FM = fmeasure(Image, Measure, ROI)
%This function measures the relative degree of focus of
%an image. It may be invoked as:
%
% FM = fmeasure(Image, Method, ROI)
%
%Where
% Image, is a grayscale image and FM is the computed
% focus value.
% Method, is the focus measure algorithm as a string.
% see 'operators.txt' for a list of focus
% measure methods.
% ROI, Image ROI as a rectangle [xo yo width heigth].
% if an empty argument is passed, the whole
% image is processed.
%
% Said Pertuz
% Abr/2010
if ~isempty(ROI)
Image = imcrop(Image, ROI);
end
WSize = 15; % Size of local window (only some operators)
switch upper(Measure)
case 'ACMO' % Absolute Central Moment (Shirvaikar2004)
if ~isinteger(Image), Image = im2uint8(Image);
end
FM = AcMomentum(Image);
case 'BREN' % Brenner's (Santos97)
[M N] = size(Image);
DH = Image;
DV = Image;
DH(1:M-2,:) = diff(Image,2,1);
DV(:,1:N-2) = diff(Image,2,2);
FM = max(DH, DV);
FM = FM.^2;
FM = mean2(FM);
case 'CONT' % Image contrast (Nanda2001)
ImContrast = inline('sum(abs(x(:)-x(5)))');
FM = nlfilter(Image, [3 3], ImContrast);
FM = mean2(FM);
case 'CURV' % Image Curvature (Helmli2001)
if ~isinteger(Image), Image = im2uint8(Image);
end
M1 = [-1 0 1;-1 0 1;-1 0 1];
M2 = [1 0 1;1 0 1;1 0 1];
P0 = imfilter(Image, M1, 'replicate', 'conv')/6;
P1 = imfilter(Image, M1', 'replicate', 'conv')/6;
P2 = 3*imfilter(Image, M2, 'replicate', 'conv')/10 ...
-imfilter(Image, M2', 'replicate', 'conv')/5;
P3 = -imfilter(Image, M2, 'replicate', 'conv')/5 ...
+3*imfilter(Image, M2, 'replicate', 'conv')/10;
FM = abs(P0) + abs(P1) + abs(P2) + abs(P3);
FM = mean2(FM);
case 'DCTE' % DCT energy ratio (Shen2006)
FM = nlfilter(Image, [8 8], #DctRatio);
FM = mean2(FM);
case 'DCTR' % DCT reduced energy ratio (Lee2009)
FM = nlfilter(Image, [8 8], #ReRatio);
FM = mean2(FM);
case 'GDER' % Gaussian derivative (Geusebroek2000)
N = floor(WSize/2);
sig = N/2.5;
[x,y] = meshgrid(-N:N, -N:N);
G = exp(-(x.^2+y.^2)/(2*sig^2))/(2*pi*sig);
Gx = -x.*G/(sig^2);Gx = Gx/sum(Gx(:));
Gy = -y.*G/(sig^2);Gy = Gy/sum(Gy(:));
Rx = imfilter(double(Image), Gx, 'conv', 'replicate');
Ry = imfilter(double(Image), Gy, 'conv', 'replicate');
FM = Rx.^2+Ry.^2;
FM = mean2(FM);
case 'GLVA' % Graylevel variance (Krotkov86)
FM = std2(Image);
case 'GLLV' %Graylevel local variance (Pech2000)
LVar = stdfilt(Image, ones(WSize,WSize)).^2;
FM = std2(LVar)^2;
case 'GLVN' % Normalized GLV (Santos97)
FM = std2(Image)^2/mean2(Image);
case 'GRAE' % Energy of gradient (Subbarao92a)
Ix = Image;
Iy = Image;
Iy(1:end-1,:) = diff(Image, 1, 1);
Ix(:,1:end-1) = diff(Image, 1, 2);
FM = Ix.^2 + Iy.^2;
FM = mean2(FM);
case 'GRAT' % Thresholded gradient (Snatos97)
Th = 0; %Threshold
Ix = Image;
Iy = Image;
Iy(1:end-1,:) = diff(Image, 1, 1);
Ix(:,1:end-1) = diff(Image, 1, 2);
FM = max(abs(Ix), abs(Iy));
FM(FM<Th)=0;
FM = sum(FM(:))/sum(sum(FM~=0));
case 'GRAS' % Squared gradient (Eskicioglu95)
Ix = diff(Image, 1, 2);
FM = Ix.^2;
FM = mean2(FM);
case 'HELM' %Helmli's mean method (Helmli2001)
MEANF = fspecial('average',[WSize WSize]);
U = imfilter(Image, MEANF, 'replicate');
R1 = U./Image;
R1(Image==0)=1;
index = (U>Image);
FM = 1./R1;
FM(index) = R1(index);
FM = mean2(FM);
case 'HISE' % Histogram entropy (Krotkov86)
FM = entropy(Image);
case 'HISR' % Histogram range (Firestone91)
FM = max(Image(:))-min(Image(:));
case 'LAPE' % Energy of laplacian (Subbarao92a)
LAP = fspecial('laplacian');
FM = imfilter(Image, LAP, 'replicate', 'conv');
FM = mean2(FM.^2);
case 'LAPM' % Modified Laplacian (Nayar89)
M = [-1 2 -1];
Lx = imfilter(Image, M, 'replicate', 'conv');
Ly = imfilter(Image, M', 'replicate', 'conv');
FM = abs(Lx) + abs(Ly);
FM = mean2(FM);
case 'LAPV' % Variance of laplacian (Pech2000)
LAP = fspecial('laplacian');
ILAP = imfilter(Image, LAP, 'replicate', 'conv');
FM = std2(ILAP)^2;
case 'LAPD' % Diagonal laplacian (Thelen2009)
M1 = [-1 2 -1];
M2 = [0 0 -1;0 2 0;-1 0 0]/sqrt(2);
