Cameras

Course web page:vision.cis.udel.edu/cv

March 22, 2003 Lecture 16

Announcements

• Read Forsyth & Ponce, Chapter 3-3.3 on camera calibration for Monday

• HW3: Some image sizes have been reduced and you don’t have to try as many window sizes

Outline

• Lenses• Discretization effects of image

capture

Ideal Pinhole Camera

from Forsyth & Ponce

Each point on the image plane collects light along one ray from the scene

Real Pinhole Cameras• Problems

– Pinholes don’t let through much light ! Dimness/exposure time trade-off

– A bigger hole (aka aperture) means that each image point sees a disk of scene points, whose contributions are averaged ! Blurring

– Very small apertures introduce diffraction effects

from Forsyth & Ponce

Real pinhole camera images

from Forsyth & Ponce

Hole too small:

Diffraction

Hole too big:

Blurring

Lenses

• Benefits: Increase light-gathering power by focusing bundles of rays from scene points onto image points

from Forsyth & Ponce

Refraction• Definition: Bending of light ray as it crosses

interface between media (e.g., air ! glass or vice versa)

• Index of refraction (IOR) n for a medium: Ratio of speed of light in vacuum to that in medium– By definition, n ¸ 1

– Examples: 1 ¼ nair < nwater < nglass

µ1: Angle of incidence

µ2: Angle of refraction

courtesy ofWolfram

Snell’s Law

• The relationship between the angle of incidence and the angle of refraction is given by:

courtesy ofWolfram

Snell’s Law: Implications• Since µ / sin µ over the range [0, ¼/2]

and the angle of refraction is given by

we can infer the following from their IORs:

n1 < n2 ) µ2 < µ1 and n1 > n2 ) µ2 > µ1

courtesy ofWolfram

So n1 < n2

in this image

divergence

convergence

Converging Light Rays

n1 < n2

n2n1

Redirecting Light

• Prisms: Light traveling from a low IOR medium to a high IOR medium and back again is bent by an amount proportional to the apex angle

courtesy of Prentice-Hall

Focusing Light with Prisms

courtesy of S. Majewski

Focusing Light with Prisms: Many Beams

Light rays intersecting the prisms at different locationshave different angles of incidence and thus wind up withdifferent focal points

courtesy of S. Majewski

Lenses as Compound Prisms

We can get the light rays to have a common focus bygradually widening the effective apex angle as we getfarther from the center of the lens

courtesy of S. Majewski

Thin Lenses

• Properties– A ray entering the lens parallel to the optical axis goes

through the focus on the other side– A ray entering the lens from the focus on one side

emerges parallel to the axis on the other side

optical axis

focus focuscourtesy of MTSU

Thin Lens Image Projection

courtesy of U. Colorado

z

Thin Lens Image Projection

z

Thin Lens Image Projection

z

Thin Lens Image Projection

z

Thin Lens Model

from Forsyth & Ponce

Depth of Field

• The thin lens equation implies that scene points at different distances from the lens are in focus at different image distances

• Only a given range of object distances produce acceptable sharpness

Field of View

FOV is defined as 2Á, where Á = tan-1 d/2f

from Forsyth & Ponce

Lens Problems

• Limited depth of field• Radial, tangential distortion:

Straight lines curved• Vignetting: Image darker at edges• Spherical aberration• Chromatic aberration: Focal length

function of wavelength

Radial Distortion

Vignetting

Analog Digital

• Sampling Aliasing • Quantization Banding• Limited dynamic range

Saturation • Temporal integration Motion

blur• Noise

1/30th sec.exposure

Sampling

• Limited spatial resolution of capture devices results in visual artifacts (i.e., aliasing)– Nyquist theorem: Must sample 2x

highest frequency component of signal to reconstruct adequately

High Dynamic Range Panoramas

courtesy of D. Lischinski

HDRmosaic

Under- andover-exposed

mosaic