From fb89f498ebdefa19f5f5fc4a639a9ff190ac09e5 Mon Sep 17 00:00:00 2001 From: Yagiz Aksoy Date: Mon, 30 Jul 2018 14:54:31 +0200 Subject: [PATCH] Initial commit --- LICENSE | 17 +++ SemanticSoftSegmentation.m | 49 +++++++++ SpectralMatting.m | 31 ++++++ Superpixels.m | 125 ++++++++++++++++++++++ affinityMatrixToLaplacian.m | 16 +++ demo.m | 40 +++++++ docia.png | Bin 0 -> 823007 bytes groupSegments.m | 21 ++++ imageGradient.m | 67 ++++++++++++ mattingAffinity.m | 101 ++++++++++++++++++ preprocessFeatures.m | 40 +++++++ readme.md | 36 +++++++ softSegmentsFromEigs.m | 187 +++++++++++++++++++++++++++++++++ sparsifySegments.m | 69 ++++++++++++ visualizeEigenvectorRedGreen.m | 9 ++ visualizeSoftSegments.m | 43 ++++++++ 16 files changed, 851 insertions(+) create mode 100644 LICENSE create mode 100644 SemanticSoftSegmentation.m create mode 100644 SpectralMatting.m create mode 100644 Superpixels.m create mode 100644 affinityMatrixToLaplacian.m create mode 100644 demo.m create mode 100644 docia.png create mode 100644 groupSegments.m create mode 100644 imageGradient.m create mode 100644 mattingAffinity.m create mode 100644 preprocessFeatures.m create mode 100644 readme.md create mode 100644 softSegmentsFromEigs.m create mode 100644 sparsifySegments.m create mode 100644 visualizeEigenvectorRedGreen.m create mode 100644 visualizeSoftSegments.m diff --git a/LICENSE b/LICENSE new file mode 100644 index 0000000..ed6eb3d --- /dev/null +++ b/LICENSE @@ -0,0 +1,17 @@ +Copyright 2018, Yagiz Aksoy. All rights reserved. + +This software is for academic use only. A redistribution of this +software, with or without modifications, has to be for academic +use only, while giving the appropriate credit to the original +authors of the software. The methods implemented as a part of +this software may be covered under patents or patent applications. + +THIS SOFTWARE IS PROVIDED BY THE AUTHOR ''AS IS'' AND ANY EXPRESS OR IMPLIED +WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND +FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR +CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR +CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR +SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON +ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING +NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF +ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. \ No newline at end of file diff --git a/SemanticSoftSegmentation.m b/SemanticSoftSegmentation.m new file mode 100644 index 0000000..ed306b4 --- /dev/null +++ b/SemanticSoftSegmentation.m @@ -0,0 +1,49 @@ + +% Semantic Soft Segmentation +% This function implements the soft segmentation approach described in +% Yagiz Aksoy, Tae-Hyun Oh, Sylvain Paris, Marc Pollefeys, Wojciech Matusik +% "Semantic Soft Segmentation", ACM TOG (Proc. SIGGRAPH) 2018 + +function [softSegments, initSoftSegments, Laplacian, affinities, features, superpixels, eigenvectors, eigenvalues] = SemanticSoftSegmentation(image, features) + + disp('Semantic Soft Segmentation') + % Prepare the inputs and superpixels + image = im2double(image); + if size(features, 3) > 3 % If the features are raw, hyperdimensional, preprocess them + features = preprocessFeatures(features, image); + else + features = im2double(features); + end + superpixels = Superpixels(image); + [h, w, ~] = size(image); + + disp(' Computing affinities') + % Compute the affinities and the Laplacian + affinities{1} = mattingAffinity(image); + affinities{2} = superpixels.neighborAffinities(features); % semantic affinity + affinities{3} = superpixels.nearbyAffinities(image); % non-local color affinity + Laplacian = affinityMatrixToLaplacian(affinities{1} + 0.01 * affinities{2} + 0.01 * affinities{3}); % Equation 6 + + disp(' Computing eigenvectors') + % Compute the eigendecomposition + eigCnt = 100; % We use 100 eigenvectors in the optimization + [eigenvectors, eigenvalues] = eigs(Laplacian, eigCnt, 'SM'); + + disp(' Initial optimization') + % Compute initial soft segments + initialSegmCnt = 40; + sparsityParam = 0.8; + iterCnt = 40; + % feeding features to the function below triggers semantic intialization + initSoftSegments = softSegmentsFromEigs(eigenvectors, eigenvalues, Laplacian, ... + h, w, features, initialSegmCnt, iterCnt, sparsityParam, [], []); + + % Group segments w.r.t. their mean semantic feature vectors + groupedSegments = groupSegments(initSoftSegments, features); + + disp(' Final optimization') + % Do the final sparsification + softSegments = sparsifySegments(groupedSegments, Laplacian, imageGradient(image, false, 6)); + + disp(' Done.') +end \ No newline at end of file diff --git a/SpectralMatting.m b/SpectralMatting.m new file mode 100644 index 0000000..1069380 --- /dev/null +++ b/SpectralMatting.m @@ -0,0 +1,31 @@ + +% Spectral Matting +% This function implements the soft segmentation approach described in +% Anat Levin, Dani Lischinski, Yair Weiss, "Spectral Matting", IEEE TPAMI, 2008. +% The parameters here are set to their default values as reported by Levin et al. + +function [softSegments, Laplacian, eigenvectors, eigenvalues] = SpectralMatting(image) + + disp('Spectral Matting') + image = im2double(image); + [h, w, ~] = size(image); + + disp(' Computing affinities') + % Compute the matting Laplacian + Laplacian = affinityMatrixToLaplacian(mattingAffinity(image)); + + disp(' Computing eigenvectors') + % Compute the eigendecomposition + eigCnt = 50; + [eigenvectors, eigenvalues] = eigs(Laplacian, eigCnt, 'SM'); + + disp(' Optimization') + % Compute the soft segments = matting components + initialSegmCnt = 20; + sparsityParam = 0.8; + iterCnt = 20; + softSegments = softSegmentsFromEigs(eigenvectors, eigenvalues, Laplacian, ... + h, w, [], initialSegmCnt, iterCnt, sparsityParam, [], []); + + disp(' Done.') +end \ No newline at end of file diff --git a/Superpixels.m b/Superpixels.m new file mode 100644 index 0000000..ba661b7 --- /dev/null +++ b/Superpixels.m @@ -0,0 +1,125 @@ + +% This class is for computing superpixel-based affinities described in the paper. +% This class requires the image graphs methods by Steve Eddins. Find it here: +% http://www.mathworks.com/matlabcentral/fileexchange/53614-image-graphs + +classdef Superpixels + properties + labels + spcount + neigh + centroids + end + methods + function obj = Superpixels(im, spcnt) + if ~exist('spcnt', 'var') || isempty(spcnt) + spcnt = 2500; + end + [L, N] = superpixels(im, spcnt, 'Compactness', 1e-20); + obj.labels = L; + obj.spcount = N; + % Find neighboring superpixels + g = adjacentRegionsGraph(L); + obj.neigh = g.Edges.Labels; + % Find centroids + s = regionprops(L, 'centroid'); + cent = cat(1, s.Centroid); + obj.centroids = round(cent(:, 2:-1:1)); + [h, w, ~] = size(im); + obj.centroids(:, 3) = sub2ind([h, w], obj.centroids(:, 1), obj.centroids(:, 2)); + end + + function regmeans = computeRegionMeans(obj, image) + [h, w, c] = size(image); + image = reshape(image, [h*w, c]); + regmeans = zeros(obj.spcount, c); + idx = label2idx(obj.labels); + for i = 1 : length(idx) + regmeans(i, :) = mean(image(idx{i}, :), 1); + end + end + + % This is for the semantic affinity, generates affinities in [-1, 1] + function W = neighborAffinities(obj, features, erfSteepness, erfCenter) + if ~exist('erfSteepness', 'var') || isempty(erfSteepness) + erfSteepness = 20; + end + if ~exist('erfCenter', 'var') || isempty(erfCenter) + erfCenter = 0.85; + end + [h, w, ~] = size(features); + N = h * w; + spMeans = obj.computeRegionMeans(features); + affs = zeros(size(obj.neigh, 1), 1); + inds1 = affs; + inds2 = affs; + for i = 1 : size(obj.neigh, 1) + ind1 = obj.neigh(i, 1); + ind2 = obj.neigh(i, 2); + affs(i) = sigmoidAff(spMeans(ind1, :), spMeans(ind2, :), erfSteepness, erfCenter); + inds1(i) = obj.centroids(ind1, 3); + inds2(i) = obj.centroids(ind2, 3); + end + W = sparse(inds1, inds2, affs, N, N); + W = W' + W; + end + + % This is for the nonlocal color affinity, generates affinities in [0, 1] + function W = nearbyAffinities(obj, image, erfSteepness, erfCenter, proxThresh) + if ~exist('erfSteepness', 'var') || isempty(erfSteepness) + erfSteepness = 50; + end + if ~exist('erfCenter', 'var') || isempty(erfCenter) + erfCenter = 0.95; + end + if ~exist('proxThresh', 'var') || isempty(proxThresh) + proxThresh = 0.2; + end + [h, w, ~] = size(image); + N = h * w; + spMeans = obj.computeRegionMeans(image); + combinationCnt = obj.spcount; + combinationCnt = combinationCnt * (combinationCnt - 1) / 2; + affs = zeros(combinationCnt, 1); + inds1 = affs; + inds2 = affs; + cnt = 1; + cents = obj.centroids(:, 1:2); + cents(:,1) = cents(:,1) / h; + cents(:,2) = cents(:,2) / w; + for i = 1 : obj.spcount + for j = i + 1 : obj.spcount + centdist = cents(i, 1:2) - cents(j, 1:2); + centdist = sqrt(centdist * centdist'); + if centdist > proxThresh + affs(cnt) = 0; + else + affs(cnt) = sigmoidAffPos(spMeans(i, :), spMeans(j, :), erfSteepness, erfCenter); + end + inds1(cnt) = obj.centroids(i, 3); + inds2(cnt) = obj.centroids(j, 3); + cnt = cnt + 1; + end + end + W = sparse(inds1, inds2, affs, N, N); + W = W' + W; + end + + function vis = visualizeRegionMeans(obj, im) + vis = label2rgb(obj.labels, obj.computeRegionMeans(im)); + end + + end +end + +function aff = sigmoidAff(feat1, feat2, steepness, center) + aff = abs(feat1 - feat2); + aff = 1 - sqrt(aff * aff'); + aff = (erf(steepness * (aff - center))); +end + +function aff = sigmoidAffPos(feat1, feat2, steepness, center) + aff = abs(feat1 - feat2); + aff = 1 - sqrt(aff * aff'); + aff = (erf(steepness * (aff - center)) + 1) / 2; +end \ No newline at end of file diff --git a/affinityMatrixToLaplacian.m b/affinityMatrixToLaplacian.m new file mode 100644 index 0000000..8d2a64f --- /dev/null +++ b/affinityMatrixToLaplacian.m @@ -0,0 +1,16 @@ + +function Lap = affinityMatrixToLaplacian(aff, normalize) + if ~exist('normalize', 'var') || isempty(normalize) + normalize = false ; + end + N = size(aff, 1); + if normalize + aa = sum(aff, 2); + D = spdiags(aa, 0 , N, N); + aa = sqrt(1./aa); + D12 = spdiags(aa, 0 , N, N); + Lap = D12 * (D - aff) * D12; + else + Lap = spdiags(sum(aff, 2), 0 , N, N) - aff; + end +end \ No newline at end of file diff --git a/demo.m b/demo.m new file mode 100644 index 0000000..9a8a774 --- /dev/null +++ b/demo.m @@ -0,0 +1,40 @@ + +% Add the ImageGraph to path (in a folder named 'ImageGraphs'). Find it here: +% http://www.mathworks.com/matlabcentral/fileexchange/53614-image-graphs +addpath(fullfile(fileparts(mfilename('fullpath')), 'ImageGraphs')); + +%% Read the image and features from the sample file +image = im2double(imread('docia.png')); +features = image(:, size(image, 2) / 2 + 1 : end, :); +image = image(:, 1 : size(image, 2) / 2, :); + +% The eigendecomposition uses a lot of memory and may render the computer +% unresponsive, so better to test it first with a small image. +image = imresize(image, 0.5); +features = imresize(features, 0.5); + +%% Semantic soft segmentation +% This function outputs many intermediate variables, if needed. +% The results may vary a bit from run to run, as there are 2 stages that use +% k-means for intialization & grouping. +sss = SemanticSoftSegmentation(image, features); + +% To use the features generated using our network implementation, +% just feed them as the 'features' variable to the function. It will do +% the prepocessing described in the paper and give the processed +% features as an output. +% If you are dealing with many images, storing the features after +% preprocessing is recommended as raw hyperdimensional features +% take a lot of space. Check the 'preprocessFeatures.m' file. + +% Visualize +figure; imshow([image features visualizeSoftSegments(sss)]); +title('Semantic soft segments'); + +% There's also an implementation of Spectral Matting included +sm = SpectralMatting(image); +% You can group the soft segments from Spectral Matting using +% semantic features, the way we presented our comparisons in the paper. +sm_gr = groupSegments(sm, features); +figure; imshow([image visualizeSoftSegments(sm) visualizeSoftSegments(sm_gr)]); +title('Matting components'); diff --git a/docia.png b/docia.png new file mode 100644 index 0000000000000000000000000000000000000000..65beb768fce5a50778606289978f8c639c348e5a GIT binary patch literal 823007 zcmV)0K+eC3P)EEplY_Gx7ORHJH)>SOibo}4J^LlOwvbLGCz zBXcerV-O&O0tw*%{r~)bBuTnEF#rH?cVU_tNl5_W7l2_@guEsJV8HWRm?V+_2v885 z1WAIB1B&d7Mk5U-kP0%)bPcmX&CfrV4H^wUV?dLH1a}XrA`5r9%YpxXraR^oVP+;# znj|H6cV5F4lv<=CNPxQoAPI*gcNZ+ee2S!vEc>jOBwY@<;0F9$<7e=n>*peRMGZ4x 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zuh;wiZaULa%Ch8?GS><%?*MN5E+Xr)*!*%`!@8~>0&V&rtKHI2=akC6Ez1HTKv?cO zrLV2H}vrFZ*WcfH2= z&j+*z{q|9J6^Mf4!YC*l@W(sSO=#fJ4*XE^m^-84QMWBb^xLTh+T5Gp6X(v-@n}qJ z8-|m^KY)(bLR%koUZ0%*nOjGA@#st;K;P%U00DHbQdtovpmiu8!}*hL9BjXT{=o50 z1bGcVm^9keC;^E~VkX2&r#8+8y2lODR?s0Y6FeF%=k6z5+-Ab@Za2&xUOnOhzdg8R z#;#{jrPHkL?ARx)3-cb$JGT{|43Wt_?@rZF{iD|(fs_A736F05CEWCv75x0@OdIOb z@ZWK;-kaFZD?ho$bnjvZUq{A(Ki~T&D@&VJ@iCkqo)>Jjp;MS#E#9yBxRi#4I9%*; z5`Ge&4 5) = 5; + + % Filter each channel of features with image as the guide + if exist('image', 'var') && ~isempty(image) + fd = size(features, 3); + maxfd = fd - rem(fd, 3); + for i = 1 : 3 : maxfd + features(:, :, i : i+2) = imguidedfilter(features(:, :, i : i+2), image, 'NeighborhoodSize', 10); + end + for i = maxfd + 1 : fd + features(:, :, i) = imguidedfilter(features(:, :, i), image, 'NeighborhoodSize', 10); + end + end + + % Run PCA and normalize to [0, 1] + simp = featuresPCA(features, 3); + for i = 1 : 3 + simp(:,:,i) = simp(:,:,i) - min(min(simp(:,:,i))); + simp(:,:,i) = simp(:,:,i) / max(max(simp(:,:,i))); + end +end + +function pcafeat = featuresPCA(features, dim) + features = double(features); + [h, w, d] = size(features); + features = reshape(features, [h*w, d]); + featmean = mean(features, 