M3 = [-1 0 0;0 2 0;0 0 -1]/sqrt(2);
F1 = imfilter(Image, M1, 'replicate', 'conv');
F2 = imfilter(Image, M2, 'replicate', 'conv');
F3 = imfilter(Image, M3, 'replicate', 'conv');
F4 = imfilter(Image, M1', 'replicate', 'conv');
FM = abs(F1) + abs(F2) + abs(F3) + abs(F4);
FM = mean2(FM);
case 'SFIL' %Steerable filters (Minhas2009)
% Angles = [0 45 90 135 180 225 270 315];
N = floor(WSize/2);
sig = N/2.5;
[x,y] = meshgrid(-N:N, -N:N);
G = exp(-(x.^2+y.^2)/(2*sig^2))/(2*pi*sig);
Gx = -x.*G/(sig^2);Gx = Gx/sum(Gx(:));
Gy = -y.*G/(sig^2);Gy = Gy/sum(Gy(:));
R(:,:,1) = imfilter(double(Image), Gx, 'conv', 'replicate');
R(:,:,2) = imfilter(double(Image), Gy, 'conv', 'replicate');
R(:,:,3) = cosd(45)*R(:,:,1)+sind(45)*R(:,:,2);
R(:,:,4) = cosd(135)*R(:,:,1)+sind(135)*R(:,:,2);
R(:,:,5) = cosd(180)*R(:,:,1)+sind(180)*R(:,:,2);
R(:,:,6) = cosd(225)*R(:,:,1)+sind(225)*R(:,:,2);
R(:,:,7) = cosd(270)*R(:,:,1)+sind(270)*R(:,:,2);
R(:,:,7) = cosd(315)*R(:,:,1)+sind(315)*R(:,:,2);
FM = max(R,[],3);
FM = mean2(FM);
case 'SFRQ' % Spatial frequency (Eskicioglu95)
Ix = Image;
Iy = Image;
Ix(:,1:end-1) = diff(Image, 1, 2);
Iy(1:end-1,:) = diff(Image, 1, 1);
FM = mean2(sqrt(double(Iy.^2+Ix.^2)));
case 'TENG'% Tenengrad (Krotkov86)
Sx = fspecial('sobel');
Gx = imfilter(double(Image), Sx, 'replicate', 'conv');
Gy = imfilter(double(Image), Sx', 'replicate', 'conv');
FM = Gx.^2 + Gy.^2;
FM = mean2(FM);
case 'TENV' % Tenengrad variance (Pech2000)
Sx = fspecial('sobel');
Gx = imfilter(double(Image), Sx, 'replicate', 'conv');
Gy = imfilter(double(Image), Sx', 'replicate', 'conv');
G = Gx.^2 + Gy.^2;
FM = std2(G)^2;
case 'VOLA' % Vollath's correlation (Santos97)
Image = double(Image);
I1 = Image; I1(1:end-1,:) = Image(2:end,:);
I2 = Image; I2(1:end-2,:) = Image(3:end,:);
Image = Image.*(I1-I2);
FM = mean2(Image);
case 'WAVS' %Sum of Wavelet coeffs (Yang2003)
[C,S] = wavedec2(Image, 1, 'db6');
H = wrcoef2('h', C, S, 'db6', 1);
V = wrcoef2('v', C, S, 'db6', 1);
D = wrcoef2('d', C, S, 'db6', 1);
FM = abs(H) + abs(V) + abs(D);
FM = mean2(FM);
case 'WAVV' %Variance of Wav...(Yang2003)
[C,S] = wavedec2(Image, 1, 'db6');
H = abs(wrcoef2('h', C, S, 'db6', 1));
V = abs(wrcoef2('v', C, S, 'db6', 1));
D = abs(wrcoef2('d', C, S, 'db6', 1));
FM = std2(H)^2+std2(V)+std2(D);
case 'WAVR'
[C,S] = wavedec2(Image, 3, 'db6');
H = abs(wrcoef2('h', C, S, 'db6', 1));
V = abs(wrcoef2('v', C, S, 'db6', 1));
D = abs(wrcoef2('d', C, S, 'db6', 1));
A1 = abs(wrcoef2('a', C, S, 'db6', 1));
A2 = abs(wrcoef2('a', C, S, 'db6', 2));
A3 = abs(wrcoef2('a', C, S, 'db6', 3));
A = A1 + A2 + A3;
WH = H.^2 + V.^2 + D.^2;
WH = mean2(WH);
WL = mean2(A);
FM = WH/WL;
otherwise
error('Unknown measure %s',upper(Measure))
end
end
%************************************************************************
function fm = AcMomentum(Image)
[M N] = size(Image);
Hist = imhist(Image)/(M*N);
Hist = abs((0:255)-255*mean2(Image))'.*Hist;
fm = sum(Hist);
end
%******************************************************************
function fm = DctRatio(M)
MT = dct2(M).^2;
fm = (sum(MT(:))-MT(1,1))/MT(1,1);
end
%************************************************************************
function fm = ReRatio(M)
M = dct2(M);
fm = (M(1,2)^2+M(1,3)^2+M(2,1)^2+M(2,2)^2+M(3,1)^2)/(M(1,1)^2);
end
%******************************************************************
A few examples of OpenCV versions:
// OpenCV port of 'LAPM' algorithm (Nayar89)
double modifiedLaplacian(const cv::Mat& src)
{
cv::Mat M = (Mat_<double>(3, 1) << -1, 2, -1);
cv::Mat G = cv::getGaussianKernel(3, -1, CV_64F);
cv::Mat Lx;
cv::sepFilter2D(src, Lx, CV_64F, M, G);
cv::Mat Ly;
cv::sepFilter2D(src, Ly, CV_64F, G, M);
cv::Mat FM = cv::abs(Lx) + cv::abs(Ly);
double focusMeasure = cv::mean(FM).val[0];
return focusMeasure;
}
// OpenCV port of 'LAPV' algorithm (Pech2000)
double varianceOfLaplacian(const cv::Mat& src)
{
cv::Mat lap;
cv::Laplacian(src, lap, CV_64F);
cv::Scalar mu, sigma;
