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
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matlab-3d/blue.bmp | Bin 0 -> 6197882 bytes
matlab-3d/gauss1d.m | 15 +++++++++++++++
matlab-3d/gauss_blur3d.m | 19 +++++++++++++++++++
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matlab-3d/validation/newcrp.bmp | Bin 0 -> 263222 bytes
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541 files changed, 583405 insertions(+), 0 deletions(-)
create mode 100644 matlab-3d/blue.bmp
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--- /dev/null
+++ b/matlab-3d/gauss1d.m
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+%This function creates a 1D gaussian window given a standard deviation
+
+function G = gauss1d(sigma)
+
+
+ % create a kernel with a radius equal to 4x sigma
+ r = sigma * 4;
+
+ % create the domain of the gaussian function (x and y)
+ gx = -r:r;
+ % calculate the gaussian function
+ a = 1/(sqrt(2*pi)*sigma);
+ b = -1/(2*sigma^2);
+ cx = gx.^2;
+ G = a.*exp(b.*cx);
\ No newline at end of file
diff --git a/matlab-3d/gauss_blur3d.m b/matlab-3d/gauss_blur3d.m
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+function Ib = gauss_blur3d(I, sigma)
+
+
+%convolve along the x-axis
+Gx = gauss1d(sigma(1));
+Ix = convn(I, Gx, 'same');
+
+%convolve along the y-axis
+Gy = gauss1d(sigma(2))';
+Iy = convn(Ix, Gy, 'same');
+
+%convolve along the z-axis
+Gz_prime = gauss1d(sigma(3));
+Gz = reshape(Gz_prime, [1, 1, length(Gz_prime)]);
+Iz = convn(Iy, Gz, 'same');
+
+Ib = Iz;
+
+
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+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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