I want to reconstruct an image of circles with noise

Hello,

i want to reconstruct a similar image of the following one from a plot.

You can find this image attached as 'copy.txt'.

This is the plot i have

What steps should i take? I have to thicken the lines of the circle-lines and give them different values. The ones presented should have high values and it should fade away.

What i have:

%Used values from now on.
savedValsX;
savedValsY;
%Size Image: 1043x981
%Size Simu Plot: detHeight = 179.4 mm, detWidth = 168.7 mm

%convert mm to pixels
imHeight = 1043;
imWidth = 981;

mmToPixFactor = round(imHeight/detHeight, 2)

%save values as pixels.

savedValsX = savedValsX.*mmToPixFactor - min(savedValsX.*mmToPixFactor);
savedValsY = savedValsY.*mmToPixFactor - min(savedValsY.*mmToPixFactor);


% Setup / initialization.
% Start out matrix as zeros.
m = zeros(1050,1000);

%Save x, y locations as int32, transpose everything.
savedValsX = floor(savedValsX)
savedValsY = floor(savedValsY)

valsX = savedValsX.';
valsY = savedValsY.';

%Delete Zero elements.
zeroX = find(valsX == 0);
zeroY = find(valsY == 0);

maxX = find(valsX > 981)
valsX(zeroX) = 1;
valsY(zeroY) = 1;

plot(valsX, valsY, "r*")

XY = [valsX, valsY];
z = 1;

indexes = sub2ind([1050, 1000], XY(:,2), XY(:,1));
m(indexes) = z;
m = flip(m,1)

Anyone know what keyword i should look after or did anyone do something familiar to this? Making an image of out a plot?

Thanks in advance!

This is the full code that i use to get the x and y values. You can find the used xy values attached as a txt.

%% define some colors and symbols for plotting
symbols = {'s','^','p','d','v','o','+','x','*','h','<','>','.','s','^','p',...
    'd','v','o','+','x','*','h','<','>','.','s','^','p','d','v','o','+','x',...
    '*','h','<','>','.','s','^','p','d','v','o','+','x','*','h','<','>','.'};
colors = {'r','g','b','c','m','y','r','g','b','c','m','y','r','g','b','c',...
    'm','y','r','g','b','c','m','y','r','g','b','c','m','y','r','g','b','c',...
    'm','y','r','g','b','c','m','y','r','g','b','c','m','y','r','g','b','c'};
lineTypes = {'-','--',':','-.'};

%% Simulation of area detector images (powder samples, position is linked to the detector center)
angleVals = 0:360;
roiX = 1000; % mm (region of interest of diffraction image, horizontal), for In radiation
roiY = 1000; % mm (region of interest of diffraction image, vertical), for In radiation
detHeight = 179.4; % mm, DECTRIS PILATUS 1M
detWidth = 168.7; % mm, DECTRIS PILATUS 1M
detPosX = 300; % mm (perpendicular horizontal to the specimen)
detPosY = 90; % mm (perpendicular vertical to the specimen)
detPosZ = 500; % mm (in the direction of specimen), for In radiation
type = 'bcc';
maxPeakArea = 1000;
peakWidth = 0.4;
wavelengthTexts = {'In-Ka1'};
usedWavelengths = [0.051212641];
% wavelengthTexts = {'Ga-Ka1'};
% usedWavelengths = [0.134011837];
xSteps = 5; % In radiation
xMax = 80; % In radiation
% define lattice and material parameters
hklBcc = [110, 200, 211, 220, 310, 222, 321, 400, 330, 420, 332, 422, 431, 521, 440, 530, ...
    442, 611, 620, 541, 622]';
a0ValFerrit = 0.28665;
% select correct values for lattice planes and lattice parameter
hklVals = hklBcc;
a0Val = a0ValFerrit;   

% determine lattice spacings of selected material
l = mod(hklVals, 10);
k = mod(floor(hklVals./10), 10);
h = floor(hklVals./100);
dVals = a0Val ./ (h.^2 + k.^2 + l.^2).^0.5;
hklInt = [h, k, l, ones(size(hklVals))];

% determine diffraction angles and diffraction radius values
angles = 2 .* asind(usedWavelengths ./ (2 .* dVals));
useful = find(imag(angles) == 0);
curHklVals = hklVals(useful);
hklUsed = curHklVals;
curAngles = angles(useful);
tthUsed = curAngles;
curRadius = detPosZ*tand(tthUsed);
radiusUsed = curRadius;
% determine spectrum
peakValsX = 0:0.1:curAngles(end) + 5;
peakData = zeros(length(curHklVals), length(peakValsX));
peakIntVals = zeros(size(curHklVals));


