I'm looking for a way to detect which of two (similar) images is sharper.
I'm thinking this could be using some measure of overall sharpness and generating a score (hypothetical example: image1 has sharpness score of 9, image2 has sharpness score of 7; so image1 is sharper)
I've done some searches for sharpness detection/scoring algorithms, but have only come across ones that will enhance image sharpness.
Has anyone done something like this, or have any useful resources/leads?
I would be using this functionality in the context of a webapp, so PHP or C/C++ is preferred.
As e.g. shown in this Matlab Central page, the sharpness can be estimated by the average gradient magnitude.
I used this in Python as
from PIL import Image
import numpy as np
im = Image.open(filename).convert('L') # to grayscale
array = np.asarray(im, dtype=np.int32)
gy, gx = np.gradient(array)
gnorm = np.sqrt(gx**2 + gy**2)
sharpness = np.average(gnorm)
A similar number can be computed with the simpler numpy.diff instead of numpy.gradient. The resulting array sizes need to be adapted there:
dx = np.diff(array)[1:,:] # remove the first row
dy = np.diff(array, axis=0)[:,1:] # remove the first column
dnorm = np.sqrt(dx**2 + dy**2)
sharpness = np.average(dnorm)
The simple method is to measure contrast -- the image with the largest differences between pixel values is the sharpest. You can, for example, compute the variance (or standard deviation) of the pixel values, and whichever produces the larger number wins. That looks for maximum overall contrast, which may not be what you want though -- in particular, it will tend to favor pictures with maximum depth of field.
Depending on what you want, you may prefer to use something like an FFT, to see which displays the highest frequency content. This allows you to favor a picture that's extremely sharp in some parts (but less so in others) over one that has more depth of field, so more of the image is reasonably sharp, but the maximum sharpness is lower (which is common, due to diffraction with smaller apertures).
Simple practical approach would be to use edge detection (more edges == sharper image).
Quick and dirty hands-on using PHP GD
function getBlurAmount($image) {
$size = getimagesize($image);
$image = imagecreatefromjpeg($image);
imagefilter($image, IMG_FILTER_EDGEDETECT);
$blur = 0;
for ($x = 0; $x < $size[0]; $x++) {
for ($y = 0; $y < $size[1]; $y++) {
$blur += imagecolorat($image, $x, $y) & 0xFF;
}
}
return $blur;
}
$e1 = getBlurAmount('http://upload.wikimedia.org/wikipedia/commons/thumb/5/51/Jonquil_flowers_at_f32.jpg/800px-Jonquil_flowers_at_f32.jpg');
$e2 = getBlurAmount('http://upload.wikimedia.org/wikipedia/commons/thumb/0/01/Jonquil_flowers_at_f5.jpg/800px-Jonquil_flowers_at_f5.jpg');
echo "Relative blur amount: first image " . $e1 / min($e1, $e2) . ", second image " . $e2 / min($e1, $e2);
(image with less blur is sharper)
More efficient approach would be to detect edges in your code, using Sobel operator. PHP example (rewriting in C++ should give huge performance boost I guess).
This paper describes a method for computing a blur factor using DWT. Looked pretty straight forward but instead of detecting sharpness it's detecting blurredness. Seems it detects edges first (simple convolution) and then uses DWT to accumulate and score it.
