From bc032feee9ff3c32748cbf4972217c24927d2ab0 Mon Sep 17 00:00:00 2001 From: Laila Saadatifard Date: Fri, 9 Oct 2015 09:47:20 -0500 Subject: [PATCH] first upload the 3d ivote code in matlab --- matlab-3d/blue.bmp | Bin 0 -> 6197882 bytes matlab-3d/gauss1d.m | 15 +++++++++++++++ matlab-3d/gauss_blur3d.m | 19 +++++++++++++++++++ matlab-3d/iblur.vol | Bin 0 -> 375000 bytes matlab-3d/img/0001.png | Bin 0 -> 132228 bytes matlab-3d/img/0002.png | Bin 0 -> 133320 bytes matlab-3d/img/0003.png | Bin 0 -> 133566 bytes matlab-3d/img/0004.png | Bin 0 -> 131374 bytes matlab-3d/img/0005.png | Bin 0 -> 131900 bytes matlab-3d/img/0006.png | Bin 0 -> 131204 bytes matlab-3d/img/0007.png | Bin 0 -> 126329 bytes matlab-3d/img/0008.png | Bin 0 -> 131004 bytes matlab-3d/img/0009.png | Bin 0 -> 131281 bytes matlab-3d/img/0010.png | Bin 0 -> 131237 bytes matlab-3d/img/0011.png | Bin 0 -> 131039 bytes matlab-3d/img/0012.png | Bin 0 -> 132789 bytes matlab-3d/img/0013.png | Bin 0 -> 128981 bytes 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a/matlab-3d/ivote2.vol b/matlab-3d/ivote2.vol new file mode 100644 index 0000000..326226a Binary files /dev/null and b/matlab-3d/ivote2.vol differ diff --git a/matlab-3d/ivote3.m b/matlab-3d/ivote3.m new file mode 100644 index 0000000..c049419 --- /dev/null +++ b/matlab-3d/ivote3.m @@ -0,0 +1,166 @@ +function [px, py] = ivote3(image, rmax, phi, iter, t0, sigma, t1) + +% This function performs iterative voting on an image in order to identify the centers of blobs + +% image = a matrix of values representing a 2D image +% rmax = estimated radius of a blob +% phi = angular range of the voting area (in radians) +% iter = number of iterations for voting +% sigma = standard deviation of the weighting filter used for voting +% t0 = initial gradient magnitude threshold (limits the # of voting pixels) +% t1 = final threshold for valid points + + + +dphi = phi / (iter); + + +%compute the gradient and gradient magnitude +[Igrad_x, Igrad_y] = gradient(image); +Igrad_mag = sqrt(Igrad_x.^2 + Igrad_y.^2); + +%represent the gradient direction in polar coordinates +Igrad_theta = atan2(Igrad_x,Igrad_y) + pi; + +%compute pixels that will be processed + +% calculate a mask representing the voting pixels +S = Igrad_mag > t0; + +Sx = size(S, 1); +Sy = size(S, 2); +S(1:rmax, :) = 0; +S(Sx - rmax:Sx, :) = 0; +S(:, 1:rmax) = 0; +S(:, Sy - rmax:Sy) = 0; + +%calculate the coordinates of all of the voting pixels + +[sx, sy] = find(S); %this provides a coordinate for each voter + +%eliminate pixels close to the image boundary + +nV = nnz(S); %calculate the number of valid pixels (voters) + +% create a meshgrid describing coordinates relative to the voter +% position +range = -rmax:rmax; +[Vx, Vy] = meshgrid(range, range); +%create a mask for the voting area +M_dist = Vx.^2 + Vy.