cv::meanStdDev(lap, mu, sigma);
double focusMeasure = sigma.val[0]*sigma.val[0];
return focusMeasure;
}
// OpenCV port of 'TENG' algorithm (Krotkov86)
double tenengrad(const cv::Mat& src, int ksize)
{
cv::Mat Gx, Gy;
cv::Sobel(src, Gx, CV_64F, 1, 0, ksize);
cv::Sobel(src, Gy, CV_64F, 0, 1, ksize);
cv::Mat FM = Gx.mul(Gx) + Gy.mul(Gy);
double focusMeasure = cv::mean(FM).val[0];
return focusMeasure;
}
// OpenCV port of 'GLVN' algorithm (Santos97)
double normalizedGraylevelVariance(const cv::Mat& src)
{
cv::Scalar mu, sigma;
cv::meanStdDev(src, mu, sigma);
double focusMeasure = (sigma.val[0]*sigma.val[0]) / mu.val[0];
return focusMeasure;
}
No guarantees on whether or not these measures are the best choice for your problem, but if you track down the papers associated with these measures, they may give you more insight. Hope you find the code useful! I know I did.
Building off of Nike's answer. Its straightforward to implement the laplacian based method with opencv:
short GetSharpness(char* data, unsigned int width, unsigned int height)
{
// assumes that your image is already in planner yuv or 8 bit greyscale
IplImage* in = cvCreateImage(cvSize(width,height),IPL_DEPTH_8U,1);
IplImage* out = cvCreateImage(cvSize(width,height),IPL_DEPTH_16S,1);
memcpy(in->imageData,data,width*height);
// aperture size of 1 corresponds to the correct matrix
cvLaplace(in, out, 1);
short maxLap = -32767;
short* imgData = (short*)out->imageData;
for(int i =0;i<(out->imageSize/2);i++)
{
if(imgData[i] > maxLap) maxLap = imgData[i];
}
cvReleaseImage(&in);
cvReleaseImage(&out);
return maxLap;
}
Will return a short indicating the maximum sharpness detected, which based on my tests on real world samples, is a pretty good indicator of if a camera is in focus or not. Not surprisingly, normal values are scene dependent but much less so than the FFT method which has to high of a false positive rate to be useful in my application.
I came up with a totally different solution.
I needed to analyse video still frames to find the sharpest one in every (X) frames. This way, I would detect motion blur and/or out of focus images.
I ended up using Canny Edge detection and I got VERY VERY good results with almost every kind of video (with nikie's method, I had problems with digitalized VHS videos and heavy interlaced videos).
I optimized the performance by setting a region of interest (ROI) on the original image.
Using EmguCV :
//Convert image using Canny
using (Image<Gray, byte> imgCanny = imgOrig.Canny(225, 175))
{
//Count the number of pixel representing an edge
int nCountCanny = imgCanny.CountNonzero()[0];
//Compute a sharpness grade:
//< 1.5 = blurred, in movement
//de 1.5 à 6 = acceptable
//> 6 =stable, sharp
double dSharpness = (nCountCanny * 1000.0 / (imgCanny.Cols * imgCanny.Rows));
}
Thanks nikie for that great Laplace suggestion.
OpenCV docs pointed me in the same direction:
using python, cv2 (opencv 2.4.10), and numpy...
gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)
numpy.max(cv2.convertScaleAbs(cv2.Laplacian(gray, 3)))
result is between 0-255. I found anything over 200ish is very in focus, and by 100, it's noticeably blurry. the max never really gets much under 20 even if it's completely blurred.
One way which I'm currently using measures the spread of edges in the image. Look for this paper:
#ARTICLE{Marziliano04perceptualblur,
author = {Pina Marziliano and Frederic Dufaux and Stefan Winkler and Touradj Ebrahimi},
title = {Perceptual blur and ringing metrics: Application to JPEG2000,” Signal Process},
journal = {Image Commun},
year = {2004},
pages = {163--172} }
It's usually behind a paywall but I've seen some free copies around. Basically, they locate vertical edges in an image, and then measure how wide those edges are. Averaging the width gives the final blur estimation result for the image. Wider edges correspond to blurry images, and vice versa.
