How may I change certain areas of a geometry (specified by point point) with reference to a geometry?

I have two pointclouds containing x,y,z cordinates of two similar geometry. Say A and B. A is suppose a square of size 1mm by 1mm. B is also a square of size 0.5mm by 0.5mm. However, in B one edge is distorted (see attached figure). Now I wish to correct it, which means, change it to sqaure of size 0.5mm by 0.5mm. Is there a way to do it?

Answer 1

[yanqi liu]

clc; clear all; close all;
[X,map,alpha] = imread('https://ww2.mathworks.cn/matlabcentral/answers/uploaded_files/852940/Picture1.png');
figure; imshow(alpha);

bw = im2bw(alpha);
bw = bwareaopen(imfill(bw, 'holes'), 1000);
bw2 = bwareafilt(bw, 2);
bw(bw2) = 0;
[r,c] = find(bw);
bw(min(r):max(r),min(c):max(c)) = 1;
bw = logical(bw);
be = imdilate(bwperim(bw), strel('disk', 3));
alpha(be) = 255;
figure; imshow(be);

figure; imshow(alpha);

[Ajay Goyal]

Dear Yanqi Liu,

As much as I understood, this code has transferred the pixels of image 2 to form a sqaure by using code:

bw(min(r):max(r),min(c):max(c)) = 1;

However, my purpose is to map the geometry in Figure 1 to Figure 2 such that shape wil alter with respect to figure 1. Please comment. What if first figure is a circle and I have to map a start shape (Figure2). Actually I have two 3D geometry with known cordinates. One of them is a reference while other has some model issues at certain areas. I have to correct those areas with reference to 1st frame

[yanqi liu]

yes，sir

map the geometry in Figure 1 to Figure 2

square---->square

circle---->circle

……

the size should use Figure2 size？

[yanqi liu]

clc; clear all; close all;
[X,map,alpha] = imread('https://ww2.mathworks.cn/matlabcentral/answers/uploaded_files/852940/Picture1.png');
figure; imshow(alpha);

bw = im2bw(alpha);
bw = bwareaopen(imfill(bw, 'holes'), 1000);
% select 1、2 block
[L,~] = bwlabel(bw);
stats = regionprops(bw);
rects = cat(1,stats.BoundingBox);
[~,id] = sort(rects, 1);
% first
bw1 = L == id(1);
[r,c] = find(bw1);
bw1 = bw1(min(r):max(r),min(c):max(c));
% second
bw2 = L == id(2);
[r,c] = find(bw2);
bw2 = bw2(min(r):max(r),min(c):max(c));
% transform bw1 to bw2
at = [];
while 1
    at =[at; abs(length(find(bw1(:)))-length(find(bw2(:))))];
    bw1 = bwmorph(bw1,'thin');
    if length(find(bw1(:)))/length(find(bw2(:))) < 0.5
        break;
    end
end
[~, ind] = min(at);
bwt = L == id(1);
for i = 1 : ind
    bwt = bwmorph(bwt,'thin');
end
% replace
bwt = logical(bwt);
be = imdilate(bwperim(bwt), strel('disk', 3));
cen1 = stats(id(1)).Centroid;
cen2 = stats(id(2)).Centroid;
ts = round(cen2-cen1);
be2 = imtranslate(be,ts);
% make to origin
alpha(be2) = 255;
figure; imshow(alpha);

[Ajay Goyal]

Dear Yanqi Liu,

Thank you for the updated code. Great work! It is working well for different problems in a 2D section (please see the attached figures.)

It will be interesting to understand how it can be modified to fit in with 3D point clouds (geometries)? For example, consider I have a sphere of radius 2mm to be mapped on a ellipsoid with axis rius of 2, 1.5 and 3mm in x, y and z direction, respectively. Please check the attached code to generate the data for mapping. Please let me know, if I could upvote all your responses. I believe, similar problems are encountered by other researchers and this discussion will help them to solve such issues. My research problem in particular is much complicated. This is one stage where I got stuck and need your help. Thanks again!

