Prior-Apprised Unsupervised Learning (PAUL) of curvilinear features

Implementation of PAUL framwork on curvilinear features. Please cite the associated publication as: Yin, S., Tien, M. & Yang, H. (2020). Prior-Apprised Unsupervised Learning of Sub-Pixel Curvilinear Features in Low Signal-to-Noise Images. Biophys. J., 118, 2458-2469.

Requirements

The code uses the following toolboxes and versions at the stage of development; earlier versions might also work:

• 'MATLAB' '9.6'
• 'Image Processing Toolbox' '10.4'
• 'Statistics and Machine Learning Toolbox' '11.5'
• 'Parallel Computing Toolbox' '7.0'
• 'MATLAB Parallel Server' '7.0'

Syntax

batchMTComputation(OutputFileName, image2D, GridSize, NumOfShifts, PSFsigma, pixelSize);
batchMTComputation(OutputFileName, image2D, GridSize, NumOfShifts, PSFsigma, pixelSize, beta);
batchMTComputation(OutputFileName, image2D, GridSize, NumOfShifts, PSFsigma, pixelSize, beta, cRatio);
batchMTComputation(OutputFileName, image2D, GridSize, NumOfShifts, PSFsigma, pixelSize, beta, cRatio, estimatedLp);
batchMTComputation(OutputFileName, image2D, GridSize, NumOfShifts, PSFsigma, pixelSize, beta, cRatio, estimatedLp, gridPtUnit);

Input arguments

• OutputFileName — the string that contains the output file name.
• image2D — numeric array of a single input image or cells of numeric arrays of multiple images. The input image needs to be square (e.g. 512 x 512 pixels). The pixel values can be 8-bit, 16-bit or double. The image can be grayscale or RGB (will be converted into grayscale in the code).
• GridSize — the side of the sub image used in stage two. It should divide the image side (e.g. for 512 x 512 images, GridSize cannot fall out of {1, 2, 4, 8, 16, 32, 64, 128, 256, 512}).
• NumOfShifts — the number of shifts applied in stage two.
• PSFsigma — the standard deviation of the approximated Gaussian point-spread function (PSF), in the unit of micrometers.
• pixelSize — the side of the pixel, in the unit of micrometers.
• beta — the beta parameter in stage one. Default is 0.5. Put [] if using the default value.
• cRatio — the ratio between 2c^2 and maximum S^2 in stage one. Default is 2 (c=max(S)). Put [] if using the default value.
• estimatedLp — the estimated persistence length of the features to be detected, in the unit of micrometers. Default is 5200. Put [] if using the default value.
• gridPtUnit — the grid point density in the final PAUL principal curve, in the unit of pixels. Default is 0.1.

Output

The output is saved in a .mat file containing the following variables:

• FinalX_central_allGps (or FinalX_central_allGps_allIMs), FinalY_central_allGps (or FinalY_central_allGps_allIMs) — x and y coordinates of the final PAUL principal curve, in the pixel space.
• FinalX_UB95_allGps (or FinalX_UB95_allGps_allIMs), FinalY_UB95_allGps (or FinalY_UB95_allGps_allIMs) — x and y coordinates of the upper bound of the final PAUL principal curve, in the pixel space.
• FinalX_LB95_allGps (or FinalX_LB95_allGps_allIMs), FinalY_LB95_allGps (or FinalY_LB95_allGps_allIMs) — x and y coordinates of the lower bound of the final PAUL principal curve, in the pixel space.
• medium95PercError (or medium95PercError_allIMs) — medians of all 95% bootstrap bounds, in the unit of pixels.

Example

Run PAUL procedure on an example image ('examples/image1.mat')

>> load('examples/image1.mat');
>> batchMTComputation('example_result',example_image,32,8,0.1376,0.076,[],5,1000);

Plot the result

load('examples/image1.mat');
load('examples/image1_result_Division_32x8.mat');
imagesc(example_image)
hold on
for i = 1:length(FinalX_central_allGps)
    plot(FinalX_central_allGps{i},FinalY_central_allGps{i},'Color',[0.3010, 0.7450, 0.9330],'LineWidth',0.6);
    plot(FinalX_UB95_allGps{i},FinalY_UB95_allGps{i},'--','Color',[0.9290, 0.6940, 0.1250],'LineWidth',0.5);
    plot(FinalX_LB95_allGps{i},FinalY_LB95_allGps{i},'--','Color',[0.9290, 0.6940, 0.1250],'LineWidth',0.5);
end