1); + features = features - ones(h*w, 1) * featmean; + covar = features' * features; + [eigvecs, ~] = eigs(covar, dim, 'LA'); + pcafeat = features * eigvecs; + pcafeat = reshape(pcafeat, [h, w, dim]); +end diff --git a/readme.md b/readme.md new file mode 100644 index 0000000..8979e1c --- /dev/null +++ b/readme.md @@ -0,0 +1,36 @@ +Semantic Soft Segmentation +================================================================= + +This repository includes the spectral segmentation approach presented in + + Yagiz Aksoy, Tae-Hyun Oh, Sylvain Paris, Marc Pollefeys and Wojciech Matusik, "Semantic Soft Segmentation", ACM Transactions on Graphics (Proc. SIGGRAPH), 2018 + +The network for semantic feature generation can be found [[here](https://github.com/iyah4888/SIGGRAPH18SSS)]. + +Please refer to the [[project page](http://people.inf.ethz.ch/aksoyy/sss/)] for more information and example data. + +The Superpixels class requires [[ImageGraphs](http://www.mathworks.com/matlabcentral/fileexchange/53614-image-graphs)]. + +License and citation +------------ + +This toolbox is provided for academic use only. +If you use this code, please cite our paper: + + @ARTICLE{sss, + author={Ya\u{g}{\i}z Aksoy and Tae-Hyun Oh and Sylvain Paris and Marc Pollefeys and Wojciech Matusik}, + title={Semantic Soft Segmentation}, + journal={ACM Transactions on Graphics (Proc. SIGGRAPH)}, + year={2018}, + pages = {72:1-72:13}, + volume = {37}, + number = {4} + } + +Credit +------------ +Parts of this implementation are taken from + + Anat Levin, Alex Rav-Acha, Dani Lischinski, "Spectral Matting", IEEE TPAMI, 2008 + +The original source code for Spectral Matting can be found [[here](http://www.vision.huji.ac.il/SpectralMatting/)]. \ No newline at end of file diff --git a/softSegmentsFromEigs.m b/softSegmentsFromEigs.m new file mode 100644 index 0000000..92fcef4 --- /dev/null +++ b/softSegmentsFromEigs.m @@ -0,0 +1,187 @@ + +% This function implements the constrained sparsification descibed in Section 3.4. +% This methodology is intriduced by Levin et al. in "Spectral Matting", and +% this function is an adapted version of their original source code. Find it here: +% http://www.vision.huji.ac.il/SpectralMatting/ + +function [softSegments, initialSegments] = softSegmentsFromEigs(eigVecs, eigVals, Laplacian, h, w, features, compCnt, maxIter, sparsityParam, imageGrad, initialSegments) + if (~exist('maxIter','var') || isempty(maxIter)) + maxIter = 20; + end + if (~exist('sparsityParam','var') || isempty(sparsityParam)) + sparsityParam = 0.9; + end + if (~exist('compCnt','var') || isempty(compCnt)) + compCnt = 10; + end + eigValCnt = size(eigVecs, 2); + if (~exist('eigVals','var') || isempty(eigVals)) + eigVals = 1e-5*eye(eigValCnt); + end + + % Initialize with k-means if an initialization (initialSegments) isn't provided + if ~exist('initialSegments', 'var') || isempty(initialSegments) + % Use the features for the k-means, if provided + if ~(~exist('features', 'var') || isempty(features)) + disp(' Computing k-means initialization using semantic features...'); + %features = featuresPCA(features, 10); + features = reshape(features, [size(features, 1) * size(features, 2), size(features, 3)]); + [initialSegments, ~, ~, ~] = fastKmeans(features, compCnt); + else + % This is the default initialization from Spectral Matting + disp(' Computing k-means initialization...'); + eigVals = abs(eigVals); % Sometimes there are -epsilon numbers that mess up the thing + initEigsCnt = 20; + initEigsWeights = diag(1 ./ diag(eigVals(2 : initEigsCnt + 1, 2 : initEigsCnt + 1) .