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imGranulometry: add imOrientedGranulo.m for orientation granulometry
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‎matImage/imGranulometry/Contents.m

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%
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% Computation of granulometry curves
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% imGranulo - Compute granulometry curve of a given image.
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% imGranuloByRegion - Granulometry curve for each region of label image.
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% imGranulo - Compute granulometry curve of a given image.
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% imGranuloByRegion - Granulometry curve for each region of label image.
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%
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% Analysis of granulometry curves
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% granuloMeanSize - Compute geometric mean of granulometric curve.
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% granuloMean - Compute arithmetic mean of granulometric curve(s).
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% granuloStd - Compute standard deviation of granulometric curve(s).
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%
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% Variations of granulometry analysis
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% imOrientedGranulo - Gray level granulometry mean size for various orientations.
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% granuloMeanSize - Compute geometric mean of granulometric curve.
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% granuloMean - Compute arithmetic mean of granulometric curve(s).
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% granuloStd - Compute standard deviation of granulometric curve(s).
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%
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% Oriented granulometry analysis
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% imDirectionalGranulo - Directional granulometries for several orientations.
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% imGranuloOrientationMap - Orientation map of directional granulometry.
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% orientedLineStrel - Create an oriented line structuring element.
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% imOrientedGranulo - Gray level granulometry mean size for various orientations.
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%
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%
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% References

‎matImage/imGranulometry/imDirectionalGranulo.m

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function [res, orientList] = imDirectionalGranulo(img, nOrients, grType, LMax, varargin)
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% Directional granulometries for several orientations.
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%
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% Usage:
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% RES = imDirectionalGranulo(IMG, NORIENT, GRTYPE, LMAX)
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%
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% Input parameters:
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% IMG: input image, 2D gray-level
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% NORIENT: the number of orientations to consider
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% GRTYPE: the type of granulomtry (only 'opening' is supported for now)
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% LMAX: the maximum size of line
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%
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%
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% Example
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% imDirectionalGranulo
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%
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% See also
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% orientedLineStrel
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%
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% Reference
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% The methodology is described in the following article:
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% "Oriented granulometry to quantify fibre orientation distributions in
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% synthetic and plant fibre composite preforms", by V. Gager, D. Legland,
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% A. Bourmaud, A. Le Duigou, F. Pierre, K. Behlouli and C. Baley. (2020),
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% Industrial Crops and Products 152, p. 112548.
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% doi: https://doi.org/10.1016/j.indcrop.2020.112548
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%
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%
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% ------
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% Author: David Legland
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% e-mail: [email protected]
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% Created: 2018-12-18, using Matlab 9.5.0.944444 (R2018b)
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% Copyright 2018 INRA - Cepia Software Platform.
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%% Input arguments
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if ~strcmp(grType, 'opening')
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error('Only ''opening'' granulometry type is currently supported');
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end
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%% Initialization
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dim = size(img);
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% create the list of angles
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orientList = linspace(0, 180, nOrients+1);
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orientList(end) = [];
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% create the list of line diameters
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% (consider only odd values to ensure symetry of the strel)
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diamList = 1:2:LMax;
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nSteps = length(diamList);
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% allocate memory for global result
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res = zeros([dim nOrients], 'double');
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% allocate memory for intermediate results
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resOp = zeros([dim nSteps+1], 'double');
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% image for normalizing granulometry curves
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refImage = double(img);
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refImage(img <= 0) = 1;
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%% Main processing
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% iterate over orientations
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for iOrient = 1:nOrients
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disp(sprintf('Orient: %d/%d', iOrient, nOrients)); %#ok<DSPS>
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% angles from horizontal, in degrees, in CW order
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% (correspond to CCW when visualizing image results)
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theta = -orientList(iOrient);
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% iterate over granulometry steps to create a stack of results
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for i = 1:nSteps
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se = orientedLineStrel(diamList(i), theta);
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resOp(:,:,i) = imopen(img, se);
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end
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% compute granulometry curve for each pixel
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gr = bsxfun(@rdivide, cat(3, zeros(dim), diff(-resOp, 1, 3)), refImage) * 100;
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% compute mean size for each position
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meanSizes = granuloMeanSize(reshape(gr, [numel(img) nSteps+1]), [diamList LMax]);
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% stores the mean size for the current orientation
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res(:,:,iOrient) = reshape(meanSizes, size(img));
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end
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‎matImage/imGranulometry/imGranuloOrientationMap.m

