Lec05.2DWarping

# Warping this will leave holes because every pixel

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Affine Transformation •  Ax = B •  Cannot take inverse directly •  Also, 4 correspondences may not be exactly represented by an affine transformation [Why ?] ⎡ྎ x1 ⎢ྎ 0 ⎢ྎ ⎢ྎ x2 ⎢ྎ ⎢ྎ 0 ⎢ྎ x3 ⎢ྎ ⎢ྎ 0 ⎢ྎ x ⎢ྎ 4 ⎢ྎ 0 ⎣ྏ y1 0 1 0 0 x1 0 y1 y2 0 y3 10 0 x2 10 0 y2 0 0 y4 0 0 x3 10 0 x4 y3 0 y4 0⎤ྏ ⎡ྎ x1 ' ⎤ྏ 1⎥ྏ ⎡ྎ a1 ⎤ྏ ⎢ྎ y1 ' ⎥ྏ ⎥ྏ ⎢ྎ ⎥ྏ ⎢ྎa ⎥ྏ ⎢ྎ x '⎥ྏ 0⎥ྏ ⎢ྎ 2 ⎥ྏ 2 ⎥ྏ ⎢ྎ ⎥ྏ 1⎥ྏ ⎢ྎ a3 ⎥ྏ ⎢ྎ y2 '⎥ྏ ⎢ྎ ⎥ྏ = ⎢ྎ ⎥ྏ 0⎥ྏ ⎢ྎa4 ⎥ྏ x3 ' ⎥ྏ ⎢ྎ ⎥ྏ ⎢ྎ a5 ⎥ྏ ⎢ྎ y3 '⎥ྏ 1⎥ྏ ⎥ྏ ⎢ྎa ⎥ྏ ⎢ྎ x '⎥ྏ 0 ⎢ྎ 6 ⎥ྏ ⎥ྏ ⎣ྏ ⎦ྏ ⎢ྎ 4 ⎥ྏ 1⎥ྏ ⎢ྎ y4 '⎥ྏ ⎦ྏ ⎣ྏ ⎦ྏ Pseudo inverse For an over-constrained linear system Ax = B A has more rows than columns Multiply by AT on both sides ATAx = ATB ATA is a square matrix of as many rows as x We can take its inverse x = (ATA)-1ATB Pseudo-inverse gives the least squares error solution! [Proof?] Recovering Best Affine Transformation n༆  n༆  n༆  n༆  n༆  n༆  In general, we may be given n correspondences Co...
View Full Document

## This note was uploaded on 03/02/2014 for the course CS 436 taught by Professor Sohaibkhan during the Winter '13 term at Lahore University of Management Sciences.

Ask a homework question - tutors are online