EECS 274 Computer Vision Cameras. Camera models –Pinhole Perspective Projection – Affine...

EECS 274 Computer Vision

Cameras

Cameras

• Camera models– Pinhole Perspective Projection– Affine Projection– Spherical Perspective Projection

• Camera with lenses• Sensing• Human eye• Reading: FP Chapter 1, S Chapter 2

Images are two-dimensional patterns of brightness values.

They are formed by the projection of 3D objects.

Figure from US Navy Manual of Basic Optics and Optical Instruments, prepared by Bureau of Naval Personnel. Reprinted by Dover Publications, Inc., 1969.

Animal eye: a looonnng time ago.

Pinhole perspective projection: Brunelleschi, XVth Century.Camera obscura: XVIth Century.

Photographic camera:Niepce, 1816.

Reproduced by permission, the American Society of Photogrammetry andRemote Sensing. A.L. Nowicki, “Stereoscopy.” Manual of Photogrammetry,Thompson, Radlinski, and Speert (eds.), third edition, 1966.

Figure from US Navy Manual of Basic Optics and Optical Instruments, prepared by Bureau of Naval Personnel. Reprinted by Dover Publications, Inc., 1969.

Parallel lines: appear to converge on a line formed by the intersection of a plane parallel to π and image plane

L in π that is parallel to image plane has no image at all

B’ and C’ have same heightA’ is half of B’

From the model C is half the size of BA is half the size of Bhn

Vanishing point

Vanishing point

The lines all converge in his right eye, drawing the viewers gaze to this place.

Pinhole Perspective Equation

z

yfy

z

xfx

z

f

y

y

x

x

zf

yy

xx

''

''

'''

'

'

'

NOTE: z is always negative

• C’ : image center• OC’: optical axis• π’ : image plane is at a positive distance f’ from the pinhole• OP’= λ OP• P: (x,y,z), P’(x’,y’,z’)

Affine projection models: Weak perspective projection

0

'where

'

'

z

fm

myy

mxx

is the magnification.

When the scene relief (depth) is small compared its distance from thecamera, m can be taken constant: weak perspective projection.

frontal-parallel plane π0 defined by z=z0

Affine projection models: Orthographic projection

yy

xx

'

' When the camera is always at a(roughly constant) distancefrom the scene, take m=-1

Planar pinhole perspective

Orthographicprojection

Spherical pinholeperspective

Pinhole too big - many directions are averaged, blurring the image

Pinhole too small- diffraction effects blur the image

Generally, pinhole cameras are dark, becausea very small set of raysfrom a particular pointhits the screen

Pinhole camera

Snell’s law (aka Descartes’ law)

Ignoring diffraction, interference

n1 sin 1 = n2 sin 2

n: index of refraction

reflection

refraction

Lenses

Snell’s law:

n1 sin 1 = n2 sin 2

Small angles:

n11 ¼ n22

Paraxial (or first-order) optics

Small angles:

n11 ¼ n22 R

nn

d

n

d

n 12

2

2

1

1

222

111

d

h

R

h

d

h

R

h

Paraxial (or first-order) optics

)1(2 and

11

'

1 e wher

''

''

n

Rf

fzz

z

yzy

z

xzx

f: focal length F, F’: focal points

Thin lenses: n=1

Thin Lenses

Depth of field and field of view• Depth of field (field of focus): objects

within certain range of distances are in acceptable focus– Depends on focal length and aperture

• Field of view: portion of scene space that are actually projected onto camera sensors– Not only defined by focal length– But also depends on effective sensor area

Depth of field

• Changing the aperture size affects depth of field– A smaller aperture increases the range in which the object is

approximately in focus– f number = f/D (f: focal length, D: diameter or aperature)

f / 5.6

f / 32

Thick lenses

• Simple lenses suffer from several aberrations• First order approximation is not sufficient• Use 3rd order Taylor approximation

Orthographic/telecentric lenses

http://www.lhup.edu/~dsimanek/3d/telecent.htm

Navitar telecentric zoom lens

Correcting radial distortion

from Helmut Dersch

SphericalAberration•rays do not intersect at one point•circle of least confusion

Distortion

ChromaticAberrationrefracted rays of different wavelengths intersect the optical axis at different points

Figure from US Navy Manual of Basic Optics and Optical Instruments, prepared by Bureau of Naval Personnel. Reprinted by Dover Publications, Inc., 1969.

pincushion barrel

Vignetting

• Aberrations can be minimized by aligning simple lenses with well-chosen shapes and refraction indexes, separated by appropriate stops• These compound lenses can still be modeled by thick lenses• However, light rays from object points off-axis are partially blocked by lens configuration vignetting brightness drop in the image periphery

Helmoltz’s SchematicEye

Reproduced by permission, the American Society of Photogrammetry andRemote Sensing. A.L. Nowicki, “Stereoscopy.” Manual of Photogrammetry,Thompson, Radlinski, and Speert (eds.), third edition, 1966.

Corena: transparent highly curved refractive componentPupil: opening at center of iris in response to illumination

Human eye

Retina: thin, layered membrane with two types of photoreceptors

• rods: very sensitive to light but poor spatial detail• cones: sensitive to spatial details but active at higher light level • generally called receptive field

Reprinted from Foundations of Vision, by B. Wandell, Sinauer Associates, Inc., (1995). 1995 Sinauer Associates, Inc.

Cones in the fovea Rods and cones in the periphery

Reprinted from Foundations of Vision, by B. Wandell, Sinauer Associates, Inc., (1995). 1995 Sinauer Associates, Inc.

Receptive field

Photographs (Niepce, “La Table Servie,” 1822)

Milestones: Daguerreotypes (1839)Photographic Film (Eastman,1889)Cinema (Lumière Brothers,1895)Color Photography (LumièreBrothers, 1908)Television (Baird, Farnsworth,Zworykin, 1920s)

CCD Devices (1970)

Collection Harlingue-Viollet. .

Sensing

360 degree field of view…

• Basic approach– Take a photo of a parabolic mirror with an orthographic lens (Nayar)– Or buy one a lens from a variety of omnicam manufacturers…

• See http://www.cis.upenn.edu/~kostas/omni.html

Digital camera

• A digital camera replaces film with a sensor array– Each cell in the array is a Charge Coupled Device

• light-sensitive diode that converts photons to electrons• other variants exist: CMOS is becoming more popular• http://electronics.howstuffworks.com/digital-camera.htm

Image sensing pipeline