This problem belongs to the field of no-reference image quality estimation. If you look it up on Google Scholar, you'll get plenty of useful references.
EDIT
Here's a plot of the blur estimates obtained for the 5 images in nikie's post. Higher values correspond to greater blur. I used a fixed-size 11x11 Gaussian filter and varied the standard deviation (using imagemagick's convert command to obtain the blurred images).
If you compare images of different sizes, don't forget to normalize by the image width, since larger images will have wider edges.
Finally, a significant problem is distinguishing between artistic blur and undesired blur (caused by focus miss, compression, relative motion of the subject to the camera), but that is beyond simple approaches like this one. For an example of artistic blur, have a look at the Lenna image: Lenna's reflection in the mirror is blurry, but her face is perfectly in focus. This contributes to a higher blur estimate for the Lenna image.
Answers above elucidated many things, but I think it is useful to make a conceptual distinction.
What if you take a perfectly on-focus picture of a blurred image?
The blurring detection problem is only well posed when you have a reference. If you need to design, e.g., an auto-focus system, you compare a sequence of images taken with different degrees of blurring, or smoothing, and you try to find the point of minimum blurring within this set. I other words you need to cross reference the various images using one of the techniques illustrated above (basically--with various possible levels of refinement in the approach--looking for the one image with the highest high-frequency content).
I tried solution based on Laplacian filter from this post. It didn't help me. So, I tried the solution from this post and it was good for my case (but is slow):
import cv2
image = cv2.imread("test.jpeg")
height, width = image.shape[:2]
gray = cv2.cvtColor(image, cv2.COLOR_BGR2GRAY)
def px(x, y):
return int(gray[y, x])
sum = 0
for x in range(width-1):
for y in range(height):
sum += abs(px(x, y) - px(x+1, y))
Less blurred image has maximum sum value!
You can also tune speed and accuracy by changing step, e.g.
this part
for x in range(width - 1):
you can replace with this one
for x in range(0, width - 1, 10):
Matlab code of two methods that have been published in highly regarded journals (IEEE Transactions on Image Processing) are available here: https://ivulab.asu.edu/software
check the CPBDM and JNBM algorithms. If you check the code it's not very hard to be ported and incidentally it is based on the Marzialiano's method as basic feature.
i implemented it use fft in matlab and check histogram of the fft compute mean and std but also fit function can be done
fa = abs(fftshift(fft(sharp_img)));
fb = abs(fftshift(fft(blured_img)));
f1=20*log10(0.001+fa);
f2=20*log10(0.001+fb);
figure,imagesc(f1);title('org')
figure,imagesc(f2);title('blur')
figure,hist(f1(:),100);title('org')
figure,hist(f2(:),100);title('blur')
mf1=mean(f1(:));
mf2=mean(f2(:));
mfd1=median(f1(:));
mfd2=median(f2(:));
sf1=std(f1(:));
sf2=std(f2(:));
That's what I do in Opencv to detect focus quality in a region:
Mat grad;
int scale = 1;
int delta = 0;
int ddepth = CV_8U;
Mat grad_x, grad_y;
Mat abs_grad_x, abs_grad_y;
/// Gradient X
Sobel(matFromSensor, grad_x, ddepth, 1, 0, 3, scale, delta, BORDER_DEFAULT);
/// Gradient Y
Sobel(matFromSensor, grad_y, ddepth, 0, 1, 3, scale, delta, BORDER_DEFAULT);
convertScaleAbs(grad_x, abs_grad_x);
convertScaleAbs(grad_y, abs_grad_y);
addWeighted(abs_grad_x, 0.5, abs_grad_y, 0.5, 0, grad);
cv::Scalar mu, sigma;
cv::meanStdDev(grad, /* mean */ mu, /*stdev*/ sigma);
focusMeasure = mu.val[0] * mu.val[0];
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I was wondering if there is a way to determine if an image is blurry or not by analyzing the image data.
Another very simple way to estimate the sharpness of an image is to use a Laplace (or LoG) filter and simply pick the maximum value. Using a robust measure like a 99.9% quantile is probably better if you expect noise (i.e. picking the Nth-highest contrast instead of the highest contrast.) If you expect varying image brightness, you should also include a preprocessing step to normalize image brightness/contrast (e.g. histogram equalization).
I've implemented Simon's suggestion and this one in Mathematica, and tried it on a few test images:
The first test blurs the test images using a Gaussian filter with a varying kernel size, then calculates the FFT of the blurred image and takes the average of the 90% highest frequencies:
testFft[img_] := Table[
(
blurred = GaussianFilter[img, r];
fft = Fourier[ImageData[blurred]];
{w, h} = Dimensions[fft];
windowSize = Round[w/2.1];
Mean[Flatten[(Abs[
fft[[w/2 - windowSize ;; w/2 + windowSize,
h/2 - windowSize ;; h/2 + windowSize]]])]]
), {r, 0, 10, 0.5}]
Result in a logarithmic plot:
The 5 lines represent the 5 test images, the X axis represents the Gaussian filter radius. The graphs are decreasing, so the FFT is a good measure for sharpness.
