METU
Department of Computer Engineering
Fall 2015
CENG 789—Digital Geometry Processing
ASSIGNMENT II
Instructor: Y. Sahillioğlu
Dec 27, 2015
Rigid Shape Registration (start early!)
Alignment Problem {100 points} Your task is to bring all 10 partial scans of the same object into
one common pose. By doing so, you will be compensating the deficiencies of the individual scans, e.g.,
invisible right ear of the bunny at the 4th pose from the top is compensated by the 5th pose once they
are aligned, or equivalently, registered.
These scans differ only by rigid transformations, i.e., rotations and translations, which are easy to compute, as described in the class. You first need to uniformly sample each scan to work with less number
of points. You will then register the first scan to the second, and then register this temporary result to
the third scan, and so on, which in turn accumulates the missing data as you process towards the last
scan. For the registration, you first decide the corresponding points between two point clouds by a simple
closest-point matching algorithm (use kd-trees for efficiency) and then compute the rigid transformation
that aligns the corresponding points well. You then recompute the closest-point correspondences based
on which a new transformation is computed. Repeat until your new transformation does not differ much
from the previous transformation, i.e., until mesh stops moving. For rotation computation use either
SVD-based approach discussed in class, or the closed-formula in Eq. 21 of the famous ICP paper: A
Method for Registration of 3-D Shapes. 20 points bonus if you do both. You may find the Eigen library
for linear algebra very handy for this assignment (and in general).
Submission This is 20% of your final grade. Use the meshes provided in ∼ys/meshes3.zip (use only
the 3D point info in the ply files). Good luck. Send to ys@ceng.metu.edu.tr your code, executable, and
resulting file(s) as well as mynotes.txt file where you mention the encountered problems and interesting
observations.