1 of 26

Introduction to computer vision I.5

Jean Ponce

jean.ponce@ens.fr

Zuhaib Akhtar za2023@nyu.edu

Ayush Jain aj3152@nyu.edu

Slides will be available after classes

2 of 26

Camera geometry�and calibration

  • Pinhole perspective projection
  • Orthographic and weak-perspective models
  • Non-standard models

3 of 26

Pinhole Perspective Equation

NOTE: z is always negative..

4 of 26

Affine projection models: Weak perspective projection

is the magnification.

When the scene relief is small compared its distance from the

Camera, m can be taken constant: weak perspective projection.

5 of 26

Affine projection models: Orthographic projection

When the camera is at a

(roughly constant) distance

from the scene, take m=-1.

6 of 26

Strong perspective:

  • Angles are not preserved

  • The projections of parallel lines intersect at one point

7 of 26

From Zisserman & Hartley

8 of 26

Strong perspective:

Angles are not preserved

The projections of parallel lines intersect at one point

Weak perspective:

Angles are better preserved

The projections of parallel lines are (almost) parallel

9 of 26

Planar pinhole

perspective

Orthographic

projection

Spherical pinhole

perspective

10 of 26

Planar pinhole

perspective

Orthographic

projection

Spherical pinhole

perspective

11 of 26

Diffraction effects

in pinhole

cameras.

Shrinking

pinhole

size

Use a lens!

12 of 26

Lenses

Snell’s law

n1 sin α1 = n2 sin α2

(Descartes’ law

for Frenchies)

13 of 26

Thin Lenses (including paraxial approximation)

14 of 26

Thick Lenses

15 of 26

Spherical

Aberration

Distortion

Chromatic

Aberration

16 of 26

Deblurring and chromatic aberration (Eboli, Sun, Ponce, 2021)

17 of 26

Deblurring and chromatic aberration (Eboli, Sun, Ponce, 2021)

18 of 26

Geometric Distortion

19 of 26

Rectification

20 of 26

Radial Distortion Model

21 of 26

A compound (aka real) lens

22 of 26

E=(Π/4) [ (d/z’)2 cos4α ] L

23 of 26

E=(Π/4) [ (d/z’)2 cos4α ] L

24 of 26

Vignetting

25 of 26

26 of 26

Challenge: Illumination – What is wrong with these pictures?