^ 0.5 )); + initEigVecs = eigVecs(:, 2 : initEigsCnt + 1) * initEigsWeights; + [initialSegments, ~, ~, ~] = fastKmeans(initEigVecs, compCnt); + end + end + softSegments = zeros(length(initialSegments), compCnt); + for i = 1 : compCnt + softSegments(:, i) = double(initialSegments == i); + end + + if ~exist('imageGrad', 'var') || isempty(imageGrad) + spMat = sparsityParam; + else + imageGrad(imageGrad > 0.2) = 0.2; + imageGrad = imageGrad + 0.8; + spMat = repmat(imageGrad(:), [1, compCnt]); + end + + % Second derivative of first and second terms in the sparsity penalty + disp(' Starting optimization...'); + thr_e = 1e-10; + w1 = 0.3; + w0 = 0.3; + e1 = w1 .^ sparsityParam * max(abs(softSegments-1), thr_e) .^ (spMat - 2); + e0 = w0 .^ sparsityParam * max(abs(softSegments), thr_e) .^ (spMat - 2); + + scld = 1; + eig_vectors = eigVecs(:, 1 : eigValCnt); + eig_values = eigVals(1 : eigValCnt, 1 : eigValCnt); + + % First iter no for removing zero components + removeIter = ceil(maxIter / 4); + removeIterCycle = ceil(maxIter / 4); + + % Compute matting component with sparsity prior + for iter = 1 : maxIter + if rem(iter, 10) == 0 + disp([' Iteration ' int2str(iter) ' of ' int2str(maxIter)]); + end + % Construct the matrices in Eq(9) in Spectral Matting + tA = zeros((compCnt - 1) * eigValCnt); + tb = zeros((compCnt - 1) * eigValCnt, 1); + for k = 1 : compCnt - 1 + weighted_eigs = repmat(e1(:, k) + e0(:, k), 1, eigValCnt) .* eig_vectors; + tA((k-1) * eigValCnt + 1 : k * eigValCnt, (k-1) * eigValCnt + 1 : k * eigValCnt) = eig_vectors' * weighted_eigs + scld * eig_values; + tb((k-1) * eigValCnt + 1 : k * eigValCnt) = eig_vectors' * e1(:,k); + end + k = compCnt; + weighted_eigs = repmat(e1(:, k) + e0(:, k), 1, eigValCnt) .* eig_vectors; + ttA = eig_vectors' * weighted_eigs + scld * eig_values; + ttb = eig_vectors' * e0(:, k) + scld * sum(eig_vectors' * Laplacian, 2); + + tA = tA + repmat(ttA, [compCnt - 1, compCnt - 1]); + tb = tb + repmat(ttb, [compCnt - 1, 1]); + + % Solve for weights + y = reshape(tA \ tb, eigValCnt, compCnt - 1); + + % Compute the matting comps from weights + softSegments = eigVecs(:, 1 : eigValCnt) * y; + softSegments(:, compCnt) = 1 - sum(softSegments(:, 1 : compCnt - 1), 2); % Sets the last one as 1-sum(others), guaranteeing \sum(all) = 1 + + % Remove matting components which are close to zero every once in a while + if iter > removeIter + nzii = find(max(abs(softSegments)) > 0.1); + compCnt = length(nzii); + softSegments = softSegments(:, nzii); + removeIter = removeIter + removeIterCycle; + end + + % Recompute the derivatives of sparsity penalties + if length(spMat(:)) == 1 + e1 = w1 .^ sparsityParam * max(abs(softSegments-1), thr_e) .^ (spMat - 2); + e0 = w0 .^ sparsityParam * max(abs(softSegments), thr_e) .^ (spMat - 2); + else + e1 = w1 .^ sparsityParam * max(abs(softSegments-1), thr_e) .^ (spMat(:, 1 : size(softSegments, 2)) - 2); + e0 = w0 .^ sparsityParam * max(abs(softSegments), thr_e) .^ (spMat(:, 1 : size(softSegments, 2)) - 2); + end + end + softSegments = reshape(softSegments, [h, w, size(softSegments, 2)]); +end + +function [idx, C, sumd, D]=fastKmeans(X,K) + % X: points in the N-by-P data matrix + % idx - an N-by-1 vector containing the cluster indices of each point + % + % c - the K cluster centroid locations in a K-by-P matrix. + % sumd - the within-cluster sums of point-to-centroid distances in a 1-by-K vector. + % distances from each point to every centroid in a N-by-K. + + startK = 5; + startK = min(K,startK); + maxIters = 100; % Defualt of matlab is 100 + + X = sign(real(X)) .