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demo_inversion_3d_zsin.m
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demo_inversion_3d_zsin.m
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% demo_inversion_3d_zsin.m
%
% 3D respiratory DVF inversion [1,2] demo script (3D-expanded 2D DVF;
% Z-axis deformation with sinusoidal profile).
%
% ----------------------------------------------------------------------
%
% Copyright (C) 2018, Department of Computer Science, Duke University
%
% This program is free software: you can redistribute it and/or modify it
% under the terms of the GNU General Public License as published by the
% Free Software Foundation, either version 3 of the License, or (at your
% option) any later version.
%
% This program is distributed in the hope that it will be useful, but
% WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General
% Public License for more details.
%
% You should have received a copy of the GNU General Public License along
% with this program. If not, see <https://www.gnu.org/licenses/>.
%
% ----------------------------------------------------------------------
%
% REFERENCES
%
% [1] A. Dubey*, A.-S. Iliopoulos*, X. Sun, F.-F. Yin, and L. Ren,
% "Iterative inversion of deformation vector fields with feedback
% control," Medical Physics, vol. 45, no. 7, pp. 3147-3160, 2018.
% - DOI: 10.1002/mp.12962
% - arXiv: 1610.08589 [cs.CV]
%
% [2] A. Dubey, "Symmetric completion of deformable registration via
% bi-residual inversion," PhD thesis, Duke University, Durham, NC, USA,
% 2018.
%
%% ==================== CLEAN UP
clear variables
close all
%% ==================== PARAMETERS
% example CT and DVF data
pathData = 'data/c-deformation.mat';
ioData = matfile( pathData );
F = ioData.F;
[szDom, ~] = dvf.sizeVf( F );
% 2D-to-3D DVF embedding
zdim = 15;
F = repmat( F, [1 1 1 zdim] ); % (NX x NY x 2 x NZ)
F = permute( F, [1 2 4 3] ); % (NX x NY x NZ x 2)
F = cat( 4, F, 3*ones( [szDom zdim] ) ); % (NX x NY x NZ x 3)
szDom = [szDom zdim];
% sinusoidal displacement scaling along Z-axis
F(:,:,:,3) = F(:,:,:,3) .* ...
reshape( sin( linspace( 0 , pi,size(F,2)) ), 1, [], 1 ) .* ...
reshape(1+cos( linspace(-pi,3*pi,size(F,1)) ), [], 1, 1 ) .* ...
reshape( -cos( linspace( 0 , pi,size(F,3)) ), 1, 1, [] );
% inversion parameters
opt.control = 'midrange';
opt.scale = 1;
opt.numIteration = 20;
opt.stopThreshold = 1e-6;
opt.accThreshold = 0;
opt.InitialValue = [];
opt.Mask = dvf.maskDomain( F );
% create an array of inversion parameters to compare multiple results
opt = repmat( opt, [8 1] );
opt(1).control = 0.0; % constant mu = 0
opt(2).control = 0.5; % constant mu = 0.5
opt(3).control = 'alternating'; % alternating
opt(4).control = 'optimal'; % pointwise optimal
opt(5).control = 'midrange'; % local midrange
opt(6).control = 'midrange'; % local midrange & acc.
opt(6).accThreshold = 1; % .
opt(7).control = 'midrange'; % local midrange & acc. & multiscale
opt(7).accThreshold = 1; % .
opt(7).scale = [0.5, 1.0]; % .
opt(7).numIteration = [4 16]; % .
opt(8).control = 'optimal'; % pointwise optimal & acc. & multiscale
opt(8).accThreshold = 1; % .
opt(8).scale = [0.5, 1.0]; % .
opt(8).numIteration = [4 16]; % .
% legend labels for each control setting
lgnd = {'\mu = 0', '\mu = 0.5', '\mu_{oe}', '\mu_*(x)', '\mu_m(x)', ...