Check Contrast Transfer Functions (CTF)
Here's an implementation
Here's an explanation
Related
I am implementing weiner filtering in python which is applied on an image blurred using disk shape point spread function, i am including code of making disk shape psf and weiner filter
def weinerFiltering(kernel,K_const,image):
#F(u,v)
copy_img= np.copy(image)
image_fft =np.fft.fft2(copy_img)
#H(u,v)
kernel_fft = np.fft.fft2(kernel,s=copy_img.shape)
#H_mag(u,v)
kernel_fft_mag = np.abs(kernel_fft)
#H*(u,v)
kernel_conj = np.conj(kernel_fft)
f = (kernel_conj)/(kernel_fft_mag**2 + K_const)
return np.abs(np.fft.ifft2(image_fft*f))
def makeDiskShape(arr,radius,centrX,centrY):
for i in range(centrX-radius,centrX+radius):
for j in range(centrY-radius,centrY+radius):
if(l2dist(centrX,centrY,i,j)<=radius):
arr[i][j]=1
return arr/np.sum(arr)
this is blurred and gaussian noised image
this is what i am getting result after weiner filtering for K value of 50
result does not seem very good, can someone help
seems noise is reduced but amount of blurred is not, shape of disk shaped psf matrix is 20,20 and radius is 9 which seems like this
Update
using power spectrum of ground truth image and noise to calculate K constant value, still i am getting strong artifacts
this is noised and blurred image
this is result after using power specturm in place of a constant K value
Reduce your value of K. You need to play around with it until you get good results. If it's too large it doesn't filter, if it's too small you get strong artifacts.
If you have knowledge of the noise variance, you can use that to estimate the regularization parameter. In the Wiener filter, the constant K is a simplification of N/S, where N is the noise power and S is the signal power. Both these values are frequency-dependent. The signal power S can be estimated by the Fourier transform of the autocorrelation function of the image to be filtered. The noise power is hard to estimate, but if you have such an estimate (or know it because you created the noisy image synthetically), then you can plug that value into the equation. Note that this is the noise power, not the variance of the noise.
The following code uses DIPlib (the Python interface we call PyDIP) to demonstrate Wiener deconvolution (disclaimer: I'm an author). I don't think it is hard to convert this code to use other libraries.
import PyDIP as dip
image = dip.ImageRead('trui.ics');
kernel = dip.CreateGauss([3,3]).Pad(image.Sizes())
smooth = dip.ConvolveFT(image, kernel)
smooth = dip.GaussianNoise(smooth, 5.0) # variance = 5.0
H = dip.FourierTransform(kernel)
F = dip.FourierTransform(smooth)
S = dip.SquareModulus(F) # signal power estimate
N = dip.Image(5.0 * smooth.NumberOfPixels()) # noise power (has same value at all frequencies)
Hinv = dip.Conjugate(H) / ( dip.SquareModulus(H) + N / S )
out = dip.FourierTransform(F * Hinv, {"inverse", "real"})
The smooth image looks like this:
The out image that comes from deconvolving the image above looks like this:
Don't expect a perfect result. The regularization term impedes a perfect inverse filtering because such filtering would enhance the noise so strongly that it would swamp the signal and produce a totally useless output. The Wiener filter finds a middle ground between undoing the convolution and suppressing the noise.
The DIPlib documentation for WienerDeconvolution explains some of the equations involved.
From pictures of tools on a sheet of paper, I'm asked to find their outline contour to vectorize them.
I'm a total beginner in computer-vision-related problems and the only thing I thought about was OpenCV and edge detection.
The result is better than what I've imagined, this is still very unreliable, especially if the source picture isn't "perfect".
I took 2 photographies of a wrench they gave me.
After playing around with opencv bindings for node, I get this:
Then, I've tried with the less-good picture:
That's totally inexploitable.
I can get something a little better by changing the Canny thresold, but that must be automatized (given that the picture is relatively correct).
So I've got a few questions:
Am I taking the right approach? Is GrabCut better for this? A combination of Grabcut and Canny edge detection? I still need vertices at the end, but I feel that GrabCut does what I want too.
The borders are rough and have certain errors. I can augment approxPolyDP's multiplier, but without a loss of precision on good parts.
Related to the above point, I'm thinking of integrating Savitzky-Golay algorithm to smooth the outline, instead of polygon simplification with approxPolyDP. Is it a good idea?