* abs(X); + + [idx, C, sumd, D]=kmeans(X,startK,'EmptyAction','singleton','Start','cluster', ... + 'Maxiter', maxIters, 'Replicates', 7); + + valid_vec = zeros(1,startK); + scr_vec = zeros(1,startK)-1; + + for compCnt = startK+1:K + % create a new cluster by splitting each cluster to two... + max_scr=-1; + clear min_C; + for cl = 1:compCnt-1 + cl_mask = idx == cl; + cl_idxs = find(cl_mask); + clX = X(cl_idxs,:); + if (size(clX,1)> 2*size(clX,2)) + if (valid_vec(cl) == 0) + [tmp_idx, tmp_C, ~, tmp_D]=kmeans(clX,2,'EmptyAction','singleton','Start','cluster', 'Maxiter', maxIters); + % chk how much the partition helps ... + scr=sum(min(D(cl_idxs,:),[],2))-sum(min(tmp_D,[],2)); + scr_vec(cl) = scr; + else % we already saved it... + scr = scr_vec(cl); + end + else + scr=-2; + scr_vec(cl) = scr; + end + if (scr > max_scr) + if (valid_vec(cl)==1) % not for the scr. Just for the idxs. + [tmp_idx, tmp_C, ~, ~]=kmeans(clX,2,'EmptyAction','singleton','Start','cluster', 'Maxiter', maxIters); + end + + max_scr = scr; + bestC = [C;tmp_C(2,:)]; + bestC(cl,:) = tmp_C(1,:); + best_cl = cl; + + best_idx = idx; + best_idx(cl_idxs) = (tmp_idx == 1)*best_cl + (tmp_idx == 2)*compCnt; + end + valid_vec(cl) = 1; + end + C = bestC; + idx = best_idx; + + valid_vec = [valid_vec, 0]; % the two new clusers are new, so their + valid_vec(best_cl) = 0; % score have not been computed yet. + scr_vec = [scr_vec, -1]; + scr_vec(best_cl) = -1; + + if (compCnt < 13) + [idx, C, sumd, D]=kmeans(X, compCnt, 'EmptyAction', 'singleton', 'Start', C, 'Maxiter', maxIters); + valid_vec = zeros(1,compCnt); + end + end + +end \ No newline at end of file diff --git a/sparsifySegments.m b/sparsifySegments.m new file mode 100644 index 0000000..92844b2 --- /dev/null +++ b/sparsifySegments.m @@ -0,0 +1,69 @@ + +% This function implements the relaxed sparsification descibed in Section 3.4 + +function softSegments = sparsifySegments(softSegments, Laplacian, imageGrad) + + sigmaS = 1; % sparsity + sigmaF = 1; % fidelity + delta = 100; % constraint + [h, w, compCnt] = size(softSegments); + N = h * w * compCnt; + + if ~exist('imageGrad', 'var') || isempty(imageGrad) + % If image gradient is not provided, set the param to the default 0.9 + spPow = 0.90; + else + % Compute the per-pixel sparsity parameter from the gradient + imageGrad(imageGrad > 0.1) = 0.1; + imageGrad = imageGrad + 0.9; + spPow = repmat(imageGrad(:), [compCnt, 1]); + end + + % Iter count for pcg and main optimization + itersBetweenUpdate = 100; + highLevelIters = 20; + + % Get rid of very low/high alpha values and normalize + softSegments(softSegments < 0.1) = 0; + softSegments(softSegments > 0.9) = 1; + softSegments = softSegments ./ repmat(sum(softSegments, 3), [1 1 size(softSegments, 3)]); + + % Construct the linear system + lap = Laplacian; + for i = 2 : compCnt + Laplacian = blkdiag(Laplacian, lap); + end + + % The alpha constraint + C = repmat(speye(h*w), [1 compCnt]); + C = C' * C; + Laplacian = Laplacian + delta * C; + + % The sparsification optimization + softSegments = softSegments(:); + compInit = softSegments; % needed for fidelity energy + for iter = 1 : highLevelIters + if rem(iter, 5) == 0 + disp([' Iteration ' int2str(iter) ' of ' int2str(highLevelIters)]); + end + [u, v] = getUandV(softSegments, spPow); % The sparsity energy + A = Laplacian + sigmaS * (spdiags(u, 0, N, N) + spdiags(v, 0, N, N)) + sigmaF * speye(N); + b = sigmaS * v + sigmaF * compInit + delta; + [softSegments, ~] = pcg(A, b, [], itersBetweenUpdate, [], [], softSegments); + end + + % One final iter for good times (everything but sparsity) + A = Laplacian + sigmaF * speye(N); + b = sigmaF * softSegments + delta; + softSegments = pcg(A, b, [], 10 * itersBetweenUpdate, [], [], softSegments); + + % Ta-dah + softSegments = reshape(softSegments, [h w compCnt]); +end + +function [u, v] = getUandV(comp, spPow) + % Sparsity terms in the energy + eps = 1e-2; + u = max(abs(comp(:)), eps) .^ (spPow - 2); + v = max(abs(1 - comp(:)), eps) .^ (spPow - 2); +end \ No newline at end of file diff --git a/visualizeEigenvectorRedGreen.m b/visualizeEigenvectorRedGreen.m new file mode 100644 index 0000000..718122e --- /dev/null +++ b/visualizeEigenvectorRedGreen.m @@ -0,0 +1,9 @@ + +function vis = visualizeEigenvectorRedGreen(eigenvector) + % negative values are shown in red, and positive in green + vis = zeros(size(eigenvector, 1), size(eigenvector, 2), 3); + vis(:,:,1) = -100 * eigenvector; + vis(:,:,2) = 100 * eigenvector; + vis(vis < 0) = 0; + vis(vis > 1) = 1; +end \ No newline at end of file diff --git a/visualizeSoftSegments.m b/visualizeSoftSegments.m new file mode 100644 index 0000000..5f14e84 --- /dev/null +++ b/visualizeSoftSegments.m @@ -0,0 +1,43 @@ + +% Assigns a distinct solid color to eact soft segment and composites +% them using the corresponding alpha calues + +function [vis, softSegments] = visualizeSoftSegments(softSegments, doOrdering) + if ~exist('doOrdering', 'var') || isempty(doOrdering) + doOrdering = false; + end + if doOrdering + % Order layers w.r.t. sum(alpha(:)) -- makes visualizations more consistent across images + order = determineAlphaOrder(softSegments); + softSegments = softSegments(:, :, order); + end + % A hard-coded set of 'distinct' colors + colors = createPalette(); + % One solid color per segment, mixed w.r.t. alpha values + vis = repmat(softSegments(:,:,1), [1 1 3]) .* repmat(colors(1,1,:), [size(softSegments, 1), size(softSegments, 2), 1]); + for i = 2 : size(softSegments, 3) + vis = vis + repmat(softSegments(:,:,i), [1 1 3]) .* repmat(colors(i,1,:), [size(softSegments, 1), size(softSegments, 2), 1]); + end +end + +function colors = createPalette() + % https://graphicdesign.stackexchange.com/questions/3682/where-can-i-find-a-large-palette-set-of-contrasting-colors-for-coloring-many-d + % From P. Green-Armytage (2010): A Colour Alphabet and the Limits of Colour Coding. + % Colour: Design & Creativity (5) (2010): 10, 1-23 + % http://eleanormaclure.files.wordpress.com/2011/03/colour-coding.pdf + colors = reshape(... + [0,117,220; 255,255,128; 43,206,72; 153,0,0; 128,128,128; 240,163,255; 153,63,0; 76,0,92;... + 0,92,49; 255,204,153; 148,255,181;... + 143,124,0; 157,204,0; 194,0,136; 0,51,128; 255,164,5;... + 255,168,187; 66,102,0; 255,0,16; 94,241,242; 0,153,143;... + 224,255,102; 116,10,255; 255,255,0; 255,80,5; 25,25,25]... + , [26, 1, 3]) / 255; + colors = [colors; colors]; +end + +function order = determineAlphaOrder(alphas) + alphas = sum(alphas, 1); + alphas = sum(alphas, 2); + alphas = reshape(alphas, [size(alphas, 3) 1]); + [~, order] = sort(alphas, 'descend'); +end \ No newline at end of file

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