This is the code for the "highest LoG" blurriness estimator: It simply applies an LoG filter and returns the brightest pixel in the filter result:
testLaplacian[img_] := Table[
(
blurred = GaussianFilter[img, r];
Max[Flatten[ImageData[LaplacianGaussianFilter[blurred, 1]]]];
), {r, 0, 10, 0.5}]
Result in a logarithmic plot:
The spread for the un-blurred images is a little better here (2.5 vs 3.3), mainly because this method only uses the strongest contrast in the image, while the FFT is essentially a mean over the whole image. The functions are also decreasing faster, so it might be easier to set a "blurry" threshold.
Yes, it is. Compute the Fast Fourier Transform and analyse the result. The Fourier transform tells you which frequencies are present in the image. If there is a low amount of high frequencies, then the image is blurry.
Defining the terms 'low' and 'high' is up to you.
Edit:
As stated in the comments, if you want a single float representing the blurryness of a given image, you have to work out a suitable metric.
nikie's answer provide such a metric. Convolve the image with a Laplacian kernel:
1
1 -4 1
1
And use a robust maximum metric on the output to get a number which you can use for thresholding. Try to avoid smoothing too much the images before computing the Laplacian, because you will only find out that a smoothed image is indeed blurry :-).
During some work with an auto-focus lens, I came across this very useful set of algorithms for detecting image focus. It's implemented in MATLAB, but most of the functions are quite easy to port to OpenCV with filter2D.
It's basically a survey implementation of many focus measurement algorithms. If you want to read the original papers, references to the authors of the algorithms are provided in the code. The 2012 paper by Pertuz, et al. Analysis of focus measure operators for shape from focus (SFF) gives a great review of all of these measure as well as their performance (both in terms of speed and accuracy as applied to SFF).
EDIT: Added MATLAB code just in case the link dies.
function FM = fmeasure(Image, Measure, ROI)
%This function measures the relative degree of focus of
%an image. It may be invoked as:
%
% FM = fmeasure(Image, Method, ROI)
%
%Where
% Image, is a grayscale image and FM is the computed
% focus value.
% Method, is the focus measure algorithm as a string.
% see 'operators.txt' for a list of focus
% measure methods.
% ROI, Image ROI as a rectangle [xo yo width heigth].
% if an empty argument is passed, the whole
% image is processed.
%
% Said Pertuz
% Abr/2010
if ~isempty(ROI)
Image = imcrop(Image, ROI);
end
WSize = 15; % Size of local window (only some operators)
switch upper(Measure)
case 'ACMO' % Absolute Central Moment (Shirvaikar2004)
if ~isinteger(Image), Image = im2uint8(Image);
end
FM = AcMomentum(Image);
case 'BREN' % Brenner's (Santos97)
[M N] = size(Image);
DH = Image;
DV = Image;
DH(1:M-2,:) = diff(Image,2,1);
DV(:,1:N-2) = diff(Image,2,2);
FM = max(DH, DV);
FM = FM.^2;
FM = mean2(FM);
case 'CONT' % Image contrast (Nanda2001)
ImContrast = inline('sum(abs(x(:)-x(5)))');
FM = nlfilter(Image, [3 3], ImContrast);
FM = mean2(FM);
case 'CURV' % Image Curvature (Helmli2001)
if ~isinteger(Image), Image = im2uint8(Image);
end
M1 = [-1 0 1;-1 0 1;-1 0 1];
M2 = [1 0 1;1 0 1;1 0 1];
P0 = imfilter(Image, M1, 'replicate', 'conv')/6;
P1 = imfilter(Image, M1', 'replicate', 'conv')/6;
P2 = 3*imfilter(Image, M2, 'replicate', 'conv')/10 ...
-imfilter(Image, M2', 'replicate', 'conv')/5;
P3 = -imfilter(Image, M2, 'replicate', 'conv')/5 ...
+3*imfilter(Image, M2, 'replicate', 'conv')/10;
FM = abs(P0) + abs(P1) + abs(P2) + abs(P3);
FM = mean2(FM);
case 'DCTE' % DCT energy ratio (Shen2006)
FM = nlfilter(Image, [8 8], #DctRatio);
FM = mean2(FM);
case 'DCTR' % DCT reduced energy ratio (Lee2009)
FM = nlfilter(Image, [8 8], #ReRatio);
FM = mean2(FM);
case 'GDER' % Gaussian derivative (Geusebroek2000)
N = floor(WSize/2);
sig = N/2.5;
[x,y] = meshgrid(-N:N, -N:N);
G = exp(-(x.^2+y.^2)/(2*sig^2))/(2*pi*sig);
Gx = -x.*G/(sig^2);Gx = Gx/sum(Gx(:));