Normally, the line of the outer border must form a simple, cuttable block. Is there a way in OpenCL to avoid that line to do impossible things, like passing on itself? - Or, simply, detect the problem? Those configurations are, of course, impossible but happen when the detection is failed (like in the second pic).
I'm searching a way to do automatic Canny thresold calculation, since I must tweak it manually for each image. Do you have a good example for that?
I noticed that converting the image to grayscale before edge detection sometimes deteriorates the result, and sometimes makes it better. Which one should I choose? (tools can be of any color btw!)
here is the source for my tests:
const cv = require('opencv');
const lowThresh = 90;
const highThresh = 90;
const nIters = 1;
const GRAY = [120, 120, 120];
const WHITE = [255, 255, 255];
cv.readImage('./files/viv1.jpg', function(err, im) {
if (err) throw err;
width = im.width()
height = im.height()
if (width < 1 || height < 1) throw new Error('Image has no size');
const out = new cv.Matrix(height, width);
im.convertGrayscale();
im_canny = im.copy();
im_canny.canny(lowThresh, highThresh);
im_canny.dilate(nIters);
contours = im_canny.findContours();
let maxArea = 0;
let biggestContour;
for (i = 0; i < contours.size(); i++) {
const area = contours.area(i);
if (area > maxArea) {
maxArea = area;
biggestContour = i;
}
out.drawContour(contours, i, GRAY);
}
const arcLength = contours.arcLength(biggestContour, true);
contours.approxPolyDP(biggestContour, 0.001 * arcLength, true);
out.drawContour(contours, biggestContour, WHITE, 5);
out.save('./tmp/out.png');
console.log('Image saved to ./tmp/out.png');
});
You'll need to add some pre-processing to clean up the image. Because you have a large variation in intensities in the image because of shadow, poor lighting, high shine on tools, etc you should equalize the image. This will help you get a better response in the regions that are currently poorly lit or have high shine.
Here's an opencv tutorial on Histogram equalization in C++: http://docs.opencv.org/2.4/doc/tutorials/imgproc/histograms/histogram_equalization/histogram_equalization.html
Hope this helps
EDIT:
You can have an automatic threshold based on some loss function(?). For eg: If you know that the tool will be completely captured in the frame, you know that you should get a high value at every column from x = 10 to x = 800(say). You could then keep reducing the threshold until you get a high value at every column from x = 10 to x = 800. This is a very naive way of doing it, but its an interesting experiment, I think, since you are generating the images yourself and have control over object placement.
You might also try running your images through an adaptive threshold first. This type of binarization is fairly adept at segmenting foreground and background in cases like this, even with inconsistent lighting/shadows (which seems to be the issue in your second example above). Adathresh will require some parameter fine-tuning, but once the entire tool is segmented from the background, Canny edge detection should produce more consistent results.
As for the roughness in your contours, you could try setting your findContours mode to one of the CV_CHAIN_APPROX methods described here.
I am trying to make a computer vision program in which it would detect litter and random trash in a noisy background such as the beach (noisy due to sand).
Original Image:
Canny Edge detection without any image processing:
I realize that a certain combination of image processing technique will help me accomplish my goal of ignoring the noisy sandy background and detect all trash and objects on the ground.
I tried to preform median blurring, play around and tune the parameters, and it gave me this:
It preforms well in terms of ignoring the sandy background, but it fails to detect some of the other many objects on the ground, possibly because it is blurred out (not too sure).
Is there any way of improving my algorithm or image processing techniques that will ignore the noisy sandy background while allowing canny edge detection to find all objects and have the program detect and draw contours on all objects.
