Revision 13e6ac9959d5e3fb8d21a97ef4ba5140b8b0cdbf (click the page title to view the current version)
Changes from beginning to 13e6ac9959d5e3fb8d21a97ef4ba5140b8b0cdbf
---
title: Pre- and co-image
categories: lecture
---
# Lecture Notes
## Image and Image Plane
+ Image Plane is the universe where the image lives
$$ \text{image}\subset\text{image plane} $$
+ The Image Plane is a 2D World
+ The Image Plane exists in a 3D World
## Pre-image
+ Preimage is the set of points in 3D projecting onto the Image Plane
+ What is projection?
+ draw a line through the 3D point and origo (the pinhole)
+ the projection is the intersection with the image plane.
+ Thus
+ $\text{preimage} = \mathsf{span}(\text{image})$
+ $\text{image} = \text{preimage}\cap\text{image plane}$
## Co-image
+ Coimage is the set of points (space) orthogonal on the preimage
$$\text{coimage} = \text{preimage}^\bot$$
$$\text{preimage} = \text{coimage}^\bot$$