Gy = -y.*G/(sig^2);Gy = Gy/sum(Gy(:));
Rx = imfilter(double(Image), Gx, 'conv', 'replicate');
Ry = imfilter(double(Image), Gy, 'conv', 'replicate');
FM = Rx.^2+Ry.^2;
FM = mean2(FM);
case 'GLVA' % Graylevel variance (Krotkov86)
FM = std2(Image);
case 'GLLV' %Graylevel local variance (Pech2000)
LVar = stdfilt(Image, ones(WSize,WSize)).^2;
FM = std2(LVar)^2;
case 'GLVN' % Normalized GLV (Santos97)
FM = std2(Image)^2/mean2(Image);
case 'GRAE' % Energy of gradient (Subbarao92a)
Ix = Image;
Iy = Image;
Iy(1:end-1,:) = diff(Image, 1, 1);
Ix(:,1:end-1) = diff(Image, 1, 2);
FM = Ix.^2 + Iy.^2;
FM = mean2(FM);
case 'GRAT' % Thresholded gradient (Snatos97)
Th = 0; %Threshold
Ix = Image;
Iy = Image;
Iy(1:end-1,:) = diff(Image, 1, 1);
Ix(:,1:end-1) = diff(Image, 1, 2);
FM = max(abs(Ix), abs(Iy));
FM(FM<Th)=0;
FM = sum(FM(:))/sum(sum(FM~=0));
case 'GRAS' % Squared gradient (Eskicioglu95)
Ix = diff(Image, 1, 2);
FM = Ix.^2;
FM = mean2(FM);
case 'HELM' %Helmli's mean method (Helmli2001)
MEANF = fspecial('average',[WSize WSize]);
U = imfilter(Image, MEANF, 'replicate');
R1 = U./Image;
R1(Image==0)=1;
index = (U>Image);
FM = 1./R1;
FM(index) = R1(index);
FM = mean2(FM);
case 'HISE' % Histogram entropy (Krotkov86)
FM = entropy(Image);
case 'HISR' % Histogram range (Firestone91)
FM = max(Image(:))-min(Image(:));
case 'LAPE' % Energy of laplacian (Subbarao92a)
LAP = fspecial('laplacian');
FM = imfilter(Image, LAP, 'replicate', 'conv');
FM = mean2(FM.^2);
case 'LAPM' % Modified Laplacian (Nayar89)
M = [-1 2 -1];
Lx = imfilter(Image, M, 'replicate', 'conv');
Ly = imfilter(Image, M', 'replicate', 'conv');
FM = abs(Lx) + abs(Ly);
FM = mean2(FM);
case 'LAPV' % Variance of laplacian (Pech2000)
LAP = fspecial('laplacian');
ILAP = imfilter(Image, LAP, 'replicate', 'conv');
FM = std2(ILAP)^2;
case 'LAPD' % Diagonal laplacian (Thelen2009)
M1 = [-1 2 -1];
M2 = [0 0 -1;0 2 0;-1 0 0]/sqrt(2);
M3 = [-1 0 0;0 2 0;0 0 -1]/sqrt(2);
F1 = imfilter(Image, M1, 'replicate', 'conv');
F2 = imfilter(Image, M2, 'replicate', 'conv');
F3 = imfilter(Image, M3, 'replicate', 'conv');
F4 = imfilter(Image, M1', 'replicate', 'conv');
FM = abs(F1) + abs(F2) + abs(F3) + abs(F4);
FM = mean2(FM);
case 'SFIL' %Steerable filters (Minhas2009)
% Angles = [0 45 90 135 180 225 270 315];
N = floor(WSize/2);
sig = N/2.5;
[x,y] = meshgrid(-N:N, -N:N);
G = exp(-(x.^2+y.^2)/(2*sig^2))/(2*pi*sig);
Gx = -x.*G/(sig^2);Gx = Gx/sum(Gx(:));
Gy = -y.*G/(sig^2);Gy = Gy/sum(Gy(:));
R(:,:,1) = imfilter(double(Image), Gx, 'conv', 'replicate');
R(:,:,2) = imfilter(double(Image), Gy, 'conv', 'replicate');
R(:,:,3) = cosd(45)*R(:,:,1)+sind(45)*R(:,:,2);
R(:,:,4) = cosd(135)*R(:,:,1)+sind(135)*R(:,:,2);
R(:,:,5) = cosd(180)*R(:,:,1)+sind(180)*R(:,:,2);
R(:,:,6) = cosd(225)*R(:,:,1)+sind(225)*R(:,:,2);
R(:,:,7) = cosd(270)*R(:,:,1)+sind(270)*R(:,:,2);
R(:,:,7) = cosd(315)*R(:,:,1)+sind(315)*R(:,:,2);
FM = max(R,[],3);
FM = mean2(FM);
case 'SFRQ' % Spatial frequency (Eskicioglu95)
Ix = Image;
Iy = Image;
Ix(:,1:end-1) = diff(Image, 1, 2);
Iy(1:end-1,:) = diff(Image, 1, 1);
FM = mean2(sqrt(double(Iy.^2+Ix.^2)));
case 'TENG'% Tenengrad (Krotkov86)
Sx = fspecial('sobel');
Gx = imfilter(double(Image), Sx, 'replicate', 'conv');
Gy = imfilter(double(Image), Sx', 'replicate', 'conv');
FM = Gx.^2 + Gy.^2;
FM = mean2(FM);
case 'TENV' % Tenengrad variance (Pech2000)
Sx = fspecial('sobel');
Gx = imfilter(double(Image), Sx, 'replicate', 'conv');
Gy = imfilter(double(Image), Sx', 'replicate', 'conv');
G = Gx.^2 + Gy.^2;
FM = std2(G)^2;
case 'VOLA' % Vollath's correlation (Santos97)
Image = double(Image);
I1 = Image; I1(1:end-1,:) = Image(2:end,:);
I2 = Image; I2(1:end-2,:) = Image(3:end,:);
Image = Image.*(I1-I2);
FM = mean2(Image);
case 'WAVS' %Sum of Wavelet coeffs (Yang2003)
[C,S] = wavedec2(Image, 1, 'db6');
H = wrcoef2('h', C, S, 'db6', 1);
V = wrcoef2('v', C, S, 'db6', 1);
D = wrcoef2('d', C, S, 'db6', 1);
FM = abs(H) + abs(V) + abs(D);
FM = mean2(FM);
case 'WAVV' %Variance of Wav...(Yang2003)
[C,S] = wavedec2(Image, 1, 'db6');
H = abs(wrcoef2('h', C, S, 'db6', 1));
