1 Ch. 4: Radiometry–Measuring Light Preview 。 The intensity of an image reflects the brightness of a scene, which in turn is determined by (a) the amount of light incident on the scene (b) the characteristic of the scene, and 。 An image I is hence often modeled as, where R: reflectance component L: illumination component R typically remains constant to changes of environmental conditions.

2 。 Separating R and L is critical in many applications. Shadow removal Highlight removal Reflection removal

3 However, image decomposition is an ill-posed problem. Additional information is required. To this end, understanding the behavior of light is important. 4.1 Light in Space ○ Radiometry: Studies the behavior (or measurement) of light, including (a) How energy is transferred from a light source to a surface (b) What happens to the energy when it arrives at a surface.

Foreshortening As a source is tilted w.r.t. the direction in which the illumination is traveling, it looks smaller to the surface viewing the source. The effect that a source has on a surface depends on how that source looks from the point of view of the surface, and vice versa.

5 ○ Hemisphere of directions (for a surface point): (a) A surface point sees the world along a hemisphere of directions centered at the point (b) The brightness of the point is computed by summing effects of all incoming directions

Solid Angle -- Describes the pattern a source generates on an unit sphere. ○ Planar angle (radian): ○ Solid angle (steradian)

7 。 Another equation for solid angle: Consider a unit sphere (r = 1) The ring length at latitude The ring area at latitude The area of a small patch on the ring with longitudinal angle

Radiance (unit: ) Radiance -- The amount of energy in direction, per unit time, per unit solid angle, per unit area, from point P

Irradiance Irradiance -- The amount of incident energy at point (P) in direction, per unit time, per unit area 。 The incoming power incident on a surface at a point is computed by summing the irradiance over the input hemisphere.

10 ○ Considering a source patch, the energy transmitted by into an infinitesimal region around direction of solid angle in time dt is

11 Let in the direction In time dt, the energy leaving for is where is the solid angle at subtended by ○ Consider patches, leaving of : the radiance

12 Let where is the solid angle at subtended by in the direction of The energy arriving from is : the irradiance arriving Substitute into the above equation

13 i.e., The energy leaving in direction of is the same as the energy direction of arriving Energy is constant along straight light, i.e., from

Example: radiometry of thin lenses

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17 (e) Image irradiance E is irrelevant to the distance z between the center of the lens and the scene patch

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Bidirectional Reflectance Distribution Function (BRDF) -- Defined as the ratio of the outgoing radiance in to the incoming irradiance in ＊ depends on both directions and

20 。 The radiance leaving a surface in due to its irradiance (from all directions):

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