Single View Metrology 3D photography course schedule Topic Feb 21 - - PowerPoint PPT Presentation

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Single View Metrology 3D photography course schedule Topic Feb 21 - - PowerPoint PPT Presentation

Sep 12, 2023 245 likes •511 views

Single View Metrology 3D photography course schedule Topic Feb 21 Introduction Feb 28 Lecture: Geometry, Camera Model, Calibration Mar 7 Lecture: Features & Correspondences Mar 14 Project Proposals Mar 21 Lecture: Epipolar Geometry

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SLIDE 1

Single View Metrology

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SLIDE 2

3D photography course schedule

Topic

Feb 21 Introduction Feb 28 Lecture: Geometry, Camera Model, Calibration Mar 7 Lecture: Features & Correspondences Mar 14 Project Proposals Mar 21 Lecture: Epipolar Geometry Mar 28 Depth Estimation + 2 papers Apr 4 Single View Geometry + 2 papers Apr 11 Active Ranging and Structured Light + 2 papers Apr 18 Project Updates

  • Apr. 25
  • -- Easter ---

May 2 SLAM + 2 papers May 9 3D & Registration + 2 papers May 16 Structure from Motion + 2 papers May 23 Shape from Silhouettes + 2 papers May 30 Final Projects (if not demo day)

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Single View Metrology

Pictures from “Single View Metrology” by A. Criminisi et al.

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Measuring in a plane

Need to compute H as well as uncertainty

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Direct Linear Transformation (DLT)

(wrap-up, compare lect. 3)

i i

Hx x   Hx x   

i i

            

i i i i

x h x h x h Hx

3 2 1 T T T

                       

i i i i i i i i i i i i i i

y x x w w y x h x h x h x h x h x h Hx x

1 2 3 1 2 3 T T T T T T

h h h x x x x x x

3 2 1

                             

T T T T T T T T T i i i i i i i i i i i i

x y x w y w

 

T i i i i

w y x      , , x

h A 

i

Normalize coordinates !

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SLIDE 6

Gold Standard algorithm

Objective Given n≥4 2D to 2D point correspondences {xi↔xi’}, determine the Maximum Likelyhood Estimation of H (this also implies computing optimal xi’=Hxi) Algorithm (i) Initialization: compute an initial estimate using normalized DLT or RANSAC (ii) Geometric minimization of reprojection error:

  • Minimize using Levenberg-Marquardt over 9 entries of h
  • r Gold Standard error:
  • compute initial estimate for optimal {xi}
  • minimize cost over {H,x1,x2,…,xn}
  • if many points, use sparse method

   

2 i 2 i

x ˆ , x x ˆ , x

i i

d d   

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SLIDE 7

Using covariance matrix in point transfer

T h h h x

J J    

Error in one image

T x x x T h h h x

J J J J      

Error in two images (or image and scene) (if h and x independent, i.e. new points)

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SLIDE 8

s=1 pixel =0.5cm (Criminisi’97)

Example:

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s=1 pixel =0.5cm

Example:

(Criminisi’97)

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SLIDE 10

Example:

(Criminisi’97)

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SLIDE 11

Monte Carlo estimation of covariance

  • To be used when previous assumptions

do not hold (e.g. non-flat within variance)

  • r to complicate to compute.
  • Simple and general, but expensive
  • Generate samples according to assumed

noise distribution, carry out computations,

  • bserve distribution of result
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SLIDE 12

Single view measurements: 3D scene

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SLIDE 13

Background: Projective geometry

  • f 1D

x ' x

2 2

 H

The cross ratio Invariant under projective transformations

3DOF (2x2-1)

 

4 2 3 1 4 3 2 1 4 3 2 1

x , x x , x x , x x , x x , x ; x , x 

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SLIDE 14

Vanishing points

  • Under perspective projection points at infinity can have a

finite image

  • The projection of 3D parallel lines intersect at vanishing

points in the image

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Basic geometry

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Basic geometry

  • Allows to relate height of point to height of camera
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Homology mapping between parallel planes

  • Allows to transfer point from one plane to another
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Single view measurements

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Single view measurements

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Forensic applications

190.6±2.9 cm 190.6±4.1 cm

  • A. Criminisi, I. Reid, and A. Zisserman.

Computing 3D euclidean distance from a single view. Technical Report OUEL 2158/98, Dept. Eng. Science, University of Oxford, 1998.

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SLIDE 21

Example

courtesy of Antonio Criminisi

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SLIDE 22

La Flagellazione di Cristo (1460) Galleria Nazionale delle Marche by Piero della Francesca (1416-1492)

http://www.robots.ox.ac.uk/~vgg/projects/SingleView/

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More interesting stuff

  • Criminisi demo

http://www.robots.ox.ac.uk/~vgg/presentations/ spie98/criminis/index.html

  • work by Derek Hoiem on learning

single view 3D structure and apps

http://www.cs.cmu.edu/~dhoiem/

  • similar work by Ashutosh Saxena on

learning single view depth

http://ai.stanford.edu/~asaxena/learningdepth/

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Administrative

  • Projects and Papers assigned !?
  • Hardware? Mobile Kinects?
  • Forum: Share Experiences
  • In two weeks: Project updates

Each team presents (5-10 min.):

  • intermediate results
  • solved/unsolved/unforeseen things
  • adaption of goals
  • … anything else relevant …
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SLIDE 25

Presentations

  • Automatic Photo Popup:

Classify in Ground/Verticals/Sky and reconstruct

  • Video Compass:

Estimate Vanishing Points and Camera Calibration