V = abs(wrcoef2('v', C, S, 'db6', 1));
D = abs(wrcoef2('d', C, S, 'db6', 1));
FM = std2(H)^2+std2(V)+std2(D);
case 'WAVR'
[C,S] = wavedec2(Image, 3, 'db6');
H = abs(wrcoef2('h', C, S, 'db6', 1));
V = abs(wrcoef2('v', C, S, 'db6', 1));
D = abs(wrcoef2('d', C, S, 'db6', 1));
A1 = abs(wrcoef2('a', C, S, 'db6', 1));
A2 = abs(wrcoef2('a', C, S, 'db6', 2));
A3 = abs(wrcoef2('a', C, S, 'db6', 3));
A = A1 + A2 + A3;
WH = H.^2 + V.^2 + D.^2;
WH = mean2(WH);
WL = mean2(A);
FM = WH/WL;
otherwise
error('Unknown measure %s',upper(Measure))
end
end
%************************************************************************
function fm = AcMomentum(Image)
[M N] = size(Image);
Hist = imhist(Image)/(M*N);
Hist = abs((0:255)-255*mean2(Image))'.*Hist;
fm = sum(Hist);
end
%******************************************************************
function fm = DctRatio(M)
MT = dct2(M).^2;
fm = (sum(MT(:))-MT(1,1))/MT(1,1);
end
%************************************************************************
function fm = ReRatio(M)
M = dct2(M);
fm = (M(1,2)^2+M(1,3)^2+M(2,1)^2+M(2,2)^2+M(3,1)^2)/(M(1,1)^2);
end
%******************************************************************
A few examples of OpenCV versions:
// OpenCV port of 'LAPM' algorithm (Nayar89)
double modifiedLaplacian(const cv::Mat& src)
{
cv::Mat M = (Mat_<double>(3, 1) << -1, 2, -1);
cv::Mat G = cv::getGaussianKernel(3, -1, CV_64F);
cv::Mat Lx;
cv::sepFilter2D(src, Lx, CV_64F, M, G);
cv::Mat Ly;
cv::sepFilter2D(src, Ly, CV_64F, G, M);
cv::Mat FM = cv::abs(Lx) + cv::abs(Ly);
double focusMeasure = cv::mean(FM).val[0];
return focusMeasure;
}
// OpenCV port of 'LAPV' algorithm (Pech2000)
double varianceOfLaplacian(const cv::Mat& src)
{
cv::Mat lap;
cv::Laplacian(src, lap, CV_64F);
cv::Scalar mu, sigma;
cv::meanStdDev(lap, mu, sigma);
double focusMeasure = sigma.val[0]*sigma.val[0];
return focusMeasure;
}
// OpenCV port of 'TENG' algorithm (Krotkov86)
double tenengrad(const cv::Mat& src, int ksize)
{
cv::Mat Gx, Gy;
cv::Sobel(src, Gx, CV_64F, 1, 0, ksize);
cv::Sobel(src, Gy, CV_64F, 0, 1, ksize);
cv::Mat FM = Gx.mul(Gx) + Gy.mul(Gy);
double focusMeasure = cv::mean(FM).val[0];
return focusMeasure;
}
// OpenCV port of 'GLVN' algorithm (Santos97)
double normalizedGraylevelVariance(const cv::Mat& src)
{
cv::Scalar mu, sigma;
cv::meanStdDev(src, mu, sigma);
double focusMeasure = (sigma.val[0]*sigma.val[0]) / mu.val[0];
return focusMeasure;
}
No guarantees on whether or not these measures are the best choice for your problem, but if you track down the papers associated with these measures, they may give you more insight. Hope you find the code useful! I know I did.
Building off of Nike's answer. Its straightforward to implement the laplacian based method with opencv:
short GetSharpness(char* data, unsigned int width, unsigned int height)
{
// assumes that your image is already in planner yuv or 8 bit greyscale
IplImage* in = cvCreateImage(cvSize(width,height),IPL_DEPTH_8U,1);
IplImage* out = cvCreateImage(cvSize(width,height),IPL_DEPTH_16S,1);
memcpy(in->imageData,data,width*height);
// aperture size of 1 corresponds to the correct matrix
cvLaplace(in, out, 1);
short maxLap = -32767;
short* imgData = (short*)out->imageData;
for(int i =0;i<(out->imageSize/2);i++)
{
if(imgData[i] > maxLap) maxLap = imgData[i];
}
cvReleaseImage(&in);
cvReleaseImage(&out);
return maxLap;
}
Will return a short indicating the maximum sharpness detected, which based on my tests on real world samples, is a pretty good indicator of if a camera is in focus or not. Not surprisingly, normal values are scene dependent but much less so than the FFT method which has to high of a false positive rate to be useful in my application.
I came up with a totally different solution.
I needed to analyse video still frames to find the sharpest one in every (X) frames. This way, I would detect motion blur and/or out of focus images.
I ended up using Canny Edge detection and I got VERY VERY good results with almost every kind of video (with nikie's method, I had problems with digitalized VHS videos and heavy interlaced videos).