Code:
from pyimagesearch.transform import four_point_transform
from matplotlib import pyplot as plt
import numpy as np
import cv2
import imutils
im = cv2.imread('images/beach_trash_3.jpg')
#cv2.imshow('Original', im)
# Histogram equalization to improve contrast
###
#im = np.fliplr(im)
im = imutils.resize(im, height = 500)
imgray = cv2.cvtColor(im,cv2.COLOR_BGR2GRAY)
# Contour detection
#ret,thresh = cv2.threshold(imgray,127,255,0)
#imgray = cv2.GaussianBlur(imgray, (5, 5), 200)
imgray = cv2.medianBlur(imgray, 11)
cv2.imshow('Blurred', imgray)
'''
hist,bins = np.histogram(imgray.flatten(),256,[0,256])
plt_one = plt.figure(1)
cdf = hist.cumsum()
cdf_normalized = cdf * hist.max()/ cdf.max()
cdf_m = np.ma.masked_equal(cdf,0)
cdf_m = (cdf_m - cdf_m.min())*255/(cdf_m.max()-cdf_m.min())
cdf = np.ma.filled(cdf_m,0).astype('uint8')
imgray = cdf[imgray]
cv2.imshow('Histogram Normalization', imgray)
'''
'''
imgray = cv2.adaptiveThreshold(imgray,255,cv2.ADAPTIVE_THRESH_GAUSSIAN_C,\
cv2.THRESH_BINARY,11,2)
'''
thresh = imgray
#imgray = cv2.medianBlur(imgray,5)
#imgray = cv2.Canny(imgray,10,500)
thresh = cv2.Canny(imgray,75,200)
#thresh = imgray
cv2.imshow('Canny', thresh)
contours, hierarchy = cv2.findContours(thresh.copy(),cv2.RETR_TREE,cv2.CHAIN_APPROX_SIMPLE)
cnts = sorted(contours, key = cv2.contourArea, reverse = True)[:5]
test = im.copy()
cv2.drawContours(test, cnts, -1,(0,255,0),2)
cv2.imshow('All contours', test)
print '---------------------------------------------'
##### Code to show each contour #####
main = np.array([[]])
for c in cnts:
epsilon = 0.02*cv2.arcLength(c,True)
approx = cv2.approxPolyDP(c,epsilon,True)
test = im.copy()
cv2.drawContours(test, [approx], -1,(0,255,0),2)
#print 'Contours: ', contours
if len(approx) == 4:
print 'Found rectangle'
print 'Approx.shape: ', approx.shape
print 'Test.shape: ', test.shape
# frame_f = frame_f[y: y+h, x: x+w]
frame_f = test[approx[0,0,1]:approx[2,0,1], approx[0,0,0]:approx[2,0,0]]
print 'frame_f.shape: ', frame_f.shape
main = np.append(main, approx[None,:][None,:])
print 'main: ', main
# Uncomment in order to show all rectangles in image
#cv2.imshow('Show Ya', test)
#print 'Approx: ', approx.shape
#cv2.imshow('Show Ya', frame_f)
cv2.waitKey()
print '---------------------------------------------'
cv2.drawContours(im, cnts, -1,(0,255,0),2)
print main.shape
print main
cv2.imshow('contour-test', im)
cv2.waitKey()
what i am understanding from your problem is: you want to segment out the foreground objects from a background which is variable in nature(sand gray level is depending on many other conditions).
there are various ways to approach this kind of problem:
Approach 1:
From your image one thing is clear that, background color pixels will always much more in numbers than foreground, simplest method to start initial segmentation is:
Convert the image into gray.
Create its histogram.
Find the peak index of the histogram, i.e. index which have maximum pixels.
above three steps give you an idea of background BUT the game is not ends here, now you can put this index value in the center and take a range of values around it like 25 above and below, for example: if your peak index is 207 (as in your case) choose a range of gray level from 75 to 225 and threshold image, As according to nature of your background above method can be used for foreground object detection, after segmentation you have to perform some post processing steps like morphological analysis to segment out different objects after extraction of objects you can apply some classification stuff for finer level of segmentation to remove false positive.
