Are you able to count the number of pixels in a 3D plot?

I am trying to find a way to count the number of red pixels in my moving plot and I was only able to find the number of white pixels in only at an angle. Would it be possible to count the total number of red pixels in a 3D plot?

clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
clear;  % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
xlabel('My x label') % Axis Labels
ylabel('My y label')
zlabel('My z label')
view([-37.5 30]) % standard 3D View
scale = 0.5; 
y = 1; % white percentage
%% range of results
d = 10; % Distance Between each point
nmesh = 3; % range
MagR = 0; % Magnetic Radius (MagR>nmesh = Strong, MagR<nmesh = weak, MagR = 0 = no Mag) 
niter = 200; % no. of jumps
[X,Y,Z] = meshgrid((-nmesh+1):nmesh-1); % create mesh
X = X * d;
Y = Y * d;
Z = Z * d;
%% random direction for X,Y,Z directions
dx = normrnd(0,1,[(size(X,1))^3 niter]);
dy = normrnd(0,1,[(size(X,1))^3 niter]);
dz = normrnd(0,1,[(size(X,1))^3 niter]);
%% Magnetised particles
c0 = nmesh;                         % center of magnetic field
for i = 1:size(dx,1)
    [ii,jj,kk] = ind2sub(size(X),i);   % row and column of force
    n = pdist2([ii jj kk],[c0 c0 c0]);         % distance to point
    if n < MagR                      % radius of magnetic force
        dx(i,:) = -cumsum(dx(i,:)*0+(jj-c0)/n);  % cosinus
        dy(i,:) = -cumsum(dy(i,:)*0+(ii-c0)/n);  % sinus
        dz(i,:) = -cumsum(dz(i,:)*0+(kk-c0)/n);
    end
end
cla
hold on
%% For Loop to plot 
for i = 1:niter-1
    X1 = X(:) + dx(:,i);
    Y1 = Y(:) + dy(:,i);
    Z1 = Z(:) + dz(:,i);
    plot3([X(:) X(:)]'+[dx(:,i+1) dx(:,i)]', ...
         [Y(:) Y(:)]'+[dy(:,i+1) dy(:,i)]',...
         [Z(:) Z(:)]'+[dz(:,i+1) dz(:,i)]','.-r','MarkerSize',5,'LineWidth',1)
    %p.MarkerSize = 10; % 6 is the default
    %p.LineWidth = 1; % 0.5 is the default
    pause(0.01)
    %% percentage readings  
    Image = getframe();
    K = sum(sum(rgb2gray(Image.cdata)==255));                                 
    percentageofwhite(y) = K/numel(rgb2gray(Image.cdata))*100;
    delete(findall(gcf,'type','text'))
    txt=text(0.0,0.95,sprintf('White Space = %0.3f%%',percentageofwhite(y)),'Units','normalized');
    y=y+1;
    %%
    xlim([-2*d 2*d]) % Axis limitsg
    ylim([-2*d 2*d])
    zlim([-2*d 2*d])
end
hold off
rotate3d on

[KALYAN ACHARJYA]

Pixels (Image)?? Is this?

red_area=100-%white_space

[Mrutyunjaya Hiremath]

@ sui zhi lau

if you study the line no 50 and 51 from your code

you can calculate Red elements count.

[sui zhi lau]

Hi Kalyan and Mrutyunjaya,

Thanks so much for answering. The 'white percentage' counter does show the number of white pixels and i can just minus the difference to find the red but I was wondering that if i shift the view of the 3D plot, would the percentages change since Image = getframe() only takes the 2D picture and analyse it after? If it does, how am i supposed to find the exact number of red pixels?

[Mrutyunjaya Hiremath]

    plot3([X(:) X(:)]'+[dx(:,i+1) dx(:,i)]', ...
         [Y(:) Y(:)]'+[dy(:,i+1) dy(:,i)]',...
         [Z(:) Z(:)]'+[dz(:,i+1) dz(:,i)]','.-r','MarkerSize',5,'LineWidth',1)

According to this, you are drawing 125 pair red points in each iteration

[sui zhi lau]

hi Mrutyunjaya,

thank you for the fast repliy! how did you get that value and how would i be able to compared the red pixels compared to the total white percentage to get a percentage of it then?

Ash

Answer 1

[darova]

Can you calculate the volume manually?

dv = [dx(:,i+1)-dx(:,i) dy(:,i+1)-dy(:,i) dz(:,i+1)-dz(:,i)];
V = V + pi*R*sqrt(sum(dv.^2,2));        % volume of all lines

[sui zhi lau]

Hi Darova,

Thank you again for the help. It does seem to work but how would I know the radius as I know the linewidth and plot size but how would i be able to convert the sizes to pixel numbers? And how would I be able to find the number of pixels for the whole plot?

[darova]

Just to be sure: you want to calculate pixels or percentage (volume)? read/white = value?