I optimized the performance by setting a region of interest (ROI) on the original image.
Using EmguCV :
//Convert image using Canny
using (Image<Gray, byte> imgCanny = imgOrig.Canny(225, 175))
{
//Count the number of pixel representing an edge
int nCountCanny = imgCanny.CountNonzero()[0];
//Compute a sharpness grade:
//< 1.5 = blurred, in movement
//de 1.5 à 6 = acceptable
//> 6 =stable, sharp
double dSharpness = (nCountCanny * 1000.0 / (imgCanny.Cols * imgCanny.Rows));
}
Thanks nikie for that great Laplace suggestion.
OpenCV docs pointed me in the same direction:
using python, cv2 (opencv 2.4.10), and numpy...
gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)
numpy.max(cv2.convertScaleAbs(cv2.Laplacian(gray, 3)))
result is between 0-255. I found anything over 200ish is very in focus, and by 100, it's noticeably blurry. the max never really gets much under 20 even if it's completely blurred.
One way which I'm currently using measures the spread of edges in the image. Look for this paper:
#ARTICLE{Marziliano04perceptualblur,
author = {Pina Marziliano and Frederic Dufaux and Stefan Winkler and Touradj Ebrahimi},
title = {Perceptual blur and ringing metrics: Application to JPEG2000,” Signal Process},
journal = {Image Commun},
year = {2004},
pages = {163--172} }
It's usually behind a paywall but I've seen some free copies around. Basically, they locate vertical edges in an image, and then measure how wide those edges are. Averaging the width gives the final blur estimation result for the image. Wider edges correspond to blurry images, and vice versa.
This problem belongs to the field of no-reference image quality estimation. If you look it up on Google Scholar, you'll get plenty of useful references.
EDIT
Here's a plot of the blur estimates obtained for the 5 images in nikie's post. Higher values correspond to greater blur. I used a fixed-size 11x11 Gaussian filter and varied the standard deviation (using imagemagick's convert command to obtain the blurred images).
If you compare images of different sizes, don't forget to normalize by the image width, since larger images will have wider edges.
Finally, a significant problem is distinguishing between artistic blur and undesired blur (caused by focus miss, compression, relative motion of the subject to the camera), but that is beyond simple approaches like this one. For an example of artistic blur, have a look at the Lenna image: Lenna's reflection in the mirror is blurry, but her face is perfectly in focus. This contributes to a higher blur estimate for the Lenna image.
Answers above elucidated many things, but I think it is useful to make a conceptual distinction.
What if you take a perfectly on-focus picture of a blurred image?
The blurring detection problem is only well posed when you have a reference. If you need to design, e.g., an auto-focus system, you compare a sequence of images taken with different degrees of blurring, or smoothing, and you try to find the point of minimum blurring within this set. I other words you need to cross reference the various images using one of the techniques illustrated above (basically--with various possible levels of refinement in the approach--looking for the one image with the highest high-frequency content).
I tried solution based on Laplacian filter from this post. It didn't help me. So, I tried the solution from this post and it was good for my case (but is slow):
import cv2
image = cv2.imread("test.jpeg")
height, width = image.shape[:2]
gray = cv2.cvtColor(image, cv2.COLOR_BGR2GRAY)
def px(x, y):
return int(gray[y, x])
sum = 0
for x in range(width-1):
for y in range(height):
sum += abs(px(x, y) - px(x+1, y))
Less blurred image has maximum sum value!
You can also tune speed and accuracy by changing step, e.g.
this part
for x in range(width - 1):
you can replace with this one
for x in range(0, width - 1, 10):
Matlab code of two methods that have been published in highly regarded journals (IEEE Transactions on Image Processing) are available here: https://ivulab.asu.edu/software
check the CPBDM and JNBM algorithms. If you check the code it's not very hard to be ported and incidentally it is based on the Marzialiano's method as basic feature.
i implemented it use fft in matlab and check histogram of the fft compute mean and std but also fit function can be done
fa = abs(fftshift(fft(sharp_img)));
fb = abs(fftshift(fft(blured_img)));
f1=20*log10(0.001+fa);
f2=20*log10(0.001+fb);
figure,imagesc(f1);title('org')
figure,imagesc(f2);title('blur')
figure,hist(f1(:),100);title('org')
figure,hist(f2(:),100);title('blur')
mf1=mean(f1(:));
mf2=mean(f2(:));
mfd1=median(f1(:));
mfd2=median(f2(:));
sf1=std(f1(:));
sf2=std(f2(:));
That's what I do in Opencv to detect focus quality in a region:
Mat grad;
int scale = 1;
int delta = 0;
int ddepth = CV_8U;
Mat grad_x, grad_y;
Mat abs_grad_x, abs_grad_y;
/// Gradient X
Sobel(matFromSensor, grad_x, ddepth, 1, 0, 3, scale, delta, BORDER_DEFAULT);
/// Gradient Y
Sobel(matFromSensor, grad_y, ddepth, 0, 1, 3, scale, delta, BORDER_DEFAULT);
convertScaleAbs(grad_x, abs_grad_x);
convertScaleAbs(grad_y, abs_grad_y);
addWeighted(abs_grad_x, 0.5, abs_grad_y, 0.5, 0, grad);
cv::Scalar mu, sigma;
cv::meanStdDev(grad, /* mean */ mu, /*stdev*/ sigma);
focusMeasure = mu.val[0] * mu.val[0];