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‎eval/GCE.m

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function [GCE_score] = GCE( assig1, assig2 )
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k1 = max( assig1 ); % number clusters
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k2 = max( assig2 );
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n = length( assig1 ); % nuber data points
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confusion = zeros( k1, k2 ); % build confusion matrix
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for i1 = 1:k1;
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for i2 = 1:k2;
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confusion( i1, i2 ) = length( find( (assig1 == i1) & (assig2 == i2 )));
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end;
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end;
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GCE_score1 = 0; GCE_score2 = 0;
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for i1 = 1:k1;
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for i2 = 1:k2;
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idx1 = find(assig1== i1);
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idx2 = find(assig2== i2);
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diff_idx1 = setdiff(idx1,idx2);
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diff_idx2 = setdiff(idx2,idx1);
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GCE_score1 = GCE_score1 + size(diff_idx1,1)*confusion( i1, i2 )/size(idx1,1);
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GCE_score2 = GCE_score2 + size(diff_idx2,1)*confusion( i1, i2 )/size(idx2,1);
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clear idx1 idx2
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end;
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end;
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GCE_score = min(GCE_score1,GCE_score2)/n;

‎eval/Rand_index.m

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function ri=Rand_index(sampleLabels1,sampleLabels2)
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% compare_segmentations
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%
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% Computes several simple segmentation benchmarks. Written for use with
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% images, but works for generic segmentation as well (i.e. if the
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% sampleLabels inputs are just lists of labels, rather than rectangular
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% arrays).
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%
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% The measures:
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% Rand Index
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%
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% The Rand Index can be easily extended to the Probabilistic Rand Index
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% by averaging the result across all human segmentations of a given
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% image:
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% PRI = 1/K sum_1^K RI( seg, humanSeg_K ).
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% With a little more work, this can also be extended to the Normalized
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% PRI.
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%
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% Inputs:
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% sampleLabels1 - n x m array whose entries are integers between 1
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% and K1
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% sampleLabels2 - n x m (sample size as sampleLabels1) array whose
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% entries are integers between 1 and K2 (not
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% necessarily the same as K1).
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% Outputs:
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% ri - Rand Index
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% gce - Global Consistency Error
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% vi - Variation of Information
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%
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% NOTE:
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% There are a few formulas here that look less-straightforward (e.g.
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% the log2_quotient function). These exist to handle corner cases
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% where some of the groups are empty, and quantities like 0 *
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% log(0/0) arise...
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%
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% Oct. 2006
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% Questions? John Wright - [email protected]
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[imWidth,imHeight]=size(sampleLabels1);
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[imWidth2,imHeight2]=size(sampleLabels2);
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N=imWidth*imHeight;
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if (imWidth~=imWidth2)||(imHeight~=imHeight2)
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disp( 'Input sizes: ' );
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disp( size(sampleLabels1) );
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disp( size(sampleLabels2) );
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error('Input sizes do not match in compare_segmentations.m');
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end;
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% make the group indices start at 1
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if min(min(sampleLabels1)) < 1
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sampleLabels1 = sampleLabels1 - min(min(sampleLabels1)) + 1;
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end
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if min(min(sampleLabels2)) < 1
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sampleLabels2 = sampleLabels2 - min(min(sampleLabels2)) + 1;
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end
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segmentcount1=max(max(sampleLabels1));
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segmentcount2=max(max(sampleLabels2));
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% compute the count matrix
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% from this we can quickly compute rand index, GCE, VOI, ect...
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n=zeros(segmentcount1,segmentcount2);
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for i=1:imWidth
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for j=1:imHeight
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u=sampleLabels1(i,j);
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v=sampleLabels2(i,j);
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n(u,v)=n(u,v)+1;
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end;
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end;
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ri = rand_index(n);
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return;
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% the performance measures
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% the rand index, in [0,1] ... higher => better
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% fast computation is based on equation (2.2) of Rand's paper.
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function ri = rand_index(n)
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N = sum(sum(n));
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n_u=sum(n,2);
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n_v=sum(n,1);
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N_choose_2=N*(N-1)/2;
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ri = 1 - ( sum(n_u .* n_u)/2 + sum(n_v .* n_v)/2 - sum(sum(n.*n)) )/N_choose_2;
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% log2_quotient
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% helper function for computing the mutual information
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% returns a matrix whose ij entry is
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% log2( a_ij / b_ij ) if a_ij, b_ij > 0
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% 0 if a_ij is 0
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% log2( a_ij + 1 ) if a_ij > 0 but b_ij = 0 (this behavior should
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% not be encountered in practice!
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function lq = log2_quotient( A, B )
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lq = log2( (A + ((A==0).*B) + (B==0)) ./ (B + (B==0)) );