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function [orientMap, resMax, rgb] = imGranuloOrientationMap(img, nOrients, grType, LMax)
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% Orientation map of directional granulometry.
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%
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% ORIMAP = imGranuloOrientationMap(IMG, NORIENT, GRTYPE, LMAX)
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%
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% [ORIMAP, RGB] = imGranuloOrientationMap(IMG, NORIENT, GRTYPE, LMAX)
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% Also returns an RGB version for display
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%
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% Example
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% imGranuloOrientationMap
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%
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% See also
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% imGranulometry, imDirectionalGranulo, granuloMeanSize
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%
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% ------
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% Author: David Legland
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% e-mail: [email protected]
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% Created: 2018-12-19, using Matlab 9.5.0.944444 (R2018b)
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% Copyright 2018 INRA - Cepia Software Platform.
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% compute the 3D array of mean size for each position and each orientation
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[res, orientList] = imDirectionalGranulo(img, nOrients, grType, LMax);
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resMax = max(res, [], 3);
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% convert to radians, over all directions
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orientRads = deg2rad(2 * orientList);
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% compute average direction for each pixel, weighted by granulometric size
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dxList = reshape(cos(orientRads), [1 1 nOrients]);
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dyList = reshape(sin(orientRads), [1 1 nOrients]);
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dxMoy = sum(bsxfun(@times, res, dxList), 3) ./ sum(res, 3);
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dyMoy = sum(bsxfun(@times, res, dyList), 3) ./ sum(res, 3);
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% create orientation map, in degrees
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orientMap = mod(rad2deg(atan2(dyMoy, dxMoy) / 2) + 180, 180);
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% optionnaly create an rgb version
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if nargout > 1
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hue = orientMap / 180;
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sat = double(img) / double(max(img(:)));
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val = ones(size(img));
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rgb = hsv2rgb(cat(3, hue, sat, val));
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end

‎matImage/imGranulometry/imOrientedGranulo.m

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% imOrientedGranulo
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%
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% See also
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% imGranulometry, imGranulo, imGranuloByRegion, granuloMeanSize
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% imGranulometry, imDirectionalGranulo, imGranulo, imGranuloByRegion,
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% granuloMeanSize
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% ------
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% Author: David Legland

‎matImage/imGranulometry/orientedLineStrel.m

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function se = orientedLineStrel(L, theta)
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% Create an oriented line structuring element.
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%
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% SE = orientedLineStrel(L, THETA)
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% Generates a binary images corresponding the linear structuring element
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% with length L and orientation THETA (in degrees).
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% The length corresponds to the approwimated Euclidean length of the
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% final structuring element.
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%
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% Example
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% % Creates a structuring element with length 10 pixels and 30 degrees
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% % orientation
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% se = orientedLineStrel(10, 30)
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% se =
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% 5x9 logical array
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%
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% 1 1 0 0 0 0 0 0 0
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% 0 0 1 1 0 0 0 0 0
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% 0 0 0 0 1 0 0 0 0
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% 0 0 0 0 0 1 1 0 0
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% 0 0 0 0 0 0 0 1 1
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%
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% See also
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% imGranulometry, imDirectionalGranulo, imGranulo
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%
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% ------
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% Author: David Legland
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% e-mail: [email protected]
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% Created: 2018-12-18, using Matlab 9.5.0.944444 (R2018b)
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% Copyright 2018 INRA - Cepia Software Platform.
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% pre-compute trigonometric quantities
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cost = cos(deg2rad(theta));
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sint = sin(deg2rad(theta));
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% compute strel size
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if abs(cost) >= abs(sint)
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% horizontal strel directions
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xRadius = round((abs(L * cost) - 1) / 2);
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yRadius = round(xRadius * abs(sint / cost));
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else
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% vertical strel directions
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yRadius = round((abs(L * sint) - 1) / 2);
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xRadius = round(yRadius * abs(cost / sint));
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end
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% allocate memory
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dim = [2*yRadius+1 2*xRadius+1];
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se = false(dim);
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if abs(cost) >= abs(sint)
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% Process horizontal strel directions
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lx = -xRadius:xRadius;
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ly = round(lx * sint / cost);
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inds = sub2ind(dim, ly + yRadius + 1, lx + xRadius + 1);
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se(inds) = true;
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else
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% Process vertical strel directions
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ly = -yRadius:yRadius;
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lx = round(ly * cost / sint);
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inds = sub2ind(dim, ly + yRadius + 1, lx + xRadius + 1);
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se(inds) = true;
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end

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