Table of Contents 1. Motivation: sports analytics 2. Points 3. Lines 4. Conics 4.1. Projection 4.2. Distortion: Objects behind the camera plane 5. Images 5.1. Projection via object decomposition 6. References 1. Motivation: sports analytics At this point, we know how to mathematically characterise the mapping between the 3D world and a 2D image capturing it. So it seems natural to wonder: what can we do with it? In this post, I will focus on a use case that I happen to be familiar with, but there are many others you can think of....

Table of Contents 1. Pinhole camera model 2. Intrinsic matrix 2.1. Setup 2.2. Homogeneous coordinates 2.3. Accounting for distortions 2.3.1. Digital images 2.3.2. Rephotographing Images 3. Extrinsic matrix 4. Homography matrix 5. References 1. Pinhole camera model When we capture something on camera, there is an interesting phenomenon going on: compression. We are taking a photograph of a 3D world, and capturing it in a 2D image. This 3D→2D space mapping inevitably leads to information loss....