1 Introduction

Intrinsic matrix:

projection: 3d⇒2d + discretization: (x,y) ⇒ (u,v)

Projection / camera matrix M

2 Intrinsic matrix

2.1 Ideal Projection Matrix

Ideal Projection for Thin Lenses / Pinhole cameras

• image or retinal plane: II’
• focal length f
• Note: z is always negative

Note: 其实这里的z，应该用符号w。它不是欧式空间的第三个坐标，是2d homogenous coordinates的第三个坐标。对应的投影后的2d 欧式坐标应该是 x‘=fx/z, y’=fy/z

Ideal Projection with the following assumptions:

Extrinsic Assumptions

• No rotation
• Camera at (0,0,0)