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SLIC_3D.m
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function [sv_image, SV_Centers ] = SLIC_3D( volume_image, expected_sv_number, bg_threshold, is_EnforeConnectivity, m_weight )
%% Feb 20, 2014
% Sam Kong
% Get segment labels of the image using slic
% For 2D Grey Image
%% main function
[ volume_width, volume_height, volume_slice] = size( volume_image );
supervoxel_size = ( volume_width * volume_height * volume_slice) / expected_sv_number;
supervoxel_step = floor( supervoxel_size^(1/3));
width_strips = round( 0.5 + volume_width / supervoxel_step );
height_strips = round( 0.5 + volume_height / supervoxel_step );
slice_strips = round( 0.5 + volume_slice / supervoxel_step );
%% compute seeds
width_err = volume_width - supervoxel_step * width_strips;
height_err = volume_height - supervoxel_step * height_strips;
slice_err = volume_slice - supervoxel_step * slice_strips;
if width_err < 0
width_strips = width_strips - 1;
width_err = volume_width - supervoxel_step * width_strips;
end
if height_err < 0
height_strips = height_strips - 1;
height_err = volume_height - supervoxel_step * height_strips;
end
if slice_err < 0
slice_strips = slice_strips - 1;
slice_err = volume_slice - supervoxel_step * slice_strips;
end
width_errperstrip = width_err / width_strips;
height_errperstrip = height_err / height_strips;
slice_errperstrip = slice_err / slice_strips;
width_off = supervoxel_step / 2;
height_off = supervoxel_step / 2;
slice_off = supervoxel_step / 2;
segmentseeds = zeros(expected_sv_number, 4);
supervoxel_number = 0;
for k = 1: slice_strips
slice_e = ( k - 1 ) * slice_errperstrip;
seed_k = floor( ( k - 1 ) * supervoxel_step + slice_off + slice_e );
for j = 1:height_strips
height_e = ( j - 1 ) * height_errperstrip;
seed_j = floor( ( j - 1) * supervoxel_step + height_off + height_e );
for i = 1:width_strips
width_e = ( i - 1 ) * width_errperstrip;
seed_i = floor( ( i - 1) * supervoxel_step + width_off + width_e );
seed_intensity = volume_image( seed_i, seed_j, seed_k );
if seed_intensity>bg_threshold
supervoxel_number = supervoxel_number + 1;
segmentseeds( supervoxel_number , : ) = [ seed_i, seed_j, seed_k, seed_intensity ];
end
end
end
end
segmentseeds = segmentseeds(1:supervoxel_number, :);
%%Pertube seeds
%segmentseeds = perturbSeeds( volume_image, segmentseeds, bg_threshold );
%% Assign segments
error_threshold = round (expected_sv_number*0.01);
sv_image = zeros( volume_width, volume_height, volume_slice ) - 1;
mat_voxel_distance = zeros( volume_width, volume_height, volume_slice) + inf;
for iter = 1:10
% assign labels
% iter
for m = 1:supervoxel_number
seed_i = segmentseeds( m, 1 );
seed_j = segmentseeds( m, 2 );
seed_k = segmentseeds( m, 3 );
seed_intensity = segmentseeds(m, 4);
i_left = seed_i - round( supervoxel_step*0.8 );
i_right = seed_i + round( supervoxel_step*0.8 );
j_left = seed_j - round( supervoxel_step*0.8 );