% determine diffraction rings
xVals = zeros(length(curRadius), length(angleVals));
yVals = zeros(length(curRadius), length(angleVals));

relValsDetCur = zeros(length(curRadius), length(angleVals));

for j = 1:length(curRadius)
    xValsCur = curRadius(j) * cosd(angleVals);
    yValsCur = curRadius(j) * sind(angleVals);
    xVals(j,:) = xValsCur;
    yVals(j,:) = yValsCur;
end
diffRingsX = xVals;
diffRingsY = yVals;

figure
hold on

curRadius = radiusUsed;
savedValsX = [];
savedValsY = [];

for j = 1:size(diffRingsX, 1)
    if curRadius(j) > 0
        curValsX = diffRingsX(j,:);
        curValsY = diffRingsY(j,:);
        relValsDetCur = curValsX >= detPosX - detWidth/2 & curValsX <= detPosX + detWidth/2 & ...
            curValsY >= detPosY - detHeight/2 & curValsY <= detPosY + detHeight/2;
        
        savedValsX = [savedValsX curValsX(relValsDetCur)];
        savedValsY = [savedValsY, curValsY(relValsDetCur)];
        plot(curValsX(relValsDetCur), curValsY(relValsDetCur), [colors{1} '*'])
        
    end
end
hold off
xlim([detPosX - detWidth/2, detPosX + detWidth/2])
ylim([detPosY - detHeight/2, detPosY + detHeight/2])
grid
title(['Detector: ' num2str(detPosX) ', ' num2str(detPosY) ', ' num2str(detPosZ) ', ' ...
    num2str(detWidth) ', ' num2str(detHeight) ', a_0=' num2str(a0Val) 'nm, ' type])

%Used values from now on.
savedValsX; savedValsY;
%Size Image: 1043x981
%Size Simu Plot: detHeight = 179.4 mm, detWidth = 168.7 mm

%convert mm to pixels
imHeight = 1043;
imWidth = 981;

mmToPixFactor = round(imHeight/detHeight, 2)

%save values as pixels.

savedValsX = savedValsX.*mmToPixFactor - min(savedValsX.*mmToPixFactor);
savedValsY = savedValsY.*mmToPixFactor - min(savedValsY.*mmToPixFactor);


% Setup / initialization.
% Start out matrix as zeros.
m = zeros(1050,1000);

%Save x, y locations as int32, transpose everything.
savedValsX = floor(savedValsX)
savedValsY = floor(savedValsY)

valsX = savedValsX.';
valsY = savedValsY.';

%Delete Zero elements.
zeroX = find(valsX == 0);
zeroY = find(valsY == 0);

maxX = find(valsX > 981)
valsX(zeroX) = 1;
valsY(zeroY) = 1;

plot(valsX, valsY, "r*")

XY = [valsX, valsY];
max(valsX)
max(valsY)
z = 1;

indexes = sub2ind([1050, 1000], XY(:,2), XY(:,1));
m(indexes) = z;
m = flip(m,1)
mImage = imagesc(m)
colorbar

Answer 1

[Image Analyst]

Maybe you want to use scatteredInterpolant(), like my attached demo. It takes x, y, value coordinates and builds up an image. You should make sure you "pin down" the borders of your image with some value, like the min of your other values, so it doesn't go crazy there.

[Hoschang Noori]

Thanks for your answer. I tried to figure it out, but I can't.

Maybe i should simplify my question:

(x,y) = coordinates of the circle points

z = brightness of the point

What i try is do insert more points with shaded brightness, like a bell curve. Something like following, for every data point.

my used code so far:

A = readmatrix('simucoord.txt')
x = A(:,1)
y = A(:,2)
z = A(:,3)
Radii = floor(A(:,4))
%plotting the data
plot3(x,y,z, 'r*')

x_center = 1.2533*10^3; %from simulation_23072020.mlx
y_center = 0;

clear x y z

%Plotting the data with the help of the Radii
th = 0:pi/50:pi;
x{1} = Radii(1) .* cos(th)-x_center;
y{1} = Radii(1) .* sin(th);
z{1} = ones(length(x{1}),1)*4;

x{2} = Radii(25) .* cos(th)-x_center;
y{2} = Radii(25) .* sin(th);
z{2} = ones(length(x{1}),1)*4;

x{3} = Radii(77) .* cos(th)-x_center;
y{3} = Radii(77) .* sin(th);
z{3} = ones(length(x{1}),1)*4

x{4} = Radii(99) .* cos(th)-x_center;
y{4} = Radii(99) .* sin(th);
z{4} = ones(length(x{1}),1)*3

x{5} = Radii(133) .* cos(th)-x_center;
y{5} = Radii(133) .* sin(th);
z{5} = ones(length(x{1}),1)*3


plot3(x{1}, y{1}, z{1}, x{2}, y{2}, z{2}, x{3}, y{3}, z{3}, x{4}, y{4}, z{4}, x{5}, y{5}, z{5})
xlim([0 1000])
ylim([0 1000])

[Image Analyst]

plot3() plots a line curve in three dimensional space. The z value is the height your circle would be above the x-y plane. And it would be in red since you said to plot a red curve.

1. If you're okay with the height of the red circle being the intensity, then I think it does that.
2. If you want the color of the circle to be z instead of red, and the location to be z=0, in the x-y plane, then you'll have to specify the 'Color' property explicitly in plot3().
3. If you would rather have an image instead of a line plot/graph then you'll have to burn the z value into the image at the corresponding (y,x) location.

I'm not sure which of those 3 scenarios you want.

[Hoschang Noori]

The third scenario sounds good. What I try is to generate a similiar image/matrix to this (without noise) from the plot.

Thanks a lot for your help!

[Image Analyst]

If you have a list of (x,y) locations, then here is how to burn it into the image:

for k = 1 : length(x)
    row = round(y(k));
    column = round(x(k));
    grayImage(row, columns) = 255; % Or 1 or whatever value you want.
end