lecture11 - EECS 442 Computer vision Multiple view geometry...

Info iconThis preview shows pages 1–14. Sign up to view the full content.

View Full Document Right Arrow Icon
EECS 442 – Computer vision Multiple view geometry Perspective Structure from Motion Reading: [HZ] Chapters: 10,18,19 [FP] Chapter: 13 Some slides of this lectures are courtesy of prof. S. Lazebnik - Perspective structure from motion problem - Ambiguities - Algebraic methods - Factorization methods - Bundle adjustment - Self-calibration
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
From the m x n correspondences x ij , estimate: •m projection matrices M i •n 3D points X j x 1 j x 2 j x m j X j motion structure M 1 M 2 M m Structure from motion problem
Background image of page 2
Structure from motion ambiguity - Position ambiguity: it is impossible based on the images alone to estimate the absolute location and pose of the scene w.r.t. a 3D world coordinate frame
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Structure from motion ambiguity -Scale ambiguity: it is impossible based on the images alone to estimate the absolute scale of the scene (i.e. house height)
Background image of page 4
Structure from motion ambiguity -The scene is determined by the images only up a similarity transformation (rotation, translation and scaling) = s / 1 0 t R 1 0 t R 1 s s H s
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
= s / 1 0 t R 1 0 t R 1 s s H s [ ] i i i i T R K M = j i j X M x = j j i j s 1 s i j x X M X H H M x ~ = = = j s X H 1 s i H M [ ] [ ] i 1 i i 1 s i i i 1 s i T R R K H T R K H M = = The calibration matrix has not changed!
Background image of page 6
• The ambiguity exists even for calibrated cameras Structure from motion ambiguity • For calibrated cameras, the similarity ambiguity is the only ambiguity [Longuet-Higgins ’81]
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Structure from motion ambiguity [ ] i i i i T R K M = j i j X M x = j X H 1 j H M • In the general case (nothing is known) the ambiguity is expressed by an arbitrary affine or projective transformation ( )( ) j i j i j X H H M X M x -1 = =
Background image of page 8
Projective ambiguity
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Affine ambiguity
Background image of page 10
Structure from motion problem Given m images of n fixed 3D points x ij = M i X j , i = 1 , … , m, j = 1 , … , n x 1 j x 2 j x m j X j M 1 M 2 M m
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Structure from motion problem mcameras M 1 …M m x 1 j x 2 j x m j X j M 1 M 2 M m = 1 a a a b a a a b a a a M 33 32 31 2 23 22 21 1 13 12 11 i
Background image of page 12
The Structure-from-Motion Problem Given m images of n fixed points X j we can write Problem: estimate the m 3 × 4 matrices M i and the n positions X j from the m × n correspondences x ij . • With no calibration info, cameras and points can only be recovered up to a 4x4 projective j i ij X M x = • Given two cameras, how many points are needed?
Background image of page 13

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 14
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 10/26/2010 for the course EECS 442 taught by Professor Savarese during the Fall '09 term at University of Michigan.

Page1 / 49

lecture11 - EECS 442 Computer vision Multiple view geometry...

This preview shows document pages 1 - 14. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online