j_right = seed_j + round( supervoxel_step*0.8 );
k_left = seed_k - round( supervoxel_step*0.8 );
k_right = seed_k + round( supervoxel_step*0.8 );
i_left = max( i_left, 2);
i_right = min( i_right, volume_width - 1);
j_left = max( j_left, 2);
j_right = min( j_right, volume_height -1);
k_left = max( k_left, 2);
k_right = min( k_right, volume_slice -1);
for voxel_k = k_left:k_right
for voxel_j = j_left:j_right
for voxel_i = i_left:i_right
voxel_intensity = volume_image( voxel_i , voxel_j, voxel_k );
if voxel_intensity>bg_threshold
distance_spatial = sqrt( ( seed_i - voxel_i)^2 + (seed_j - voxel_j)^2 + (seed_k - voxel_k)^2 );
distance_intensity = abs( seed_intensity - voxel_intensity );
distance_np = distance_intensity + 2* distance_spatial * m_weight / supervoxel_step;
if distance_np < mat_voxel_distance( voxel_i , voxel_j, voxel_k )
mat_voxel_distance( voxel_i , voxel_j, voxel_k ) = distance_np;
sv_image( voxel_i , voxel_j, voxel_k ) = m;
end
end
end
end
end
end
% recompute seeds
sigma_i = zeros( 1, supervoxel_number );
sigma_j = zeros( 1, supervoxel_number );
sigma_k = zeros( 1, supervoxel_number );
sigma_intensity = zeros( 1, supervoxel_number );
sigma_voxelnumber = zeros( 1, supervoxel_number );
for voxel_k = 1:volume_slice
for voxel_j = 1:volume_height
for voxel_i = 1:volume_width
voxel_label = sv_image( voxel_i , voxel_j, voxel_k );
if voxel_label>0
voxel_intensity = volume_image( voxel_i , voxel_j, voxel_k );
sigma_i( voxel_label ) = sigma_i( voxel_label ) + voxel_i;
sigma_j( voxel_label ) = sigma_j( voxel_label ) + voxel_j;
sigma_k( voxel_label ) = sigma_k( voxel_label ) + voxel_k;
sigma_intensity( voxel_label ) = sigma_intensity( voxel_label ) + voxel_intensity;
sigma_voxelnumber( voxel_label) = sigma_voxelnumber( voxel_label) + 1;
end
end
end
end
sigma_voxelnumber( sigma_voxelnumber<1) = 1;
i_segmentseeds = segmentseeds;
i_segmentseeds(:,1) = round ( sigma_i./sigma_voxelnumber );
i_segmentseeds(:,2) = round ( sigma_j./sigma_voxelnumber );
i_segmentseeds(:,3) = round ( sigma_k./sigma_voxelnumber );
i_segmentseeds(:,4) = sigma_intensity./sigma_voxelnumber;
%check error
i_seederror = abs(i_segmentseeds(:,1:3) - segmentseeds(:,1:3));
i_seederror_sum = sum( i_seederror(:));
segmentseeds = i_segmentseeds;
%i_seederror_sum
if i_seederror_sum < error_threshold
break;
end
end
% SV_Centers = segmentseeds( :, 1:3 );
%% Enforce Connectivity
if is_EnforeConnectivity == true
widthNeighbour = [ -1, 0, 1, 0, 1, 1, -1, -1, 0, 0 ];
heightNeighbour = [ 0, -1, 0, 1, -1, 1, 1, -1, 0, 0 ];
sliceNeighbour = [ 0, 0, 0, 0, 0, 0, 0, 0, 1, -1];
sv_image_en = zeros( volume_width, volume_height, volume_slice ) - 1;
voxel_i_vec = zeros( 1, volume_width * volume_height * volume_slice );
voxel_j_vec = zeros( 1, volume_width * volume_height * volume_slice );
voxel_k_vec = zeros( 1, volume_width * volume_height * volume_slice );
adj_label = 1;
label = 1;
for voxel_k = 1: volume_slice
