Find positions within a microscope image or series of images of single or multiple colloids.
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img_out = bpass( img_in, hpass, lpass, bckgrnd, display )
Three step image manipulation starting with a high pass filter to remove long scale variations. The high pass filtered image, img_hpass is then filtered with a low pass filter, to remove pixel noise. Finally, img_lpass, has any pixel values below backgrnd set to zero. Any step can be skipped with a false argument.
img_in 2D array of image pixel values.
hpass Set to true for high pass filtering. Set to false to skip.
lpass Set to true to apply a gaussian filter with a strength calculated from img_in. Provide any positive integer for manual control of the gaussian kernel. Set to false to skip. For either true or int value, if the strength of the filter is equal to 1 the image is assumed to be good enough and lpass and will be skipped.
backgrnd Resets any pixel values below backgrnd to 0. Set to 'false' to skip.
display Display img_in, img_hpass, img_lpass and img_out. And calculates pixel distribution at each stage of the filtering. This can be usefully when optimising your input arguments. Set to false or leave blank to skip.
Returns img_out 2D array of filtered image pixel values.
img_hpass and img_lpass can be returned with
[ img_out, img_hpass ] = bpass() and
[ img_out, ~, img_lpass ] = bpass(), respectively.
est_pks = pkfnd( img, threshold, excl_dia )
Find colloid positions in an image with pixel accuracy. The output here is expected to be an argument in cntrd(). Rarely would the output here be sufficient for analysis of particle dynamics.
All non-zero pixels within the exclusion radius floor( excl_dia / 2 ) of the image edges are eliminated. Checks each pixel and eliminates all but the brightest within a 3x3 array centered on the current pixel. After which remaining pixels are then checked to see if it is the brightest in a n x n array centered on the current pixel where n = excl_dia.
img_in 2D array of image pixel values. Ideally each colloid is represented by only a few non-zero pixels.
threshold Eliminates pixel values below threshold.
excl_dia Diameter, in pixels, over which to exclude all but the brightest pixel. Also excludes pixels within excl_dia / 2 of image edges.
Returns est_pks N x 2 array containing, pixelated coordinates of local maxima.
cntrds = cntrd( img_in, est_pks, excl_dia, apply_mask )
Calculates the centroid of a colloid to sub-pixel accuracy.
img_in 2D array of image pixel values. Ideally each colloid is represented by as many pixels as possible.
est_pks Coordinates of central pixel for each colloid.
excl_dia Diameter, in pixels, over which to calculate the centroid.
Returns cntrds N x 4 array containing, centroids, the corresponding brightest pixel and estimated radius.
cntrds(:,1) x-coordinates
cntrds(:,2) y-coordinates
cntrds(:,3) brightest pixel
cntrds(:,4) estimated radii
Note that sub-pixel accuracy is dependent on the number of pixels over which the centroid is calculated. To check for pixel bias, plot a histogram of the fractional parts of the resulting locations. For example,
hist( cntrds( :, 1 ) ./ floor( cntrds( :, 1 ) ) ).
A brightfield image, where monodisperse colloids are focused to maximize the contrast between colloids centre and the background, but not saturating any pixels.
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img_in |
In the above image there is negligible noise and negligible variation across the image. We can skip the long pass and high pass filtering steps and just apply a backgrnd to zero all of the background pixels whilst retaining as many as possible pixels per colloid.
img_out = bpass( img_in, false, false, 65 ) ;
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img_out |
Now we can find the coordinates of the brightest pixel for each colloid with pkfnd().
est_pks = pkfnd( img_out, 172, 11 )
With pkfnd() we can apply a much higher threshold than with bpass() so as to reduce the number of candidate pixels per colloid. You can also check this by returning the total number of candidate pixels after the applied threshold with,
[ est_pks, input_pk_pxs] = pkfnd( img_out, 172, 9 )
Ideally input_pk_pxs is minimized without loosing any colloids.
Finally, we pass the est_pks to cntrd() along with our filtered image img_out, an exclusion diameter in pixels, and a boolean,
cntrds = cntrd( img_in, est_pks, 11, true )
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img_result |
The above image shows the original image with the centroid markers (green crosshair), the excl_dia (green square) and the estimated radii (red circles).
It is advisable to check for pixel biasing by looking at the fractional components of the resulting centroids,
hist( mod( cntrd( :, 1 ), 1 ) ) for example.
For a significant number of centroids, the distribution of the fractional component of the centroids should have a uniform distribution.
If you have a particularly noisy image, the high frequency noise will propagate through to the calculated centroid.
Try running noise_on_pos.m found in test/ where an image of a colloid with a random, uniform distribution of pixel noise is used to calculate the centroid with and without filtering the image with a low pass filter.
An example image with noise and the resulting filtered image with bpass( img_noise, false, 5, 80) is shown below.
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| Noisy image and filtered image. |
To demonstrates the effect of noise, the distribution of the calculated centroids for 105 images with random uniform noise is shown below.
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| Centroid distribution for unfiltered and filtered images. |
Aggressive filtering with the low pass filter can result in sub-pixel biasing due to ringing artifacts. The larger the lpass argument the higher the suppression of the high frequencies variations and the image becomes bandlimited, leading to ringing at points of high contrast (ie from background pixels to colloid pixels).
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| Centroids resulting from ringing artifacts and resulting distribution. |
The Matlab Particle Tracking Code was originally developed by Daniel Blair and Eric Dufresne, based on the IDL algorithms developed by David Grier, John Crocker and Eric Weeks.
Original Matlab code is distributed at https://site.physics.georgetown.edu/matlab/
Original IDL code is distributed at https://physics.emory.edu/faculty/weeks/idl/