'\mu_m(x) & acc', '\mu_m(x) & acc & MS', '\mu_*(x) & acc & MS'};
% slices for image and spectral measure maps visualization
slices = [108 51 10]; %14];
% IC residual percentile curve visualization options
prcIcMeasure = [50 90 95 98 100];
argVisIcCurve = {'-o', 'LineWidth', 2};
clrIcCurve = [0.8650 0.8110 0.4330; % yellow
0.9718 0.5553 0.7741; % pink
0.6859 0.4035 0.2412; % brown
1.0000 0.5482 0.1000; % orange
0.6365 0.3753 0.6753; % purple
0.3718 0.7176 0.3612; % green
0.2941 0.5447 0.7494; % blue
0.9047 0.1918 0.1988]; % red
% IC residual maps visualization options
zIdx = slices(3);
climIcMgn = [0 1]; % color-axis limits
% image-space visualization options
climImg = [-1 1]; % color-axis limits
%% ==================== (BEGIN)
fprintf( '\n***** BEGIN (%s) *****\n\n', mfilename );
%% ==================== VISUALIZATION: REFERENCE & STUDY IMAGES
fprintf( '...visualizing synthetic reference and study images...\n' );
IRef = util.imageGridSmooth( szDom, [15 15 5] );
IStd = dvf.imdeform( IRef, F );
hFig = vis.mfigure;
hFig.Name = 'reference and study (deformed) images';
% reference image
vis.imageSlices( IRef, 'slices', slices, 'colormap', gray, ...
'title', 'reference image', 'caxis', climImg, ...
'rows', 2, 'columns', 3, 'startIndex', 1 );
% study (deformed) image
vis.imageSlices( IStd, 'slices', slices, 'colormap', gray, ...
'title', 'study image', 'caxis', climImg, ...
'rows', 2, 'columns', 3, 'startIndex', 4 );
%% ==================== VISUALIZATION: SPECTRAL NTDC MEASURES
fprintf( '...calculating & visualizing spectral NTDC measures...\n' );
[CtrlIdx, Rho, Det, Lambda] = dvf.ntdcMeasures( F );
hFig = vis.mfigure;
hFig.Name = 'spectral NTDC measures of forward DVF';
% control index
vis.imageSlices( CtrlIdx, 'slices', slices, 'colormap', jet, ...
'title', 'algebraic control index', ...
'rows', 3, 'columns', 3, 'startIndex', 1 );
% NTDC spectral radius
vis.imageSlices( Rho, 'slices', slices, 'colormap', jet, ...
'title', 'NTDC spectral radius', ...
'rows', 3, 'columns', 3, 'startIndex', 4 );
% determinant map
vis.imageSlices( Det, 'slices', slices, 'colormap', jet, ...
'title', 'determinant map', ...
'rows', 3, 'columns', 3, 'startIndex', 7 );
%% ==================== INVERSION
fprintf( '...computing inverse with %d iteration schemes...\n', length(opt) );
G = cell( size(opt) );
prctRG = cell( size(opt) );
prctRF = cell( size(opt) );
RG = cell( size(opt) );
RF = cell( size(opt) );
for i = 1 : length(opt)
fprintf( ' - scheme #%d (%s)...\n', i, lgnd{i} );
opt(i).control = dvf.feedbackControlVal( Lambda, opt(i).control );
[G{i}, ~, ~, prctRG{i}, prctRF{i}] = dvf.inversion( F, opt(i) );
RG{i} = dvf.icResidual( G{i}, F );
RF{i} = dvf.icResidual( F, G{i} );
end
%% ==================== VISUALIZATION: IC RESIDUALS PER ITERATION
fprintf( '...visualizing step-wise IC residual percentile curves...\n' );
% resolution-normalized iteration steps
kstep = cell( size(opt) );
for i = 1 : length(opt)
kstep{i} = arrayfun( @(s,k) repmat( s^2 + (s~=1)/k, [1 k] ), ...
opt(i).scale, opt(i).numIteration, ...
'UniformOutput', false );
kstep{i} = cumsum( horzcat( 0, kstep{i}{:} ) );
end
hFig = vis.mfigure;
hFig.Name = 'step-wise IC residual percentile curves';
numPrct = length( prcIcMeasure );
% legend
subplot( 5, numPrct, (1:numPrct), ...