[Ajay Goyal]

clc; clear; close all

%% Reference geometry is a sphere of radius 2 units

[x,y,z]=sphere;

x=2*x(:);y=2*y(:);z=2*z(:);

%% Geometry to be morphed is an ellipsoid with centre (0,0,0) and axis radius of 2, 1.5 and 3 units along x, y and z directions

[x1,y1,z1]=ellipsoid(0,0,0,2,1.5,3);

x1=x1(:);y1=y1(:); z1=z1(:);

%% creating point clouds of both data. We can ship this is not needed

ptCloud1 = pointCloud([x y z]);

ptCloud2 = pointCloud([x1 y1 z1]);

%% plotting the data

plot3(x,y,z,'k*')

hold on, plot3(x1,y1,z1,'r*')

axis square

[yanqi liu]

clc; clear; close all
%% Reference geometry is a sphere of radius 2 units
[x,y,z]=sphere;
x=2*x(:);y=2*y(:);z=2*z(:);
%% Geometry to be morphed is an ellipsoid with centre (0,0,0) and axis radius of 2, 1.5 and 3 units along x, y and z directions
[x1,y1,z1]=ellipsoid(0,0,0,2,1.5,3);
x1=x1(:);y1=y1(:); z1=z1(:);
%% creating point clouds of both data. We can ship this is not needed
% ptCloud1 = pointCloud([x y z]);
% ptCloud2 = pointCloud([x1 y1 z1]);
%% plotting the data
plot3(x,y,z,'k*')
axis square

% first
[xf1,xps1] = mapminmax(x,-1,1);
[yf1,yps1] = mapminmax(y,-1,1);
[zf1,zps1] = mapminmax(z,-1,1);
% second
[xf2,xps2] = mapminmax(x1,-1,1);
[yf2,yps2] = mapminmax(y1,-1,1);
[zf2,zps2] = mapminmax(z1,-1,1);
% make first to second
xf = mapminmax('reverse', mapminmax('apply', x1, xps1), xps2);
yf = mapminmax('reverse', mapminmax('apply', y1, yps1), yps2);
zf = mapminmax('reverse', mapminmax('apply', z1, zps1), zps2);
% plot
figure;
plot3(xf,yf,zf,'k*')
axis square

[Ajay Goyal]

Dear Yanqi,

I really appreciate your valuable help. I am pleased to vote your answer. Please note that your code for 3D is not working. The resulting geometry is same (ellipsoid) and not closer to sphere. There is no difference between any point (xf-x1, yf-y1, and zf-z1 are all zero at each point).

[yanqi liu]

yes，sir，may be check

[x, y, z] and [xf, yf, zf]

is it right？

clc; clear; close all
%% Reference geometry is a sphere of radius 2 units
[x,y,z]=sphere;
x=2*x(:);y=2*y(:);z=2*z(:);
%% Geometry to be morphed is an ellipsoid with centre (0,0,0) and axis radius of 2, 1.5 and 3 units along x, y and z directions
[x1,y1,z1]=ellipsoid(0,0,0,2,1.5,3);
x1=x1(:);y1=y1(:); z1=z1(:);
%% creating point clouds of both data. We can ship this is not needed
% ptCloud1 = pointCloud([x y z]);
% ptCloud2 = pointCloud([x1 y1 z1]);
%% plotting the data
plot3(x,y,z,'k*')
hold on;
plot3(x1,y1,z1,'ro')
axis square

% loop
at = [];
rs = [];
x1t = x1;y1t = y1;z1t = z1;
rate = 1;
while 1
    at =[at; norm(x1-x)+norm(y1-y)+norm(z1-z)];
    rs = [rs; rate*0.9];
    rate = rate-0.01;
    x1t = x1t*rate;
    y1t = y1t*rate;
    z1t = z1t*rate;
    if norm(x1t)+norm(y1t)+norm(z1t) < 0.3*norm(x1)+norm(y1)+norm(z1)
        break;
    end
end
[~, ind] = min(at);
xf = x1*rs(ind);
yf = y1*rs(ind);
zf = z1*rs(ind);

% plot
figure;
plot3(x,y,z,'k*')
hold on;
plot3(xf,yf,zf,'bs')
plot3(x1,y1,z1,'ro')
axis square
legend('first','fist->second','second');

[Ajay Goyal]

Dear Users,

This is indeed a beautiful code developed by yanqi liu. It can now be used for morphing 3D pointclouds as well. Thanks Yanqi Liu.