‎eval/VI.m

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function [ distance, H1given2, H2given1, I12 ] = VI( assig1, assig2 )
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%function distance = VI( assig1, assig2 )
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%
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% Computes the Variation of Information distance between two clusterings
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% given by assig1,2. The values in assig1 must range between 1 and k1,
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% the number of clusters in assig1. Similarly for assig2.
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%
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%
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%assig1, assig2(1,n) = vectors of integers from 1:k that represent the
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% assignment to clusters. must have the same length
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%
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k1 = max( assig1 ); % number clusters
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k2 = max( assig2 );
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n = length( assig1 ); % nuber data points
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confusion = zeros( k1, k2 ); % build confusion matrix
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for i1 = 1:k1;
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for i2 = 1:k2;
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confusion( i1, i2 ) = length( find( (assig1 == i1) & (assig2 == i2 )));
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end;
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end;
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confusion = confusion/n;
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p1 = sum( confusion, 1 );
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p2 = sum( confusion, 2 );
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idummy = find( confusion > 0 );
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pdummy = p2*p1;
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cdummy = confusion;
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cdummy( idummy ) = confusion( idummy )./pdummy( idummy );
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I12 = sum( sum( confusion.* locallog( cdummy )));
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H1given2 = -sum( p1.*locallog( p1 ))-I12;
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H2given1 = -sum( p2.*locallog( p2 ))-I12;
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distance = H1given2 + H2given1;
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%distance = -sum( p1.*locallog( p1 ))-sum( p2.*locallog( p2 ))-2*sum( sum( confusion.* locallog( cdummy )));
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distance = distance/log(2);
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I12 = I12/log(2);
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H1given2 = H1given2/log(2);
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H2given1 = H2given1/log(2);
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‎eval/compare_image_boundary_error.m

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%A MATLAB Toolbox
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%
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%Compare two segmentation results using the Boundary Displacement Error
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%
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%IMPORTANT: The input two images must have the same size!
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%
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%Authors: John Wright, and Allen Y. Yang
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%Contact: Allen Y. Yang <[email protected]>
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%
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%(c) Copyright. University of California, Berkeley. 2007.
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%
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%Notice: The packages should NOT be used for any commercial purposes
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%without direct consent of their author(s). The authors are not responsible
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%for any potential property loss or damage caused directly or indirectly by the usage of the software.
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function [averageError, returnStatus] = compare_image_boundary_error(imageLabels1, imageLabels2);
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returnStatus = 0;
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[imageX, imageY] = size(imageLabels1);
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if imageX~=size(imageLabels2,1) | imageY~=size(imageLabels2,2)
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error('The sizes of the two comparing images must be the same.');
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end
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if isempty(find(imageLabels1~=imageLabels1(1)))
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% imageLabels1 only has one group
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boundary1 = zeros(size(imageLabels1));
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boundary1(1,:) = 1;
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boundary1(:,1) = 1;
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boundary1(end,:) = 1;
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boundary1(:,end) = 1;
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else
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% Generate boundary maps
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[cx,cy] = gradient(imageLabels1);
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[boundaryPixelX{1},boundaryPixelY{1}] = find((abs(cx)+abs(cy))~=0);
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boundary1 = abs(cx) + abs(cy) > 0;
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end
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if isempty(find(imageLabels2~=imageLabels2(1)))
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% imageLabels2 only has one group
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boundary2 = zeros(size(imageLabels2));
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boundary2(1,:) = 1;
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boundary2(:,1) = 1;
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boundary2(end,:) = 1;
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boundary2(:,end) = 1;
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else
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% Generate boundary maps
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[cx,cy] = gradient(imageLabels2);
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[boundaryPixelX{2},boundaryPixelY{2}] = find((abs(cx)+abs(cy))~=0);
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boundary2 = abs(cx) + abs(cy) > 0;
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end
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% boundary1 and boundary2 are now binary boundary masks. compute their
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% distance transforms:
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D1 = bwdist(boundary1);
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D2 = bwdist(boundary2);
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% compute the distance of the pixels in boundary1 to the nearest pixel in
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% boundary2:
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dist_12 = sum(sum(boundary1 .* D2 ));
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dist_21 = sum(sum(boundary2 .* D1 ));
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avgError_12 = dist_12 / sum(sum(boundary1));
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avgError_21 = dist_21 / sum(sum(boundary2));
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averageError = (avgError_12 + avgError_21) / 2;

