I want to reconstruct an image of circles with noise

Question

Hoschang Noori 2020-7-18

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/567153-i-want-to-reconstruct-an-image-of-circles-with-noise

评论： Image Analyst 2020-7-24

在 MATLAB Online 中打开

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

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Answer 1

Image Analyst 2020-7-18

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/567153-i-want-to-reconstruct-an-image-of-circles-with-noise#answer_467688

scatteredInterpolant_Demo.m

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.

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Hoschang Noori 2020-7-23

在 MATLAB Online 中打开

simucoord.txt

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])

Hoschang Noori 2020-7-24

编辑：Hoschang Noori 2020-7-24

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 2020-7-24

在 MATLAB Online 中打开

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

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