Megabangetz’s Weblog

Rekontruksi 3D

Listing program stereo.m

% STEREO

%

% Usage: pt3D = stereo(im1, im2, c1, c2)

%

% Where: im1 and im2 are the two stereo images

% C1 and C2 are the calibration matrices

% for these two images respectively

%

% The function will prompt you to digitise some points in the first image

% (finishing by clicking the right button). The function then

% prompts you to digitise the equivalent points (which you must digitise

% in exactly the same sequence) in the second image.

% The function then solves the stereo equations

% and returns the 3D coordinates of the points in pt3D.

function [XYZ, uv1, uv2] = stereo(im1, im2, C1, C2)

fprintf(1, ‘Digitise some points in figure 1\n’);

figure(1)

imshow(im1);

[u1,v1] = digipts;

uv1 = [u1,v1]‘;

fprintf(1, ‘Digitise some points in figure 2\n’);

figure(2)

imshow(im2);

[u2,v2] = digipts;

uv2 = [u2,v2]‘;

% check if same number of points are selected

if length(u1) ~= length(u2)

fprintf(1, ‘Same number of points not selected\n’);

end

for i = 1:length(u1)

a = [C1(1:2,1:3) - [u1(i)*C1(3,1:3); v1(i)*C1(3,1:3)];

C2(1:2,1:3) – [u2(i)*C2(3,1:3); v2(i)*C2(3,1:3)]];

c = [u1(i) - C1(1,4);

v1(i) - C1(2,4);

u2(i) - C2(1,4);

v2(i) - C2(2,4)];

b(:, i) = a \ c;

end

XYZ = b’;

Image ’stereo1.jpg’

Image ”stereo2.jpg’

Dengan menjalankan program stereo.m, maka didapatkan koordinat 3D dari titik-titik sudut ketiga bangun ruang pada gambar diatas sebagai berikut:

pt3D =

-287.7542 156.7465 143.2885

-176.6269 162.0598 144.3627

-175.6786 19.8716 141.7267

-290.0593 13.4079 144.3193

-287.5655 157.5390 10.9533

-286.3338 13.6666 9.4036

-172.4321 17.1203 3.2873

-83.8519 -66.6201 1.3714

-66.1821 -141.0900 122.3533

20.2680 -179.4214 -6.0719

-134.6197 -204.2349 -2.2669

136.6957 -93.6632 63.9256

207.1254 -91.0740 63.7992

201.4685 -162.9965 60.2827

138.5328 -155.1594 59.2890

132.6638 -94.1806 -4.4145

134.7488 -160.4601 -9.8006

206.4264 -163.0088 -8.9430

Panjang sisi balok

slengths =

143.3608 111.2594 142.2157 114.5926

114.5926 138.5048 114.1181 134.9674

134.9674 143.8860 132.3377 143.3608

114.7735 132.3377 111.2594 134.9674

134.9674 142.2157 138.5048 145.3295

145.3295 114.1181 143.8860 114.7735

nface =

4 1 2 3 4

4 3 7 6 4

4 6 5 1 4

8 5 1 2 8

8 2 3 7 8

8 7 6 5 8

Panjang sisi limas

slengths =

143.1594 159.4866 153.6897

143.1594 155.5672 146.7257

153.6897 156.9089 146.7257

159.4866 156.9089 155.5672

nface =

1 2 3 1

1 2 4 1

1 3 4 1

2 3 4 2

Panjang sisi kubus

slengths =

61.6981 70.4773 72.2303 63.4295

63.4295 69.4031 71.7281 69.3959

69.3959 66.5307 68.4608 61.6981

70.7170 68.4608 70.4773 69.3959

69.3959 72.2303 69.4031 66.8054

66.8054 71.7281 66.5307 70.7170

nface =

4 1 2 3 4

4 3 7 6 4

4 6 5 1 4

8 5 1 2 8

8 2 3 7 8

8 7 6 5 8

Untuk menampilkan dua view yang berbeda dari rekonstruksi 3D kubus, balok dan limas dengan koordinat titik sudut estimasi dari kubus dan balok yang tidak kelihatan, juga sumbu koordinat yang mengindikasikan bidang dasar, jalankan fungsi rekon.m

Listing fungsi rekon.m

function rekon()

im1 = imread(‘stereo1.jpg’ );

im2 = imread(‘stereo2.jpg’ );

C1 = [0.6596 -0.7391 -0.0615 363.4235;

-0.1851 -0.1387 -0.9437 342.7417;

0.0005 0.0003 -0.0003 1.0000];

C2 = [0.9234 -0.2221 -0.0257 347.7796;

-0.0741 -0.2278 -0.9168 339.8960;

0.0002 0.0004 -0.0002 1.0000];

pt3D = stereo(im1, im2, C1, C2)

figure(3)

cube(pt3D(1:7,:));

tetrahedron(pt3D(8:11,:));

cube(pt3D(12:18,:));

% label coordinate axes

text(100,0,0,’x');

text(0,100,0,’y');

text(0,0,100,’z');

% draw in a set of coordinate axes

axislength = 100*eye(3);

for i=1:3

line([0, axislength(i,1)], [0, axislength(i,2)], [0, axislength(i,3)]);

end

axis equal; box on; rotate3D on; grid on;

end

function cube(cubepts3D)

% determine hidden vertex

cubepts3D(8,: ) = – cubepts3D(4,: ) + cubepts3D(6,: ) + cubepts3D(2,: );

% define faces from standard numbering

cubefaces = [4 1 2 3

4 3 7 6

4 6 5 1

8 5 1 2

8 2 3 7

8 7 6 5];

% draw ‘patcheds’ from vertice and face matrix

patch(‘Faces’,cubefaces,’Vertices’,cubepts3D, ‘FaceColor’, ‘none’)

fprintf(1, ‘Length matrix of face sides\n’);

[slengths, nface] = sidelengths(cubepts3D, cubefaces)

end

function tetrahedron(tetrahedronpts3D)

% define faces from standard numbering

tetrahedronfaces = [1 2 3

1 2 4

1 3 4

2 3 4];

% draw ‘patcheds’ from vertice and face matrix

patch(‘Faces’,tetrahedronfaces,’Vertices’,tetrahedronpts3D, ‘FaceColor’, ‘none’)

fprintf(1, ‘Length matrix of face sides\n’);

[slengths, nface] = sidelengths(tetrahedronpts3D, tetrahedronfaces)

end

function [slengths, nface] = sidelengths(pt3D, face)

[rows, cols] = size(face);

nface = [face face(:,1)];

for i=1:cols

for j=1:rows

slengths(j,i) = norm(pt3D(nface(j,i),:)-pt3D(nface(j,i+1),:));

end

end

end

Hasilnya (dilihat dari 2 sisi yang berbeda):