Approach 2:
Play with some statistics of the image pixels, like make a small data set of gray values and
Label them class 1 and 2, for example 1 for sand and 2 for foreground,
Find out mean and variance(std deviation) of pixels from both the classes, and also calculate probability for both the class ( num_pix_per_class/total_num_pix), now store these stats for later use,
Now come back to image and take every pixel one by one and apply a gaussian pdf: 1/2*pisigma(exp(-(pix - mean)/2*sigma)); at the place of mean put the mean calculated earlier and at the sigma put std deviation calculated earlier.
after applying stage 3 you will get two probability value for each pixel for two classes, just choose the class which have higher probability.
Approach 3:
Approach 3 is more complex than above two: you can use some texture based operation to segment out sand type texture, but for applying texture based method i will recommend supervised classification than unsupervised(like k-means).
Different texture feature which you can use are:
Basic:
Range of gray levels in a defined neighborhood.
local mean and variance or entropy.
Gray Level Co-occurrence Matrices (GLCM).
Advanced:
Local Binary Patterns.
Wavelet Transform.
Gabor Transform. etc.
PS: In my opinion you should give a try to approach 1 and 2. it can solve lot of work. :)
For better results you should apply many algorithms. The OpenCV-tutorials focus always on one feature of OpenCV. The real CV-applications should use as many as possible techniques and algorithms.
I've used to detect biological cells in noisy pictures and I gained very good results applying some contextual information:
Expected size of cells
The fact that all cells have similar size
Expected number of cells
So I changed many parameters and tried to detect what I'm looking for.
If using edge detection, the sand would give rather random shapes. Try to change the canny parameters and detect lines, rects, circles, ets. - any shapes more probable for litter. Remember the positions of detected objects for each parameters-set and at the and give the priority to those positions (areas) where the shapes were detected most times.
Use color-separation. The peaks in color-histogram could be the hints to the litter, as the distribution of sand-colors should be more even.
For some often appearing, small objects like cigarette-stubs you can apply object matching.
P.S:
Cool application! Jus out of curiosity, are yoou going to scan the beach with a quadcopter?
If you want to detect objects on such uniform background, you should start by detecting the main color in the image. Like that you will detect all the sand, and the objects will be in the remaining parts. You can take a look to papers published by Arnaud LeTrotter and Ludovic Llucia who both used this type of "main color detection".
How can I threshold this blurry image to make the digits as clear as possible?
In a previous post, I tried adaptively thresholding a blurry image (left), which resulted in distorted and disconnected digits (right):
Since then, I've tried using a morphological closing operation as described in this post to make the brightness of the image uniform:
If I adaptively threshold this image, I don't get significantly better results. However, because the brightness is approximately uniform, I can now use an ordinary threshold:
This is a lot better than before, but I have two problems:
I had to manually choose the threshold value. Although the closing operation results in uniform brightness, the level of brightness might be different for other images.
Different parts of the image would do better with slight variations in the threshold level. For instance, the 9 and 7 in the top left come out partially faded and should have a lower threshold, while some of the 6s have fused into 8s and should have a higher threshold.
I thought that going back to an adaptive threshold, but with a very large block size (1/9th of the image) would solve both problems. Instead, I end up with a weird "halo effect" where the centre of the image is a lot brighter, but the edges are about the same as the normally-thresholded image:
Edit: remi suggested morphologically opening the thresholded image at the top right of this post. This doesn't work too well. Using elliptical kernels, only a 3x3 is small enough to avoid obliterating the image entirely, and even then there are significant breakages in the digits:
Edit2: mmgp suggested using a Wiener filter to remove blur. I adapted this code for Wiener filtering in OpenCV to OpenCV4Android, but it makes the image even blurrier! Here's the image before (left) and after filtering with my code and a 5x5 kernel:
Here is my adapted code, which filters in-place:
private void wiener(Mat input, int nRows, int nCols) { // I tried nRows=5 and nCols=5
Mat localMean = new Mat(input.rows(), input.cols(), input.type());
Mat temp = new Mat(input.rows(), input.cols(), input.type());
Mat temp2 = new Mat(input.rows(), input.cols(), input.type());
// Create the kernel for convolution: a constant matrix with nRows rows
// and nCols cols, normalized so that the sum of the pixels is 1.
