Lecture 19: Absolute Orientation in Closed Form, Outliers and Robustness, RANSAC

TL;DR

Photogrammetry examines methods for absolute orientation and uniform sampling of the sphere.

Transcript

[SQUEAKING] [RUSTLING] [CLICKING] BERTHOLD HORN: We're talking about photogrammetry and, in particular, absolute orientation. And we're drilling down into more details for this one than we will for the other aspects of photogrammetry because a lot of it's going to be based on what we're doing here. And we found that rotation is the part that's awkw... Read More

Key Insights

• 🖐️ Rotation is the most challenging aspect of photogrammetry and representation of rotations plays an important role in solving the problem.
• 😚 Unit quaternions are a preferred notation for representing rotations in photogrammetry due to their closed-form solution and objective best-fit.
• 😥 Sampling the sphere requires a uniform distribution of points, which can be achieved by projecting points in a cube onto the surface of the sphere and rejecting outliers.
• 🥋 Regular polyhedra, such as tetrahedra, hexahedra, octahedra, dodecahedra, and icosahedra, can be used to divide the surface of a sphere for uniform sampling.

Questions & Answers

Q: What is the advantage of using unit quaternions in absolute orientation?

Unit quaternions provide a closed-form solution to the least worst problems, allowing objective best-fit answers compared to other notations.

Q: What are the two main operations in photogrammetry?

The composition of rotations (multiplication) and rotation of a vector (using q and q conjugate) are the two operations of interest in photogrammetry.

Q: How many points are needed for absolute orientation?

At least three points are needed for absolute orientation in photogrammetry.

Q: How can we deal with outliers in photogrammetry?

The RANSAC method is a way to deal with outliers in photogrammetry. It involves randomly selecting points, performing a best fit, and checking how many points agree with the fit.

Summary & Key Takeaways

• Photogrammetry explores the concept of photogrammetry and focuses on absolute orientation and sampling the sphere.

• Absolute orientation involves determining the rotation and translation of an object by using multiple photographs.

• Sampling the sphere involves finding a uniform distribution of points on the surface of a sphere.