^2 < rmax^2; +M_theta = atan2(Vx, Vy); + +pxPerRow = size(image,1); + +g_v_prime = zeros(nV, ceil(rmax^2*phi/3)); +validPoints = zeros(nV,1); + +for i = 1: iter + + t_iter = tic; + + %set the vote image to zeros + Ivote = zeros(size(image)); + + for v = 1:nV + + %determine the position of the current voter + vx = sx(v); + vy = sy(v); + + %determine the orientation (theta) of the current voter + vtheta = Igrad_theta(vx, vy); + + % find the angular distance between M_theta and V_theta at each + ang_diff = abs(M_theta - vtheta); + M_diff = min(2*pi - ang_diff,ang_diff) t0; + +%Set the boundaries of the threshold image to zero +It(1:rmax, :, :) = 0; +It(ps(1) - rmax:ps(1), :,:) = 0; +It(:, 1:rmax, :) = 0; +It(:, ps(2) - rmax:ps(2),:) = 0; +It(:, :, 1:rmax) = 0; +It(:,:, ps(3) - rmax:ps(3)) = 0; + +%get the indices of all of the nonzero values in the threshold image +% (voter positions) +[Itx,Ity,Itz] = ind2sub(size(It),find(It)); +Vi = find(It); +nV = nnz(It); + +% create a meshgrid describing coordinates relative to the voter position +range = -rmax:rmax; %create an array of values between -rmax and rmax +[mx, my, mz] = meshgrid(range, range, range); %create a template describing local pixel position in a small cube +m_mag = sqrt(mx.^2 + my.^2 + mz.^2); %create a template describing the distance from the center of a small cube + +% create a mask for the voting area +M_dist = m_mag <= rmax; %mask for the voting area distance (all values < rmax from the center) + +%calculate the direction vector between a pixel and voter +LV_x = mx./m_mag; +LV_y = my./m_mag; +LV_z = mz./m_mag; + +%number of pixels in the voting area of each voter (initialize to zero) +validPixels = (zeros(nV,1)); + +%indices of pixels in the voting area of each voter +% indices reference the 3D image +g_v_prime = (zeros(nV, (rmax^3))); + +%--------------Display current data------------------------- +% subplot(3, 3, 1), +% imagesc(squeeze(I(:, :, ceil(size(I, 3)/2)))); +% +% subplot(3, 3, 2), +% imagesc(squeeze(I(:, ceil(size(I, 2)/2), :))); +% +% subplot(3, 3, 3), +% imagesc(squeeze(I( ceil(size(I, 1)/2), :, :))); +% % +% subplot(3, 3, 4), +% imagesc(squeeze(Iblur(:, :, ceil(size(Iblur, 3)/2)))); +% +% subplot(3, 3, 5), +% imagesc(squeeze(Iblur(:, ceil(size(Iblur, 2)/2), :))); +% +% subplot(3, 3, 6), +% imagesc(squeeze(Iblur(ceil(size(Iblur, 1)/2), :, :))); +% +% subplot(3, 3, 7), +% imagesc(squeeze(Imag(:, :, ceil(size(Imag, 3)/2)))); +% +% subplot(3, 3, 8), +% imagesc(squeeze(Imag(:, ceil(size(Imag, 2)/2), :))); +% +% subplot(3, 3, 9), +% imagesc(squeeze(Imag(ceil(size(Imag, 1)/2), :, :))); +% +% colormap(gray); + +%% vote +tic; +%for each iteration (in iterative voting) +for itr = 1 : iter + + %initialize the vote image to zero + Ivote = (zeros(size(I))); + + %for each voter (nonzero pixels in the threshold image It) + for v = 1: nV + + %get the cartesian coordinates of the voter v in the main image I + vx = Itx(v); + vy = Ity(v); + vz = Itz(v); + vi = Vi(v); + + %retreive the gradient magnitude at the voter position + %vmag = Imag(vx,vy,vz); + vmag = Imag(vi); + + %retrieve the gradient + gx = Igrad_x(vi); + gy = Igrad_y(vi); + gz = Igrad_z(vi); + + %calculate the gradient magnitude + dmag = sqrt (gx^2 + gy^2 + gz^2); + + %calculate the normalized gradient direction + dx = gx / dmag; + dy = gy / dmag; + dz = gz / dmag; + + %calculate the angle between the voter direction and the pixel direction + cos_diff = LV_x .