Smoothing of histogram with a low-pass filter in MATLAB

I have an image and my aim is to binarize the image. I have filtered the image with a low pass Gaussian filter and have computed the intensity histogram of the image.

I now want to perform smoothing of the histogram so that I can obtain the threshold for binarization. I used a low pass filter but it did not work. This is the filter I used.

h = 开发者_运维知识库fspecial('gaussian', [8 8],2);

Can anyone help me with this? What is the process with respect to smoothing of a histogram?

imhist(Ig);

Thanks a lot for all your help.

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I've been working on a very similar problem recently, trying to compute a threshold in order to exclude noisy background pixels from MRI data prior to performing other computations on the images. What I did was fit a spline to the histogram to smooth it while maintaining an accurate fit of the shape. I used the splinefit package from the file exchange to perform the fitting. I computed a histogram for a stack of images treated together, but it should work similarly for an individual image. I also happened to use a logarithmic transformation of my histogram data, but that may or may not be a useful step for your application.

[my_histogram, xvals] = hist(reshape(image_volume), 1, []), number_of_bins);
my_log_hist = log(my_histogram);
my_log_hist(~isfinite(my_log_hist)) = 0;   % Get rid of NaN values that arise from empty bins (log of zero = NaN)
figure(1), plot(xvals, my_log_hist, 'b');
hold on
breaks = linspace(0, max_pixel_intensity, numberofbreaks);
xx = linspace(0, max_pixel_intensity, max_pixel_intensity+1);
pp = splinefit(xvals, my_log_hist, breaks, 'r');
plot(xx, ppval(pp, xx), 'r');

Note that the spline is differentiable and you can use ppdiff to get the derivative, which is useful for finding maxima and minima to help pick an appropriate threshold. The numberofbreaks is set to a relatively low number so that the spline will smooth the histogram. I used linspace in the example to pick the breaks, but if you know that some portion of the histogram exhibits much greater curvature than elsewhere, you'd want to have more breaks in that region and less elsewhere in order to accurately capture the shape of the histogram.

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To smooth the histogram you need to use a 1-D filter. This is easily done using the filter function. Here is an example:

I = imread('pout.tif');
h = imhist(I);
smooth_h = filter(normpdf(-4:4, 0,1),1,h);

Of course you can use any smoothing function you choose. The mean would simply be ones(1,8).

Since your goal here is just to find the threshold to binarize an image you could just use the graythresh function which uses Otsu's method.