Assignment 4 part 2: Measure resolution
Overview
In this part of the assignment, you will measure the resolution of your microscope using image processing code that you will develop.
This is part 2 of Assignment 4.
Measuring resolution
EstimateResolutionFromPsfImage takes a point-source image and estimates the resolution of an optical system. It uses the built-in MATLAB function im2bw to locate bright regions and regionprops to measure attributes of each connected region of bright pixels. After rejecting outliers, the function uses nlinfit to estimate best fit Gaussian parameters for each bright spot. The optional second argument controls the rejection range for outliers.
There are four subfunctions that should be included in the same m-file as EstimateResolutionFromPsfImage.
function [ Resolution, StandardError, BestFitData ] = EstimateResolutionFromPsfImage( ImageData, OutlierTolerancePercentage ) if( nargin < 2 ) OutlierTolerancePercentage = [ 0.7 1.3]; end ImageData = im2double(ImageData); figure(1); imshow( ImageData ); hold on; title( 'PSF Image' ); % create bilevel image mapping bright regions thresholdLevel = 0.5 * ( max( ImageData(:) ) + median( ImageData(:) ) ); % this may not work in all cases binaryImage = im2bw( ImageData, thresholdLevel ); % increase the size of each connected region using dilation dilatedImage = imdilate( binaryImage, strel( 'disk', 7, 0 ) ); % remove objects touching the edges dilatedImage = imclearborder( dilatedImage ); % assign a unique object number to each connected region of pixels labeledImage = bwlabel( dilatedImage ); % draw a red circle around labeled objects CircleObjectsInImage( labeledImage, [ 1 0 0 ] ); % compute the parameters of each object identified in the image objectProperties = regionprops( dilatedImage, ImageData, ... 'Area', 'Centroid', 'PixelList', 'PixelValues', 'MaxIntensity' ); % eliminate outliers -- PSF beads that are touching, aggregates, etc... % begin by eliminating objects whose areas are outliers, as occurs when % beads are too close medianArea = median( [ objectProperties.Area ] ); outliers = [ objectProperties.Area ] > OutlierTolerancePercentage(2) * medianArea | [ objectProperties.Area ] < OutlierTolerancePercentage(1) * medianArea; if( sum( outliers ) > 0 ) dilatedImage = RemoveObjectsFromImage( dilatedImage, objectProperties( outliers ) ); objectProperties( outliers ) = []; % remove outliers end CircleObjectsInImage( dilatedImage, [ 1 1 0 ] ); % next eliminate intensity outliers medianMaxIntensity = median( [ objectProperties.MaxIntensity ] ); outliers = [ objectProperties.MaxIntensity ] > OutlierTolerancePercentage(2) * medianMaxIntensity | [ objectProperties.MaxIntensity ] < OutlierTolerancePercentage(1) * medianMaxIntensity; outliers = outliers | [ objectProperties.MaxIntensity ] > 0.995; if( sum( outliers ) > 0 ) dilatedImage = RemoveObjectsFromImage( dilatedImage, objectProperties( outliers ) ); objectProperties( outliers ) = []; end % circle all the remaining objects in green CircleObjectsInImage( dilatedImage, [ 0 1 0 ] ); LabelObjectsInImage( objectProperties ); hold off; BestFitData = cell(1, length(objectProperties)); % use nlinfit to fit a Gaussian to each object for ii = 1:length(objectProperties) % initial guess for sigma based on area of bright spot maximumPixelValue = max( objectProperties(ii).PixelValues ); darkPixelValue = median( objectProperties(ii).PixelValues ); pixelCountAboveHalf = sum( objectProperties(ii).PixelValues > .5 * ( maximumPixelValue + darkPixelValue ) ); sigmaInitialGuess = 0.8 * sqrt( pixelCountAboveHalf / 2 / pi / log(2) ); initialGuesses = [ ... objectProperties(ii).Centroid(1), ... % yCenter objectProperties(ii).Centroid(2), ... % xCenter max(objectProperties(ii).PixelValues) - min(objectProperties(ii).PixelValues), ... % amplitude