for voxel_j = 1:volume_height
for voxel_i = 1:volume_width
if 1 > sv_image_en( voxel_i, voxel_j, voxel_k ) && volume_image( voxel_i, voxel_j, voxel_k ) > bg_threshold
sv_image_en( voxel_i, voxel_j, voxel_k ) = label;
voxel_i_vec(1) = voxel_i;
voxel_j_vec(1) = voxel_j;
voxel_k_vec(1) = voxel_k;
for n = 1:length(widthNeighbour)
voxel_x = voxel_i_vec(1) + widthNeighbour(n);
voxel_y = voxel_j_vec(1) + heightNeighbour(n);
voxel_z = voxel_k_vec(1) + sliceNeighbour(n);
if ( voxel_x>=1 && voxel_x<=volume_width ) &&( voxel_y>=1 && voxel_y<=volume_height ) &&( voxel_z>=1 && voxel_z<=volume_slice )
if sv_image_en( voxel_x, voxel_y, voxel_z ) >= 1 && volume_image( voxel_i, voxel_j, voxel_k ) > bg_threshold
adj_label = sv_image_en( voxel_x, voxel_y, voxel_z );
end
end
end
voxel_count = 1;
c = 1;
while c<=voxel_count
for n=1:length(widthNeighbour)
voxel_x = voxel_i_vec(c) + widthNeighbour(n);
voxel_y = voxel_j_vec(c) + heightNeighbour(n);
voxel_z = voxel_k_vec(c) + sliceNeighbour(n);
if ( voxel_x>=1 && voxel_x<=volume_width ) &&( voxel_y>=1 && voxel_y<=volume_height )&&( voxel_z>=1 && voxel_z<=volume_slice )
if volume_image( voxel_x, voxel_y, voxel_z ) > bg_threshold && 1>sv_image_en( voxel_x, voxel_y, voxel_z ) && sv_image( voxel_x, voxel_y, voxel_z )==sv_image( voxel_i, voxel_j, voxel_k )
voxel_count = voxel_count +1;
voxel_i_vec(voxel_count) = voxel_x;
voxel_j_vec(voxel_count) = voxel_y;
voxel_k_vec(voxel_count) = voxel_z;
sv_image_en( voxel_x, voxel_y, voxel_z ) = label;
end
end
end
c = c +1;
end
% voxel_count
if voxel_count< round( supervoxel_size/5 )
% if voxel_count< 5
for c = 1:voxel_count
sv_image_en( voxel_i_vec(c), voxel_j_vec(c), voxel_k_vec(c) ) = adj_label;
end
label = label -1;
end
label = label +1;
end
end
end
end
sv_image = sv_image_en;
end
supervoxel_number = max( sv_image(:) );
SV_Centers = zeros( supervoxel_number, 3 );
sigma_i = zeros( 1, supervoxel_number );
sigma_j = zeros( 1, supervoxel_number );
sigma_k = zeros( 1, supervoxel_number );
temp = zeros( 1, supervoxel_number );
temp(1:length(sigma_intensity)) = sigma_intensity ;
sigma_intensity = temp;
sigma_voxelnumber = zeros( 1, supervoxel_number );
for voxel_k = 1:volume_slice
for voxel_j = 1:volume_height
for voxel_i = 1:volume_width
voxel_label = sv_image( voxel_i , voxel_j, voxel_k );
if voxel_label>0
voxel_intensity = volume_image( voxel_i , voxel_j, voxel_k );
sigma_i( voxel_label ) = sigma_i( voxel_label ) + voxel_i;
sigma_j( voxel_label ) = sigma_j( voxel_label ) + voxel_j;
sigma_k( voxel_label ) = sigma_k( voxel_label ) + voxel_k;
sigma_intensity( voxel_label ) = sigma_intensity( voxel_label ) + voxel_intensity;
sigma_voxelnumber( voxel_label) = sigma_voxelnumber( voxel_label) + 1;
end
end
end
end
sigma_voxelnumber( sigma_voxelnumber<1) = 1;
SV_Centers(:,1) = round ( sigma_i./sigma_voxelnumber );
SV_Centers(:,2) = round ( sigma_j./sigma_voxelnumber );
SV_Centers(:,3) = round ( sigma_k./sigma_voxelnumber );
end