Mat kernel = new Mat(nRows, nCols, CvType.CV_32F, new Scalar(1.0 / (double) (nRows * nCols)));
// Get the local mean of the input. localMean = convolution(input, kernel)
Imgproc.filter2D(input, localMean, -1, kernel, new Point(nCols/2, nRows/2), 0);
// Get the local variance of the input. localVariance = convolution(input^2, kernel) - localMean^2
Core.multiply(input, input, temp); // temp = input^2
Imgproc.filter2D(temp, temp, -1, kernel, new Point(nCols/2, nRows/2), 0); // temp = convolution(input^2, kernel)
Core.multiply(localMean, localMean, temp2); //temp2 = localMean^2
Core.subtract(temp, temp2, temp); // temp = localVariance = convolution(input^2, kernel) - localMean^2
// Estimate the noise as mean(localVariance)
Scalar noise = Core.mean(temp);
// Compute the result. result = localMean + max(0, localVariance - noise) / max(localVariance, noise) * (input - localMean)
Core.max(temp, noise, temp2); // temp2 = max(localVariance, noise)
Core.subtract(temp, noise, temp); // temp = localVariance - noise
Core.max(temp, new Scalar(0), temp); // temp = max(0, localVariance - noise)
Core.divide(temp, temp2, temp); // temp = max(0, localVar-noise) / max(localVariance, noise)
Core.subtract(input, localMean, input); // input = input - localMean
Core.multiply(temp, input, input); // input = max(0, localVariance - noise) / max(localVariance, noise) * (input - localMean)
Core.add(input, localMean, input); // input = localMean + max(0, localVariance - noise) / max(localVariance, noise) * (input - localMean)
}
Some hints that you might try out:
Apply the morphological opening in your original thresholded image (the one which is noisy at the right of the first picture). You should get rid of most of the background noise and be able to reconnect the digits.
Use a different preprocessing of your original image instead of morpho closing, such as median filter (tends to blur the edges) or bilateral filtering which will preserve better the edges but is slower to compute.
As far as threshold is concerned, you can use CV_OTSU flag in the cv::threshold to determine an optimal value for a global threshold. Local thresholding might still be better, but should work better with the bilateral or median filter
I've tried thresholding each 3x3 box separately, using Otsu's algorithm (CV_OTSU - thanks remi!) to determine an optimal threshold value for each box. This works a bit better than thresholding the entire image, and is probably a bit more robust.
Better solutions are welcome, though.
If you're willing to spend some cycles on it there are de-blurring techniques that could be used to sharpen up the picture prior to processing. Nothing in OpenCV yet but if this is a make-or-break kind of thing you could add it.
There's a bunch of literature on the subject:
http://www.cse.cuhk.edu.hk/~leojia/projects/motion_deblurring/index.html
http://www.google.com/search?q=motion+deblurring
And some chatter on the OpenCV mailing list:
http://tech.groups.yahoo.com/group/OpenCV/message/20938
The weird "halo effect" that you're seeing is likely due to OpenCV assuming black for the color when the adaptive threshold is at/near the edge of the image and the window that it's using "hangs over" the edge into non-image territory. There are ways to correct for this, most likely you would make an temporary image that's at least two full block-sizes taller and wider than the image from the camera. Then copy the camera image into the middle of it. Then set the surrounding "blank" portion of the temp image to be the average color of the image from the camera. Now when you perform the adaptive threshold the data at/near the edges will be much closer to accurate. It won't be perfect since its not a real picture but it will yield better results than the black that OpenCV is assuming is there.
