A Unified Formula for Affine Transformations between Calibrated Cameras

TL;DR

This paper derives a closed-form affine transformation formula that maps local image patches between two calibrated camera views, depending on camera pose, image coordinates, and surface normals.

Contribution

It introduces a unified, explicit formula for affine transformations in calibrated stereo views, linking geometry and surface normals.

Findings

Provides a closed-form expression for affine transformations.

Links transformation parameters to camera pose and surface normals.

Facilitates improved image patch correspondence in stereo vision.

Abstract

In this technical note, we derive a closed-form expression for the affine transformation mapping local image patches between two calibrated views. We show that the transformation is a function of the relative camera pose, the image coordinates, and the local surface normal.