Number of pixels differs, it depends on window size. Here is an example

f = figure(1);
plot([0 1 2],[0 1 1],'linew',2)       % plot some data

set(f,'position', [200 100 500 400])  % set small window
axis equal
fr = getframe;
A1 = fr.cdata;                        % small image

set(f,'position', [200 100 600 500])  % set larger window
fr = getframe;
A2 = fr.cdata;                        % large image

blue = @(A) A(:,:,1) < 10 & A(:,:,2) < 10 & A(:,:,3) > 240;
white= @(A) sum(A,3) > 250*3;

    % get colors from images
A1b = blue(A1);                       
A2b = blue(A2);                       
A1w = white(A1);
A2w = white(A2);
    % check if colors are correct
figure
subplot(211)
imshowpair(A1b,A2b,'montage')
subplot(212)
imshowpair(A1w,A2w,'montage')

sum(A1b(:))/sum(A1w(:))
sum(A2b(:))/sum(A2w(:))

Result

ans =
    0.0078
ans =
    0.0065

As you see the data remain the same, window size changes only. But ratio of blue/white changes

So can you tell what are you trying to calculate?

[sui zhi lau]

Yes, I just wanted to compare the red and white pixels in terms of a ratio. So the comparison of red and white volume works as well. so red/white = value? -> can be either pixels or volume.

So the number of pixels does not matter.

[darova]

I think it's You should define some linewidth (radius). Can't calculate ratio without this

[darova]

I made a mistake in my first post

dv = cat(3,dx,dy,dz);
dv1 = pi*R*sqrt(sum(dv.^2,3));        % volume of each line
V = sum(dv1(:));

[sui zhi lau]

Yes i get that linewidth is the radius but i was wondering what values should i use for R when im unsure with the linewidth pixels. Or do i just use the properties given from plot3. And once i solve for the red volume, how do i find the white's volume?

[darova]

White volume looks simple

white = 40*40*40 - red

[sui zhi lau]

Yes but what do i replace R with? For example i put my linewidth as 0.5, do i take my R as 0.5 ?

[darova]

yes.

Answer 2

[Mrutyunjaya Hiremath]

@ sui zhi lau,

Outside Loop

totalData = 0;
whitePixData = 40*40*40;

Inside Loop

redPixData(y) = sum(sqrt(((dx(:,i+1) - dx(:,i)).^2) + ((dy(:,i+1) - dy(:,i)).^2) + ((dz(:,i+1) - dz(:,i)).^2)));
totalData = totalData + redPixData(y);
percentageofred(y) = (totalData/whitePixData)*100;
txt=text(0.0,0.95,sprintf('White Space = %0.3f%%',percentageofred(y)),'Units','normalized');

[sui zhi lau]

I tried this but I think the totalData does not reflect the values correctly as for example,

Gives me a red percentage of 1614%

clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
clear;  % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
xlabel('My x label') % Axis Labels
ylabel('My y label')
zlabel('My z label')
view([-37.5 30]) % standard 3D View
nmesh = 5;
niter = 100;
scale = 0.5;
y = 1;
totalData = 0;
%%
d = 3;
[X,Y,Z] = meshgrid(0:nmesh-1); % create mesh
X = X * d
Y = Y * d
Z = Z * d

whitePixData = (d*(nmesh-1))^3;
%%
dx = normrnd(0,1,[nmesh^3 niter]);
dy = normrnd(0,1,[nmesh^3 niter]);
dz = normrnd(0,1,[nmesh^3 niter]);
cla
%plot3(X(:),Y(:),Z(:),'ob')         % plot starting points
hold on
%plot(X,Y,'k')                % plot grid
%plot(X',Y','k')
for i = 1:niter-1
    s=5;
    %s = normrnd(45,1)
    X1 = X(:) + dx(:,i);
    Y1 = Y(:) + dy(:,i);
    Z1 = Z(:) + dz(:,i);
    q = quiver3(X1, Y1, Z1, dx(:,i+1)-dx(:,i), dy(:,i+1)-dy(:,i),dz(:,i+1)-dz(:,i),'r')
    q.LineWidth = s;
    q.ShowArrowHead = 'off';
     %plot([X(:) X(:)]'+[dx(:,i+1) dx(:,i)]', ...
         %[Y(:) Y(:)]'+[dy(:,i+1) dy(:,i)]','.-r')
    pause(0.02)
    %% percentage readings  
    redPixData(y) = sum(sqrt(((dx(:,i+1) - dx(:,i)).^2) + ((dy(:,i+1) - dy(:,i)).^2) + ((dz(:,i+1) - dz(:,i)).^2)));
    totalData = totalData + redPixData(y);
    percentageofred(y) = (totalData/whitePixData)*100;
    delete(findall(gcf,'type','text'))
    txt=text(0.0,0.95,sprintf('Red Percentage = %0.3f%%',percentageofred(y)),'Units','normalized');
    y = y+1;
    xlim([0 d*nmesh])
    ylim([0 d*nmesh])
    zlim([0 d*nmesh])
end
hold off
rotate3d on

[Mrutyunjaya Hiremath]

because, we are not considering the elimination of overlapping area.

[sui zhi lau]

How would you consider with elimination of overlapping areas?