sigmaInitialGuess, ... % (objectProperties(ii).BoundingBox(3) - 6) / 4, ... % sigma min(objectProperties(ii).PixelValues) ]; BestFitData{ii} = nlinfit( objectProperties(ii).PixelList, objectProperties(ii).PixelValues, @Gaussian2DFitFunction, initialGuesses ); % plot data, initial guess, and fit for each peak figure(2) clf % generate a triangle mesh from the best fit solution found by % nlinfit and plot it gd = delaunay( objectProperties(ii).PixelList(:,1), ... objectProperties(ii).PixelList(:,2) ); trimesh( gd, objectProperties(ii).PixelList(:,1), ... objectProperties(ii).PixelList(:,2), ... Gaussian2DFitFunction(BestFitData{ii}, ... objectProperties(ii).PixelList ) ) hold on % plot initial guesses -- commented out to make plots less % cluttered. put this back in to debug initial guesses % plot3( objectProperties(ii).PixelList(:,1), ... % objectProperties(ii).PixelList(:,2), ... % Gaussian2DFitFunction(initialGuesses, ... % objectProperties(ii).PixelList ), 'rx' ) % plot image data plot3( objectProperties(ii).PixelList(:,1), ... objectProperties(ii).PixelList(:,2), ... objectProperties(ii).PixelValues, 'gx', 'LineWidth', 3) title(['Image data vs. Best Fit for Object Number ' num2str(ii)]); end allPeakData = vertcat( BestFitData{:} ); Resolution = mean( allPeakData(:,4) ) ./ 0.336; StandardError = std( allPeakData(:,4) ./ 0.336 ) ./ sqrt( length( BestFitData ) ); end function out = Gaussian2DFitFunction( Parameters, Coordinates ) yCenter = Parameters(1); xCenter = Parameters(2); amplitude = Parameters(3); sigma = Parameters(4); offset = Parameters(5); out = amplitude * ... exp( -(( Coordinates(:, 1) - yCenter ).^2 + ( Coordinates(:, 2) - xCenter ).^2 ) ... ./ (2 * sigma .^ 2 )) + offset; end function CircleObjectsInImage( LabelImage, BorderColor ) boundaries = bwboundaries( LabelImage ); numberOfBoundaries = size( boundaries ); for k = 1 : numberOfBoundaries thisBoundary = boundaries{k}; plot(thisBoundary(:,2), thisBoundary(:,1), 'Color', BorderColor, 'LineWidth', 2); end end function LabelObjectsInImage( ObjectProperties ) labelShift = -9; fontSize = 10; for ii = 1:length(ObjectProperties) unweightedCentroid = ObjectProperties(ii).Centroid; % Get centroid. text(unweightedCentroid(1) + labelShift, unweightedCentroid(2), ... num2str(ii), 'FontSize', fontSize, 'HorizontalAlignment', ... 'Right', 'Color', [0 1 0]); end end function OutputBinaryImage = RemoveObjectsFromImage( InputBinaryImage, ObjectProperties ) OutputBinaryImage = InputBinaryImage; eliminatedPixels = vertcat( ObjectProperties.PixelList ); allObjectIndexes = sub2ind( size( InputBinaryImage ), ... eliminatedPixels(:, 2), eliminatedPixels(:,1) ); OutputBinaryImage( allObjectIndexes ) = 0; end % initial version 9/23/2013 by SCW
Testing the code
Measure the resolution of your microscope
- Make an image of a sample of 170 nm fluorescent beads with the 40X objective. (Several dozens to hundreds of PSF spheres should be captured in your image.)
- Use 12-bit mode on the camera and make sure to save the image in a format that preserves all 12 bits.
- Ensure that the image is exposed properly.
- Over-exposed images will give inaccurate results.
- Under-exposed images will be difficult to process and yield noisy results.
- This procedure is extremely sensitive to the focus adjustment.
- To minimize photobleaching, do not expose of the beads to the light source and longer than necessary.
- Be sure to save the image and the histogram for your lab report.
- Use image processing functions to locate non-overlapping, single beads in the image.
- Use nonlinear regression to fit a Gaussian to each bead image.
- Convert the Gaussian parameters to resolution.
- This page has example MATLAB code.
Report the resolution you measured and discuss sources of error in the measurement. |
Back to Assignment 4 Overview
Back to Assignment 4 Part 1
On to Assignment 4 Part 3