Registering non-corresponding point clouds

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SUMMARY

The discussion focuses on the challenge of registering non-corresponding point clouds that represent similar geometric shapes. The primary method suggested is the Iterative Closest Point (ICP) algorithm, which requires defining a disparity function to measure the distance between the two point sets. Additionally, performing Principal Component Analysis (PCA) on both point clouds can help establish a common coordinate system for effective rotation and translation. These techniques are essential for achieving accurate registration of the point clouds.

PREREQUISITES
  • Understanding of point cloud data representation (xyz coordinates)
  • Familiarity with the Iterative Closest Point (ICP) algorithm
  • Knowledge of Principal Component Analysis (PCA)
  • Basic concepts of rigid transformations (translation and rotation)
NEXT STEPS
  • Research the implementation of the Iterative Closest Point (ICP) algorithm in Python using libraries like Open3D
  • Explore methods for defining disparity functions for non-corresponding point clouds
  • Learn about Principal Component Analysis (PCA) and its application in point cloud registration
  • Investigate alternative algorithms for point cloud registration, such as the Coherent Point Drift (CPD) method
USEFUL FOR

This discussion is beneficial for computer vision researchers, robotics engineers, and data scientists working with 3D point cloud data and seeking to improve registration techniques for non-corresponding datasets.

preet
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I'm interested in the problem of registering non-corresponding (but similar) point clouds.

I have two sets of point cloud data (points in xyz) representing the same geometric shape. However, the point cloud data does not correspond -- both clouds have a different number of points and there is no relation between the two clouds other than the fact that they represent a similar geometric shape.

The goal is to register one of these point clouds to the other one using only rigid transformation (translation, rotation).

I'm not sure how to approach this problem -- a lot of the information I've found on the internet points the Iterative Closest Point algorithm, which involves defining a function to measure the disparity between the two point sets and then minimizing it to converge to a solution. However, I don't know how to define a function to measure the disparity between the two point sets I've described, since the points do not correspond.

tldr;
How do I define a 'distance' or 'disparity' function between two sets of point clouds that do not correspond but represent a similar geometric structure?

TiA,

-preet
 
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One possibility is to perform a principal component analysis on both clouds of data, producing a coordinate system for each cloud. Then rotate/translate one cloud of data so that its coordinate system matches the other's.
 

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