Photogrammetric Computer Vision

Computer Vision in Engineering – Prof. Dr. Rodehorst M.Sc. Mariya Kaisheva

Photogrammetric Computer Vision Assignment 5

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Winter Semester 20/21 Submission Deadline: 17.01.21 13:30 am

VI. Projective and direct Euclidean reconstruction

With knowledge of the relative orientation, spatial object coordinates can be triangulated from

corresponding image points. If the parameters of the interior orientation are unknown, then only a

projective reconstruction is possible. Using at least five control points, this intermediate result can

be transformed quite simply into a Euclidean reconstruction.

1. Projective reconstruction:

Since the manual matching of image points is quite laborious and boring, a text file bh.dat

with many homologous image points is made available for the image pair showing the bust of


a) Read the homologous image coordinates 1 2x x in the format (x1, y1, x2, y2), e.g. with

fh = fopen(‘bh.dat’, ‘r’);

A = fscanf(fh, ‘%f%f%f%f’, [4 inf]);


x1 = A(1:2, :); x2 = A(3:4, :);

and use your function from exercise 4 in order to determine the relative orientation of the

images with the fundamental matrix F.

b) Implement a new function, which defines two corresponding projection matrices PN and P’

by means of F.

c) Realize a function for the linear triangulation of projective object points XP1 and try to

visualize the computed spatial object coordinates, e.g. using

figure; scatter3(X(1,:), X(2,:), X(3,:), 10, ‘filled’);

axis square; view(32, 75);

2. Direct Euclidean reconstruction:

a) Read the control point information from the provided file pp.dat in the format (x1, y1, x2, y2,

XE, YE, ZE) and triangulate projective object points XP2 from the five homologous image points

1 2x x using the already computed projection matrices PN and P’.

b) Extend your algorithm from exercise 2 for the planar 2D homography to a spatial 3D

homography H. Determine the spatial transformation of the five projective object points XP2

to the corresponding Euclidean object points XE.

c) Apply this transformation H to all object points of your projective reconstruction XP1 and

visualize the result of the Euclidean reconstruction spatially.

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