* dx + LV_y .* dy + LV_z .* dz; + ang_diff = acos(cos_diff); + + %create an angular mask for the voting area + M_angle = cos_diff > cos(ang); + + %combine the two masks to mask out the voting angle + M = M_angle .* M_dist; + + % get the coordinates of each pixel in the final voter mask M + pi = find(M); + + %calculate the number of pixels in the voting region + npts = nnz(M); + validPixels(v) = npts; + + %convert every index in the voting area from a local 3D index to a global 3D index (into the original image I) + global_px = vx + mx(pi); + global_py = vy + my(pi); + global_pz = vz + mz(pi); + + %convert the global 3D index of each point into a global 1D index + global_pi = sub2ind(ps, global_px, global_py, global_pz); + + g_v_prime (v, 1:npts) = global_pi; + + + Ivote( global_pi ) = Ivote( global_pi ) + vmag; + + end + + if itr ==1 + Ivote1 = Ivote; + + elseif itr ==2 + Ivote2 = Ivote; + + elseif itr ==3 + Ivote3 = Ivote; + + elseif itr ==4 + Ivote4 = Ivote; + + elseif itr == 5 + Ivote5 = Ivote; + end + t_v1 = toc; + disp(['voting done. time =',num2str(t_v1)]); + + figure, imagesc(squeeze(Ivote(:, :, ceil(size(Ivote, 3)/2),:))); colormap(gray); + + % update the voting direction + tic; + for v = 1: nV + % coordinates of the current voter + vx = Itx(v); + vy = Ity(v); + vz = Itz(v); + + %get the local value of the voting image + local_Ivote = Ivote(g_v_prime(v,1:validPixels(v))); + + %find the index of the maximum value + [~, local_max_idx] = max(local_Ivote); + + %convert this into a global subscript + [gx, gy, gz] = ind2sub(size(Ivote), g_v_prime(v,local_max_idx)); + + %compute the vector from the voter position to this position + dx = gx - vx; + dy = gy - vy; + dz = gz - vz; + Igrad_x(vx, vy, vz) = dx; + Igrad_y(vx, vy, vz) = dy; + Igrad_z(vx, vy, vz) = dz; + + end + + tdir1 = toc; + display (['updating dir done. time = ', num2str(tdir1)]); + ang = ang - d_ang; + end + + +%% +t = 10; +out = Ivote; +out(out=t) = 255; +out = imregionalmax(out); + +out1(:,:,:,1) = mat2gray(Iblur); +out1(:,:,:,2) = mat2gray(out); +out1(:,:,:,3) = mat2gray(Iblur); + + + +figure(2); + +subplot(2, 3, 1), +imagesc(squeeze(Iblur(:, :, ceil(size(Iblur, 3)/2)))); + +subplot(2, 3, 2), +imagesc(squeeze(Iblur(:, ceil(size(Iblur, 2)/2), :))); + +subplot(2, 3, 3), +imagesc(squeeze(Iblur( ceil(size(Iblur, 1)/2), :, :))); + +subplot(2, 3, 4), +imagesc( squeeze( out1(:, :, ceil(size(Ivote, 3)/2),:) ) ); + +subplot(2, 3, 5), +imagesc(squeeze(out1(:, ceil(size(Ivote, 2)/2), :, :))); + +subplot(2, 3, 6), +imagesc(squeeze(out1( ceil(size(Ivote, 1)/2), :, :, :))); + +colormap(gray); +%% +% figure, imagesc(squeeze(Iblur(:, :, ceil(size(Iblur, 3)/2)))); colormap(gray); +% figure, imagesc(squeeze(Ivote(:, :, ceil(size(Ivote, 