TD 6 - Iterative closest points

Files to download today

Here are some files to download (and extract to the main folder of your Eclipse project):

OFF.zip: examples of points clouds.

Libraries to add (project /LIB):

Jcg.jar: library for the manipulation of 3d geometry
TC.jar: input/output from files.
Jama.jar: linear algebra library.

For the implementation of ICP:

src.zip: classes defining main methods for rendering point clouds and implementing ICP

TD6 documentation: instructions

Important: here is an interesting paper illustrating how to implement ICP (with both 3x3 matrices and quaternions).

1. Iterative closest point (with rotation matrices)

ICP with Matrices and SVD

Given two 3d point clouds P1 and P2 (class PointSet), we want to compute the rigid transformation that maps P2 to P1, by implementing the Iterative closest point method with rotation matrices.

complete the class IterativeClosestPoint (which extends class RigidTransformation_3).

Suggestion: in order to implement ICP, we suggest to you to follow the explanation given in this paper (section 3.1).


Initial point clouds	after 1 iteration	after 3 iterations	after 5 iterations

1.1 Rigid transformation for corresponded point clouds

complete methods getRotation(...) and getTranslation(...), for the case of two point clouds P and Q whose points are matching (so we can assume point q[i]=p[i]).

1.2 implement ICP

Now we want to solve the problem above (computing a rigid transformation), for two point clouds whose points are not matched.

modify methods getRotation(...) and getTranslation(...), for dealing with arbitrary point clouds P and Q (now we cannot assume point q[i]=p[i]).

1.3 Check convergence of ICP

Now we want to check whether the ICP iterations converge.

compute and print (at each iteration) the sum of distances between closest neighbors and check that such distances do decrease.

2. Normals estimation

2.1 Computing normals of point clouds

Given a 3d point cloud P1 (class PointSet), we want to compute an estimation of normals as explained in the lecture (using co-variance matrix).

complete the class PointSet (complete the method getKNearestNeighbors).
complete the class NormalEstimator (which contains the method computeNormals).

Use the class PointCloudViewer to test your code (press 'n' to compute normals)

3. Outliers computation

3.1 Computing outliers of point clouds

Given a 3d point cloud P1 (class PointSet), we want to compute the outliers as explained in the lecture (again using co-variance matrix).

complete the class OutliersComputation (which contains the method computeOutliers).

Use the class PointCloudViewer to test your code

4. Point-to-Plane ICP (optional)

4.1 Computing outliers of point clouds (bonus)

Given two 3d point clouds P1 and P2 (class PointSet), implement the point-to-plane variant of ICP (as described in the lecture).

complete the class PointToPlaneICP and compare to the standard ICP method (compare convergence rates).

TD 6 - Iterative closest point

The goal of this TD session is to implement the iterative closest point algorithm (using both 3x3 matrices)

1. Getting started (a Processing frame for rendering 3d point clouds)