'NextPlot', 'ReplaceChildren', 'ColorOrder', clrIcCurve )
plot( nan( 2, length(opt) ), argVisIcCurve{:} );
title( 'step-wise IC residual percentile curves' )
legend( lgnd, 'Orientation', 'horizontal', 'Location', 'south' )
axis( gca, 'off' )
drawnow
for p = 1 : numPrct % ---- each percentile
% srudy IC residuals
subplot( 5, numPrct, p + (1:2)*numPrct )
hold on
for i = 1 : length(opt)
plot( kstep{i}, prctRG{i}(p,:), argVisIcCurve{:}, ...
'Color', clrIcCurve(i,:) );
end
ylabel( sprintf( 's_k[%d%%]', prcIcMeasure(p) ) );
xlabel( 'amortizerd iteration step (k)' )
set( gca, 'YScale', 'log' )
grid on
drawnow
% reference IC residuals
subplot( 5, numPrct, p + (3:4)*numPrct )
hold on
for i = 1 : length(opt)
plot( kstep{i}, prctRF{i}(p,:), argVisIcCurve{:}, ...
'Color', clrIcCurve(i,:) );
end
ylabel( sprintf( 'r_k[%d%%]', prcIcMeasure(p) ) );
xlabel( 'amortized iteration step (k)' )
set( gca, 'YScale', 'log' )
grid on
drawnow
end % for (p)
%% ==================== VISUALIZATION: IC RESIDUAL MAPS
fprintf( '...visualizing final IC residual maps...\n' );
fprintf( ' - white pixels indicate NaN (out-of-bounds) values\n' );
% calculate point-wise IC residual magnitudes
RGMgn = cellfun( @(r) sqrt( sum( r.^2, 4 ) ), RG, 'UniformOutput', false );
RFMgn = cellfun( @(r) sqrt( sum( r.^2, 4 ) ), RF, 'UniformOutput', false );
% study IC residuals
hFig = vis.mfigure;
hFig.Name = 'study IC residual maps';
for i = 1 : length(opt)
subplot( 2, 4, i )
pcolor( RGMgn{i}(:,:,zIdx).' )
axis image
shading flat
colormap jet
caxis( climIcMgn )
colorbar
title( {sprintf( 'study IC residuals (%s)', lgnd{i} ), ...
sprintf( '(axial slice z = %d)', zIdx )} )
drawnow
end
% reference IC residuals
hFig = vis.mfigure;
hFig.Name = 'reference IC residual maps';
for i = 1 : length(opt)
subplot( 2, 4, i )
pcolor( RFMgn{i}(:,:,zIdx).' )
axis image
shading flat
colormap jet
caxis( climIcMgn )
colorbar
title( {sprintf( 'reference IC residuals (%s)', lgnd{i} ), ...
sprintf( '(axial slice z = %d)', zIdx )} )
drawnow
end
%% ==================== VISUALIZATION: RECOVERED REFERENCE IMAGE
fprintf( '...reference image recovery...\n' );
fprintf( ' - I_rec(x) := I_std(x + v(x))\t' );
fprintf( ' [I_std(y) = I_ref(y + u(y))]\n' );
fprintf( ' = I_ref(x + v(x) + u(x + v(x)))\n' );
fprintf( ' = I_ref(x + s(x))\n' );
% ---------- calculation
fprintf( ' - calculation...\n' );
IRefRec = cell( size(opt) );
for i = 1 : length(opt)
IRefRec{i} = dvf.imdeform( IRef, RG{i} );
end
% ---------- visualization
fprintf( ' - difference image visualization (I_ref - I_rec)...\n' );
hFig = vis.mfigure;
hFig.Name = 'image-space errors in reference image recovery';
for i = 1 : length(opt)
subplot( 2, 4, i )
pcolor( (IRef(:,:,zIdx) - IRefRec{i}(:,:,zIdx)).' );
axis image
shading flat
caxis( climImg )
colormap parula
colorbar
title( {lgnd{i}, 'I_{ref}(x) - I_{ref}(x+s(x))'} )
drawnow
end
%% ==================== (END)
fprintf( '\n***** END (%s) *****\n\n', mfilename );
%%------------------------------------------------------------
%
% AUTHORS
%
% Alexandros-Stavros Iliopoulos [email protected]
%
% RELEASE
%
% 1.0.2 - December 21, 2018
%
% ------------------------------------------------------------