3)/2),:))); colormap(gray); +% figure, imagesc(squeeze(Iblur(:, ceil(size(Iblur, 2)/2), :))); colormap(gray); +% figure, imagesc(squeeze(I(:, ceil(size(Ivote, 2)/2), :))); colormap(gray); +% % figure, imagesc(squeeze(Iblur( ceil(size(Iblur, 1)/2), :, :))); colormap(gray); +% figure, imagesc(squeeze(Ivote( ceil(size(Ivote, 1)/2), :, :))); colormap(gray); +% +fid0 = fopen('iblur.vol', 'w'); +fwrite(fid0, Iblur); +fclose(fid0); + +fid1 = fopen('ivote1.vol', 'w'); +fwrite(fid1, Ivote1); +fclose(fid1); + +fid2 = fopen('ivote2.vol', 'w'); +fwrite(fid2, Ivote2); +fclose(fid2); + +fid3 = fopen('ivote3.vol', 'w'); +fwrite(fid3, Ivote3); +fclose(fid3); + diff --git a/matlab-3d/main.m b/matlab-3d/main.m new file mode 100644 index 0000000..783af62 --- /dev/null +++ b/matlab-3d/main.m @@ -0,0 +1,300 @@ +clc; +clear; +disp('***************** NEW RUN *********************'); +total = tic; + + +% ******* Initialize voting parameters ************************************** +rmax = 7; %maximum radius of the cell +ang_deg = 15.1; %half the angular range of the voting area +ang = ang_deg * pi / 180; +iter = 3; %number of voting iterations +t0 = 1.2; %threshold color +sigma = [4, 4, 2]; +% t = 0.1; +d_ang= ang / (iter); + +% ******** Testing parameters ****************************************** +% p = [100, 50, 100]; +% ps = [200, 200, 100]; +ps = [100, 50, 40]; +r = 7; +I = syn_Img(r , ps); +% volfile = 'img\nissl-rat.vol'; +% fid = fopen(volfile); % open the file that include the image +% S = fread(fid, 3, 'int32'); +% X = S(1); +% Y = S(2); +% Z = S(3); +% +% % load the VOL data into a 2D matrix +% I = fread(fid,[X Y*Z], 'uint8'); +% fclose(fid); +% +% %change this to a 3D matrix +% I = (reshape(I, [X, Y, Z])); +% +% % invert the intensity +% I = 255 - I; + +%perform a gaussian blur +Iblur = gauss_blur3d(I, sigma); + +%%crop out a small subregion of I and Iblur +% Iblur = Iblur(p(1):p(1)+ps(1)-1, p(2):p(2)+ps(2)-1, p(3):p(3)+ps(3)-1); +% I = I(p(1):p(1)+ps(1)-1, p(2):p(2)+ps(2)-1, p(3):p(3)+ps(3)-1); + +% +% compute the gradient +[Igrad_y, Igrad_x, Igrad_z] = gradient(Iblur); + +%calculate the gradient magnitude +Imag = sqrt(Igrad_x .^ 2 + Igrad_y .^ 2 + Igrad_z .^2); +I_theta1 = acos(Igrad_x./Imag); +I_theta2 = acos(Igrad_y./Imag); +I_theta3 = acos(Igrad_z./Imag); + +%set a threshold for the gradient magnitude +It = Imag > t0; + +%Set the boundaries of the threshold image to zero +It(1:rmax, :, :) = 0; +It(ps(1) - rmax:ps(1), :,:) = 0; +It(:, 1:rmax, :) = 0; +It(:, ps(2) - rmax:ps(2),:) = 0; +It(:, :, 1:rmax) = 0; +It(:,:, ps(3) - rmax:ps(3)) = 0; + +%get the indices of all of the nonzero values in the threshold image +% (voter positions) +[Itx,Ity,Itz] = ind2sub(size(It),find(It)); +Vi = find(It); +nV = nnz(It); + +% create a meshgrid describing coordinates relative to the voter position +range = -rmax:rmax; %create an array of values between -rmax and rmax +[mx, my, mz] = meshgrid(range, range, range); %create a template describing local pixel position in a small cube +m_mag = sqrt(mx.