lecture13 - EECS 442 Computer vision Radiometry Elements of...

This preview shows pages 1–12. Sign up to view the full content.

EECS 442 – Computer vision Radiometry Reading: [FP] Chapters: 4,5 Some slides of this lectures are courtesy of prof. J. Ponce, prof F. Li, and prof S. Lazebnik • Elements of Radiometry •Rad iance • Irradiance •BRDF • Shading models • Photometric Stereo

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

View Full Document
What determines the brightness of an image pixel? The light source(s) The surface normal The surface Properties The optics The sensor characteristics Image Formation: Radiometry So far: • Relationship between surface geometry and sensor
What determines the brightness of an image pixel? The light source(s) The surface normal The surface properties The optics The sensor characteristics Image Formation: Radiometry Today: We study how light is transferred: •From light source to surface •From surface to sensor

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

View Full Document
The Illumination and Viewing Hemi-sphere ) φ , ( θ i i ) φ , ( θ o o y) (x, n r y) (x, ρ At infinitesimal, each point has a tangent plane, and thus a hemisphere W. The ray of light is indexed by the polar coordinates φ ) , ( θ Æ Introduce concept of solid angle
Measuring Angle • The solid angle sub- tended by an object from a point P is the area of the projection of the object onto the unit sphere centered at P • Definition is analogous to projected angle in 2D • If I’m at P, and I look out, solid angle tells me how much of my view is filled with an object p object p

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

View Full Document
Angles and Solid Angles R L l = = θ 2 R A a = = Ω (radians) (steradians)
Infinitesimal small angle r cos dl d θ φ= φ d dl t P The angle subtended by an infinitesimal element from a point P n

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

View Full Document
2 cos r dA d θ ω= A P Infinitesimal small solid angle The solid angle subtended by an infinitesimal patch from a point P
δ 2 P = L( P, v ) δ A δω δ t δ 2 P = L( P, v ) cos θδ A δω δ t DEFINITION: The radiance L( P, v ) is the power (=energy per unit time) traveling at point P in a given direction v ( per unit area perpendicular to this direction) (per unit solid angle) Radiance Used to measure the distribution of light in space Energy δ 2 P transmitted by a patch δ A into solid angle δω Fore shortening

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

View Full Document
The irradiance is the power (per unit area incident on a surface). δ E= ±L i ( P , v i ) δω i cos θ i E= H L i (P, v i ) cos θ i d ω i Irradiance () φ θ , E Used for representing incoming power δ 2 P= δ E δ A=L i ( P , v i ) cos θ i δω i δΑ δ t Radiance in a region of solid angle d ω i cos dA
Radiance (L ): energy carried by a ray • Power per unit area perpendicular to the direction of travel, per unit solid angle • Units: Watts per square meter per steradian (W m -2 sr -1 )

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

View Full Document
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

lecture13 - EECS 442 Computer vision Radiometry Elements of...

This preview shows document pages 1 - 12. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online