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

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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
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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
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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
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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
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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
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Angles and Solid Angles R L l = = θ 2 R A a = = Ω (radians) (steradians)
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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
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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
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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
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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
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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 )
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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.

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

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