^2 + my.^2 + mz.^2); %create a template describing the distance from the center of a small cube + +% create a mask for the voting area +M_dist = m_mag <= rmax; %mask for the voting area distance (all values < rmax from the center) + +%calculate the direction vector between a pixel and voter +LV_x = mx./m_mag; +LV_y = my./m_mag; +LV_z = mz./m_mag; + +%number of pixels in the voting area of each voter (initialize to zero) +validPixels = (zeros(nV,1)); + +%indices of pixels in the voting area of each voter +% indices reference the 3D image +g_v_prime = (zeros(nV, (rmax^3))); + +%--------------Display current data------------------------- +% subplot(3, 3, 1), +% imagesc(squeeze(I(:, :, ceil(size(I, 3)/2)))); +% +% subplot(3, 3, 2), +% imagesc(squeeze(I(:, ceil(size(I, 2)/2), :))); +% +% subplot(3, 3, 3), +% imagesc(squeeze(I( ceil(size(I, 1)/2), :, :))); +% % +% subplot(3, 3, 4), +% imagesc(squeeze(Iblur(:, :, ceil(size(Iblur, 3)/2)))); +% +% subplot(3, 3, 5), +% imagesc(squeeze(Iblur(:, ceil(size(Iblur, 2)/2), :))); +% +% subplot(3, 3, 6), +% imagesc(squeeze(Iblur(ceil(size(Iblur, 1)/2), :, :))); +% +% subplot(3, 3, 7), +% imagesc(squeeze(Imag(:, :, ceil(size(Imag, 3)/2)))); +% +% subplot(3, 3, 8), +% imagesc(squeeze(Imag(:, ceil(size(Imag, 2)/2), :))); +% +% subplot(3, 3, 9), +% imagesc(squeeze(Imag(ceil(size(Imag, 1)/2), :, :))); +% +% colormap(gray); + +%% vote +tic; +%for each iteration (in iterative voting) +for itr = 1 : iter + + %initialize the vote image to zero + Ivote = (zeros(size(I))); + + %for each voter (nonzero pixels in the threshold image It) + for v = 1: nV + + %get the cartesian coordinates of the voter v in the main image I + vx = Itx(v); + vy = Ity(v); + vz = Itz(v); + vi = Vi(v); + + %retreive the gradient magnitude at the voter position + %vmag = Imag(vx,vy,vz); + vmag = Imag(vi); + + %retrieve the gradient + gx = Igrad_x(vi); + gy = Igrad_y(vi); + gz = Igrad_z(vi); + + %calculate the gradient magnitude + dmag = sqrt (gx^2 + gy^2 + gz^2); + + %calculate the normalized gradient direction + dx = gx / dmag; + dy = gy / dmag; + dz = gz / dmag; + + %calculate the angle between the voter direction and the pixel direction + cos_diff = LV_x .* dx + LV_y .* dy + LV_z .* dz; + ang_diff = acos(cos_diff); + + %create an angular mask for the voting area + M_angle = cos_diff > cos(ang); + + %combine the two masks to mask out the voting angle + M = M_angle .* M_dist; + + % get the coordinates of each pixel in the final voter mask M + pi = find(M); + + %calculate the number of pixels in the voting region + npts = nnz(M); + validPixels(v) = npts; + + %convert every index in the voting area from a local 3D index to a global 3D index (into the original image I) + global_px = vx + mx(pi); + global_py = vy + my(pi); + global_pz = vz + mz(pi); + + %convert the global 3D index of each point into a global 1D index + global_pi = sub2ind(ps, global_px, global_py, global_pz); + + g_v_prime (v, 1:npts) = global_pi; + + + Ivote( global_pi ) = Ivote( global_pi ) + vmag; + + end + + if itr ==1 + Ivote1 = Ivote; + + elseif itr ==2 + Ivote2 = Ivote; + + elseif itr ==3 + Ivote3 = Ivote; + + elseif itr ==4 + Ivote4 = Ivote; + + elseif itr == 5 + Ivote5 = Ivote; + end + t_v1 = toc; + disp(['voting done. time =',num2str(t_v1)]); + + figure, imagesc(squeeze(Ivote(:, :, ceil(size(Ivote, 3)/2),:))); colormap(gray); + + % update the voting direction + tic; + for v = 1: nV + % coordinates of the current voter + vx = Itx(v); + vy = Ity(v); + vz = Itz(v); + + %get the local value of the voting image + local_Ivote = Ivote(g_v_prime(v,1:validPixels(v))); + + %find the index of the maximum value + [~, local_max_idx] = max(local_Ivote); + + %convert this into a global subscript + [gx, gy, gz] = ind2sub(size(Ivote), g_v_prime(v,local_max_idx)); + + %compute the vector from the voter position to this position + dx = gx - vx; + dy = gy - vy; + dz = gz - vz; + Igrad_x(vx, vy, vz) = dx; + Igrad_y(vx, vy, vz) = dy; + Igrad_z(vx, vy, vz) = dz; + + end + + tdir1 = toc; + display (['updating dir done. time = ', num2str(tdir1)]); + ang = ang - d_ang; + end + + +%% +t = 10; +out = Ivote; +out(out=t) = 255; +out = imregionalmax(out); + +out1(:,:,:,1) = mat2gray(Iblur); +out1(:,:,:,2) = mat2gray(out); +out1(:,:,:,3) = mat2gray(Iblur); + + + +figure(2); + +subplot(2, 3, 1), +imagesc(squeeze(Iblur(:, :, ceil(size(Iblur, 3)/2)))); + +subplot(2, 3, 2), +imagesc(squeeze(Iblur(:, ceil(size(Iblur, 2)/2), :))); + +subplot(2, 3, 3), +imagesc(squeeze(Iblur( ceil(size(Iblur, 1)/2), :, :))); + +subplot(2, 3, 4), +imagesc( squeeze( out1(:, :, ceil(size(Ivote, 3)/2),:) ) ); + +subplot(2, 3, 5), +imagesc(squeeze(out1(:, ceil(size(Ivote, 2)/2), :, :))); + +subplot(2, 3, 6), +imagesc(squeeze(out1( ceil(size(Ivote, 1)/2), :, :, :))); + +colormap(gray); +%% +% figure, imagesc(squeeze(Iblur(:, :, ceil(size(Iblur, 3)/2)))); colormap(gray); +% figure, imagesc(squeeze(Ivote(:, :, ceil(size(Ivote, 3)/2),:))); colormap(gray); +% figure, imagesc(squeeze(Iblur(:, ceil(size(Iblur, 2)/2), :))); colormap(gray); +% figure, imagesc(squeeze(I(:, ceil(size(Ivote, 2)/2), :))); colormap(gray); +% % figure, imagesc(squeeze(Iblur( ceil(size(Iblur, 1)/2), :, :))); colormap(gray); +% figure, imagesc(squeeze(Ivote( ceil(size(Ivote, 1)/2), :, :))); colormap(gray); +% +fid0 = fopen('iblur.vol', 'w'); +fwrite(fid0, Iblur); +fclose(fid0); + +fid1 = fopen('ivote1.vol', 'w'); +fwrite(fid1, Ivote1); +fclose(fid1); + +fid2 = fopen('ivote2.vol', 'w'); +fwrite(fid2, Ivote2); +fclose(fid2); + +fid3 = fopen('ivote3.vol', 'w'); +fwrite(fid3, Ivote3); +fclose(fid3); + diff --git a/matlab-3d/old-matlab.m b/matlab-3d/old-matlab.m new file mode 100644 index 0000000..135356b --- /dev/null +++ b/matlab-3d/old-matlab.m @@ -0,0 +1,232 @@ +clc; +clear; +disp('***************** NEW RUN *********************'); +total = tic; + + +% ******* Initialize voting parameters ************************************** +rmax = 9; %maximum radius of the cell +ang_deg = 15.1; %half the angular range