Regards,

Ajay

[Ajay Goyal]

Dear Yanqi,

I was checking that in both geometries, number of points are same (441). Well it should be like that otherwise we could do further calculations. Fair enough! In some cases, if there are more points than the other, problem can be solved using "pcdownsample" command. It reduces number of points without effecting the shape of geometry.

In addition to that; two points are corresponding such as x(1) corresponds to x1(1), x(2) corresponds to x1(2) and so on. In most cases, we could not get the correspondence. For example, please see the attached pictures. Point 1-4 are not corresponding but only 5. Can we solve such issues? Is there a way via which we can renumber them such that correspondence can be maintained.

Regards,

Ajay

[yanqi liu]

yes，sir，may be make relation between them，such as

clc; clear all; close all;
[X,map,alpha] = imread('https://ww2.mathworks.cn/matlabcentral/answers/uploaded_files/855030/Picture1.png');
figure; imshow(alpha);
bw = im2bw(alpha);
bw2 = bwareaopen(imfill(bw, 'holes'), 1000);
bw2 = bwareafilt(bw2, 2);
bw3 = bw;
bw3(bw2) = 0;
bw4 = bw;
bw4(~bw2) = 0;
[L,num] = bwlabel(bw4);
statsp = regionprops(L);
areap = cat(1,statsp.Area);
[~,id] = sort(areap, 'descend');
bw4a = L == id(1);
bw4b = L == id(2);
cen1 = statsp(id(1)).Centroid;
cen2 = statsp(id(2)).Centroid;
ts = round(cen1-cen2);
bw4b2 = imtranslate(bw4b,ts);
bw4ab = logical(bw4a+bw4b2);
% locate every number
[r, c] = find(bw4);
stats = regionprops(bw3);
pts1 = [];
pts2 = [];
for i = 1 : length(stats)
    ceni = stats(i).Centroid;
    disi = pdist2(ceni, [c, r]);
    [~,ind] = min(disi);
    hold on;
    plot([ceni(1) c(ind)], [ceni(2) r(ind)], 'r-', 'LineWidth', 2);
    if bw4a(r(ind), c(ind))
        pts1 = [pts1; c(ind) r(ind)];
    end
    if bw4b(r(ind), c(ind))
        pts2 = [pts2; c(ind) r(ind)];
    end
end

% compute
pts3 = pts2;
pts3(:,1) = pts3(:,1)+ts(1);
pts3(:,2) = pts3(:,2)+ts(2);
figure; imshow(bw4ab);
hold on;
plot(pts1(:,1), pts1(:,2), 'm*');
plot(pts3(:,1), pts3(:,2), 'ro');
% get relation
relation = [];
for i = 1 : size(pts3,1)
    disi = pdist2(pts1, pts3(i,:));
    [~,ind] = min(disi);
    relation = [relation; i, ind];
    plot([pts3(i,1) pts1(ind,1)], [pts3(i,2) pts1(ind,2)], 'r-', 'LineWidth', 2);
end

figure; imshow(alpha);
hold on;
for i = 1 : size(relation, 1)
    plot([pts1(relation(i, 2), 1) pts2(relation(i, 1), 1)], [pts1(relation(i, 2), 2) pts2(relation(i, 1), 2)], 'm-', 'LineWidth', 2);
end

now，we can get the point relation

[Ajay Goyal]

Thank you very much my friend. It will solve the purpose. I am home quarantined since yesterday and will try to study it on Monday, if report is in my favor :). Take care Regards, Dr. Ajay

[yanqi liu]

it is my pleasure，in thie question，we use the loop iteration for compute，and choose the best result. of course，may be use some parameter to adjust