Table of contents

1. Introduction
   1. Basics
   2. Account for other issues in image frame
   3. Intrinsic and Extrinsic Decomposition
      1. Lesson Learnt:
   4. Final Version of Camera Model (I prefer this)

Introduction

Basics

In the above image, the division by Z happens implicitly due to homogenous coordinate notation

Account for other issues in image frame

We will introduce 3 coordinate systems below:

1. Camera Coordinate Frame
2. Image Coordinate Frame (where homogenous notation is used as there is no z-axis information)
3. World Coordinate Information

Sometimes the camera coordinate frame and the image coordinate frame is misaligned as shown below:

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Intrinsic and Extrinsic Decomposition

Lesson Learnt:

If we follow the how a 3D point gets left multiplied by extrinsic and then by intrinsic the coordinate frame intuition we derive is:

(3D Point -> Extrinsic -> Intrinsic) = (World Frame -> Camera Frame -> Image Frame)

t = Translation (last column of extrinsic matrix) R = Rotation (first 3x3 part of extrinsic matrix)

Final Version of Camera Model (I prefer this)