My proposal assumes you can identify the sudoku cells, which I think, is not asking too much. Trying to apply morphological operators (although I really like them) and/or binarization methods as a first step is the wrong way here, in my opinion of course. Your image is at least partially blurry, for whatever reason (original camera angle and/or movement, among other reasons). So what you need is to revert that, by performing a deconvolution. Of course asking for a perfect deconvolution is too much, but we can try some things.
One of these "things" is the Wiener filter, and in Matlab, for instance, the function is named deconvwnr. I noticed the blurry to be in the vertical direction, so we can perform a deconvolution with a vertical kernel of certain length (10 in the following example) and also assume the input is not noise free (assumption of 5%) -- I'm just trying to give a very superficial view here, take it easy. In Matlab, your problem is at least partially solved by doing:
f = imread('some_sudoku_cell.png');
g = deconvwnr(f, fspecial('motion', 10, 90), 0.05));
h = im2bw(g, graythresh(g)); % graythresh is the Otsu method
Here are the results from some of your cells (original, otsu, otsu of region growing, morphological enhanced image, otsu from morphological enhanced image with region growing, otsu of deconvolution):
The enhanced image was produced by performing original + tophat(original) - bottomhat(original) with a flat disk of radius 3. I manually picked the seed point for region growing and manually picked the best threshold.
For empty cells you get weird results (original and otsu of deconvlution):
But I don't think you would have trouble to detect whether a cell is empty or not (the global threshold already solves it).
EDIT:
Added the best results I could get with a different approach: region growing. I also attempted some other approaches, but this was the second best one.
When applying a Gaussian blur to an image, typically the sigma is a parameter (examples include Matlab and ImageJ).
How does one know what sigma should be? Is there a mathematical way to figure out an optimal sigma? In my case, i have some objects in images that are bright compared to the background, and I need to find them computationally. I am going to apply a Gaussian filter to make the center of these objects even brighter, which hopefully facilitates finding them. How can I determine the optimal sigma for this?
There's no formula to determine it for you; the optimal sigma will depend on image factors - primarily the resolution of the image and the size of your objects in it (in pixels).
Also, note that Gaussian filters aren't actually meant to brighten anything; you might want to look into contrast maximization techniques - sounds like something as simple as histogram stretching could work well for you.
edit: More explanation - sigma basically controls how "fat" your kernel function is going to be; higher sigma values blur over a wider radius. Since you're working with images, bigger sigma also forces you to use a larger kernel matrix to capture enough of the function's energy. For your specific case, you want your kernel to be big enough to cover most of the object (so that it's blurred enough), but not so large that it starts overlapping multiple neighboring objects at a time - so actually, object separation is also a factor along with size.
Since you mentioned MATLAB - you can take a look at various gaussian kernels with different parameters using the fspecial('gaussian', hsize, sigma) function, where hsize is the size of the kernel and sigma is, well, sigma. Try varying the parameters to see how it changes.
I use this convention as a rule of thumb. If k is the size of kernel than sigma=(k-1)/6 . This is because the length for 99 percentile of gaussian pdf is 6sigma.
You have to find a min/max of a function G such that G(X,sigma) where X is a set of your observations (in your case, your image grayscale values) , This function can be anything that maintain the "order" of the intensities of the iamge, for example, this can be done with the 1st derivative of the image (as G),
fil = fspecial('sobel');
im = imfilter(I,fil);
imagesc(im);
colormap = gray;
this gives you the result of first derivative of an image, now you want to find max sigma by
maximzing G(X,sigma), that means that you are trying a few sigmas (let say, in increasing order) until you reach a sigma that makes G maximal. This can also be done with second derivative.
Given the central value of the kernel equals 1 the dimension that guarantees to have the outermost value less than a limit (e.g 1/100) is as follows:
double limit = 1.0 / 100.0;
size = static_cast<int>(2 * std::ceil(sqrt(-2.0 * sigma * sigma * log(limit))));
if (size % 2 == 0)
{
size++;
}