‎eval/compare_segmentations.m

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%A MATLAB Toolbox
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%
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%Compare two segmentation results using
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%1. Probabilistic Rand Index
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%2. Variation of Information
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%3. Global Consistency Error
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%
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%IMPORTANT: The two input images must have the same size!
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%
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%Authors: John Wright, and Allen Y. Yang
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%Contact: Allen Y. Yang <[email protected]>
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%
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%(c) Copyright. University of California, Berkeley. 2007.
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%
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%Notice: The packages should NOT be used for any commercial purposes
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%without direct consent of their author(s). The authors are not responsible
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%for any potential property loss or damage caused directly or indirectly by the usage of the software.
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function [ri,gce,vi]=compare_segmentations(sampleLabels1,sampleLabels2)
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% compare_segmentations
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%
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% Computes several simple segmentation benchmarks. Written for use with
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% images, but works for generic segmentation as well (i.e. if the
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% sampleLabels inputs are just lists of labels, rather than rectangular
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% arrays).
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%
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% The measures:
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% Rand Index
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% Global Consistency Error
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% Variation of Information
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%
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% The Rand Index can be easily extended to the Probabilistic Rand Index
34+
% by averaging the result across all human segmentations of a given
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% image:
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% PRI = 1/K sum_1^K RI( seg, humanSeg_K ).
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% With a little more work, this can also be extended to the Normalized
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% PRI.
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%
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% Inputs:
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% sampleLabels1 - n x m array whose entries are integers between 1
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% and K1
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% sampleLabels2 - n x m (sample size as sampleLabels1) array whose
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% entries are integers between 1 and K2 (not
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% necessarily the same as K1).
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% Outputs:
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% ri - Rand Index
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% gce - Global Consistency Error
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% vi - Variation of Information
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%
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% NOTE:
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% There are a few formulas here that look less-straightforward (e.g.
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% the log2_quotient function). These exist to handle corner cases
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% where some of the groups are empty, and quantities like 0 *
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% log(0/0) arise...
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%
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% Oct. 2006
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% Questions? John Wright - [email protected]
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[imWidth,imHeight]=size(sampleLabels1);
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[imWidth2,imHeight2]=size(sampleLabels2);
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N=imWidth*imHeight;
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if (imWidth~=imWidth2)||(imHeight~=imHeight2)
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disp( 'Input sizes: ' );
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disp( size(sampleLabels1) );
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disp( size(sampleLabels2) );
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error('Input sizes do not match in compare_segmentations.m');
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end;
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% make the group indices start at 1
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if min(min(sampleLabels1)) < 1
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sampleLabels1 = sampleLabels1 - min(min(sampleLabels1)) + 1;
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end
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if min(min(sampleLabels2)) < 1
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sampleLabels2 = sampleLabels2 - min(min(sampleLabels2)) + 1;
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end
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segmentcount1=max(max(sampleLabels1));
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segmentcount2=max(max(sampleLabels2));
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% compute the count matrix
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% from this we can quickly compute rand index, GCE, VOI, ect...
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n=zeros(segmentcount1,segmentcount2);
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for i=1:imWidth
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for j=1:imHeight
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u=sampleLabels1(i,j);
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v=sampleLabels2(i,j);
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n(u,v)=n(u,v)+1;
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end;
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end;
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ri = rand_index(n);
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gce = global_consistancy_error(n);
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vi = variation_of_information(n);
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return;
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% the performance measures
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% the rand index, in [0,1] ... higher => better
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% fast computation is based on equation (2.2) of Rand's paper.
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function ri = rand_index(n)
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N = sum(sum(n));
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n_u=sum(n,2);
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n_v=sum(n,1);
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N_choose_2=N*(N-1)/2;
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ri = 1 - ( sum(n_u .* n_u)/2 + sum(n_v .* n_v)/2 - sum(sum(n.*n)) )/N_choose_2;
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% global consistancy error (from BSDS ICCV 01 paper) ... lower => better
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function gce = global_consistancy_error(n)
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N = sum(sum(n));
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marginal_1 = sum(n,2);
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marginal_2 = sum(n,1);
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% the hackery is to protect against cases where some of the marginals are
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% zero (should never happen, but seems to...)
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E1 = 1 - sum( sum(n.*n,2) ./ (marginal_1 + (marginal_1 == 0)) ) / N;
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E2 = 1 - sum( sum(n.*n,1) ./ (marginal_2 + (marginal_2 == 0)) ) / N;
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gce = min( E1, E2 );
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% variation of information a "distance", in (0,vi_max] ... lower => better
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function vi = variation_of_information(n)
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N = sum(sum(n));
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joint = n / N; % the joint pmf of the two labels
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marginal_2 = sum(joint,1); % row vector
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marginal_1 = sum(joint,2); % column vector
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H1 = - sum( marginal_1 .* log2(marginal_1 + (marginal_1 == 0) ) ); % entropy of the first label
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H2 = - sum( marginal_2 .* log2(marginal_2 + (marginal_2 == 0) ) ); % entropy of the second label
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MI = sum(sum( joint .* log2_quotient( joint, marginal_1*marginal_2 ) )); % mutual information
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vi = H1 + H2 - 2 * MI;
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% log2_quotient
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% helper function for computing the mutual information
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% returns a matrix whose ij entry is
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% log2( a_ij / b_ij ) if a_ij, b_ij > 0
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% 0 if a_ij is 0
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% log2( a_ij + 1 ) if a_ij > 0 but b_ij = 0 (this behavior should
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% not be encountered in practice!
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function lq = log2_quotient( A, B )
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lq = log2( (A + ((A==0).*B) + (B==0)) ./ (B + (B==0)) );

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