of the voting area +ang = ang_deg * pi / 180; +iter = 1; %number of voting iterations +t0 = 1.2; %threshold color +sigma = [4, 4, 2]; +% t = 10; +d_ang= ang / (iter); + +% ******** Testing parameters ****************************************** +p = [100, 50, 100] ; +ps = [50, 50, 25] - 1; +% p = [100, 100, 100] ; +% ps = [300, 300, 150] - 1; + +volfile = 'img\nissl-rat.vol'; +fid = fopen(volfile); % open the file that include the image +S = fread(fid, 3, 'int32'); +X = S(1); +Y = S(2); +Z = S(3); + +% load the VOL data into a 2D matrix +I = fread(fid,[X Y*Z], 'uint8'); +fclose(fid); + +%change this to a 3D matrix +I = single(reshape(I, [X, Y, Z])); + +% invert the intensity +I = 255 - I; + +%perform a gaussian blur +I_blur = gauss_blur3d(I, sigma); + +% compute the gradient +[Igrad_x, Igrad_y, Igrad_z] = gradient(I_blur); + +%%crop out a small subregion of I +Isub_x = Igrad_x(p(1):p(1)+ps(1), p(2):p(2)+ps(2), p(3):p(3)+ps(3)); +Isub_y = Igrad_y(p(1):p(1)+ps(1), p(2):p(2)+ps(2), p(3):p(3)+ps(3)); +Isub_z = Igrad_z(p(1):p(1)+ps(1), p(2):p(2)+ps(2), p(3):p(3)+ps(3)); + +%calculate the gradient magnitude +Imag = sqrt(Isub_x .^ 2 + Isub_y .^ 2 + Isub_z .^2); +I_theta = acos(Isub_z./Imag); +I_phi = atan(Isub_y./Isub_x); + + +%set a threshold for the gradient magnitude +It = Imag > t0; + +% +% thresholding +It_x = size(It,1); +It_y = size(It,2); +It_z = size(It,3); +% +It(1:rmax, :, :) = 0; +It(It_x - rmax:It_x, :,:) = 0; +It(:, 1:rmax, :) = 0; +It(:, It_y - rmax:It_y,:) = 0; +It(:, :, 1:rmax) = 0; +It(:,:, It_z - rmax:It_z) = 0; + +% +[Itx,Ity,Itz] = (ind2sub(size(It),find(It))); +Itx = single(Itx); +Ity = single(Ity); +Itz = single(Itz); +nV = nnz(It); + + +% create a meshgrid describing coordinates relative to the voter position +range = single(-rmax):single(rmax); +[mx, my, mz] = (meshgrid(range, range, range)); +m_mag = sqrt(mx.^2 + my.^2 + mz.^2); + +% create a mask for the voting area +M_dist = mx.^2 + my.^2 + mz.^2 < rmax^2; +M_theta = acos(mz./m_mag); +M_phi = atan(my./mx); +M_phi (my ==0 & mx ==0) = 0; +pxPerRow = single(size(It,1)); +pxPerCol = single(size(It,2)); +validPoints = single(zeros(nV,1)); + +% g_v_prime = zeros(nV, ceil(rmax^2*ang/3)); +g_v_prime = single(zeros(nV, (rmax^3))); + + + +disp('first part done.'); +%% vote +tic; + for itr = 1 : iter + + Ivote = single(zeros(size(It))); + for v = 1: 1 + +% + % coordinates of the current voter + vx = Itx(v); + vy = Ity(v); + vz = Itz(v); +% + vtheta= I_theta(vx,vy,vz); + vphi = I_phi(vx,vy,vz); + vmag = Imag(vx,vy,vz); +% ang_diff = single(zeros([2*rmax+1 2*rmax+1 2*rmax+1])); +% for i=1: 2*rmax +1 +% for j=1: 2*rmax+1 +% for k = 1:2*rmax+1 +% ang_diff(i,j,k) = acos(dot([Isub_x(vx,vy,vz) Isub_y(vx,vy,vz) Isub_z(vx,vy,vz)], [mx(i,j,k) my(i,j,k) mz(i,j,k)])/(vmag*norm([mx(i,j,k) my(i,j,k) mz(i,j,k)]))); +% end +% end +% end + ang_diff = acos(((sin(M_theta).*sin(vtheta)).*cos(vphi - M_phi)) + cos(M_theta).*cos(vtheta)); + M_diff = min(2*pi - 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