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Unformatted text preview: Computer Vision Radiometry Bahadir K. Gunturk 2 Radiometry Radiometry is the part of image formation concerned with the relation among the amounts of light energy emitted from light sources, reflected from surfaces, and registered by sensors. Bahadir K. Gunturk 3 Foreshortening A big source, viewed at a glancing angle, must produce the same effect as a small source viewed frontally. This phenomenon is known as foreshortening . Bahadir K. Gunturk 4 Solid Angle Solid angle is defined by the projected area of a surface patch onto a unit sphere of a point . (Solid angle is subtended by a point and a surface patch.) Bahadir K. Gunturk 5 Solid Angle Arc length r d r d Bahadir K. Gunturk 6 Solid Angle Solid angle is defined by the projected area of a surface patch onto a unit sphere of a point . 2 sin sin dA rd r d r d d = = 2 2 2 sin 4 TotalArea r d d r = = = = dA 2 sin dA dw d d r = = Bahadir K. Gunturk 7 Solid Angle Similarly, solid angle due to a line segment is r dl d Bahadir K. Gunturk 8 Foreshortening A point on a surface sees the world along a hemisphere of directions centered at the point. Bahadir K. Gunturk 9 Radiance The distribution of light in space is a function of position and direction. The appropriate unit for measuring the distribution of light in space is radiance , which is defined as the power (the amount of energy per unit time) traveling at some point in a specified direction, per unit area perpendicular to the direction of travel , per unit solid angle. In short, radiance is the amount of light radiated from a point (into a unit solid angle, from a unit area). Radiance = Power / (solid angle x foreshortened area) W/sr/m2 W is Watt, sr is steradian, m2 is metersquared Bahadir K. Gunturk 10 Radiance Radiance from dS to dR Radiance = Power / (solid angle x foreshortened area) Bahadir K. Gunturk 11 Radiance Example: Infinitesimal source and surface patches Source Illuminated surface 2 1 1 2 1 1 2 2 1 1 ( , ) cos cos cos d r d L dw dA dA dA = = x x x Radiance at x1 leaving to x2 2 2 2 cos dA dw r = Radiance = Power / (solid angle x foreshortened area) Bahadir K. Gunturk 12 Radiance Source Illuminated surface Power at x1 leaving to x2 2 2 2 cos dA dw r = 1 1 2 1 1 ( , ) cos d L dw dA = x x x 1 1 2 2 2 1 1 2 ( , ) cos cos L dA dA r = x x x Radiance = Power / (solid angle x foreshortened area) Bahadir K. Gunturk 13 Radiance The medium is vacuum, that is, it does not absorb energy. Therefore, the power reaching point x2 is equal to the power leaving for x2 from x1....
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 Spring '08
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