Basic Principles of Surface Reflectance Thanks to Srinivasa Narasimhan, Ravi Ram

Basic Principles of Surface Reflectance Thanks to Srinivasa Narasimhan, Ravi Ram www.phwiki.com

Basic Principles of Surface Reflectance Thanks to Srinivasa Narasimhan, Ravi Ram

Lewis, Judith, Contributing Editor has reference to this Academic Journal, PHwiki organized this Journal Basic Principles of Surface Reflectance Thanks to Srinivasa Narasimhan, Ravi Ramamoorthi, Pat Hanrahan Radiometry in addition to Image Formation Image Intensities Image intensities = f ( normal, surface reflectance, illumination ) Note: Image intensity underst in addition to ing is an under-constrained problem! source sensor surface element normal Need to consider light propagation in a cone

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Radiometric Concepts (1) Solid Angle : ( steradian ) What is the solid angle subtended by a hemisphere (solid angle subtended by ) ( as long as eshortened area) (surface area) (2) Radiant Intensity of Source : Light Flux (power) emitted per unit solid angle ( watts / steradian ) (3) Surface Irradiance : ( watts / m2 ) Light Flux (power) incident per unit surface area. Does not depend on where the light is coming from! source

The Fundamental Assumption in Vision Surface Camera No Change in Radiance Lighting Radiance Properties Radiance is constant as it propagates along ray Derived from conservation of flux Fundamental in Light Transport. Scene Radiance L Lens Image Irradiance E Camera Electronics Scene Image Irradiance E Relationship between Scene in addition to Image Brightness Measured Pixel Values, I Non-linear Mapping! Linear Mapping! Be as long as e light hits the image plane: After light hits the image plane: Can we go from measured pixel value, I, to scene radiance, L

Relation Between Image Irradiance E in addition to Scene Radiance L f z surface patch image plane image patch Relation Between Image Irradiance E in addition to Scene Radiance L f z surface patch image plane image patch Relation between Pixel Values I in addition to Image Irradiance E The camera response function relates image irradiance at the image plane to the measured pixel intensity values. Camera Electronics Image Irradiance E Measured Pixel Values, I (Grossberg in addition to Nayar)

Radiometric Calibration Important preprocessing step as long as many vision in addition to graphics algorithms such as photometric stereo, invariants, de-weathering, inverse rendering, image based rendering, etc. Use a color chart with precisely known reflectances. Irradiance = const Reflectance Pixel Values 3.1% 9.0% 19.8% 36.2% 59.1% 90% Use more camera exposures to fill up the curve. Method assumes constant lighting on all patches in addition to works best when source is far away (example sunlight). Unique inverse exists because g is monotonic in addition to smooth as long as all cameras. 0 255 0 1 g The Problem of Dynamic Range The Problem of Dynamic Range Dynamic Range: Range of brightness values measurable with a camera (Hood 1986) High Exposure Image Low Exposure Image We need 5-10 million values to store all brightnesses around us. But, typical 8-bit cameras provide only 256 values!! Today’s Cameras: Limited Dynamic Range

Images taken with a fish-eye lens of the sky show the wide range of brightnesses. High Dynamic Range Imaging Capture a lot of images with different exposure settings. Apply radiometric calibration to each camera. Combine the calibrated images ( as long as example, using averaging weighted by exposures). (Debevec) (Mitsunaga) Computer Vision: Building Machines that See Lighting Scene We need to underst in addition to the Geometric in addition to Radiometric relations between the scene in addition to its image. Computer Graphics: Rendering things that Look Real Lighting Scene We need to underst in addition to the Geometric in addition to Radiometric relations between the scene in addition to its image.

Basic Principles of Surface Reflection Surface Appearance Image intensities = f ( normal, surface reflectance, illumination ) Surface Reflection depends on both the viewing in addition to illumination direction. source sensor surface element normal BRDF: Bidirectional Reflectance Distribution Function x y z source viewing direction surface element normal incident direction Irradiance at Surface in direction Radiance of Surface in direction BRDF :

Important Properties of BRDFs x y z source viewing direction surface element normal incident direction BRDF is only a function of 3 variables : Rotational Symmetry (Isotropy): Appearance does not change when surface is rotated about the normal. Helmholtz Reciprocity: (follows from 2nd Law of Thermodynamics) Appearance does not change when source in addition to viewing directions are swapped. Derivation of the Scene Radiance Equation From the definition of BRDF: Derivation of the Scene Radiance Equation – Important! From the definition of BRDF: Write Surface Irradiance in terms of Source Radiance: Integrate over entire hemisphere of possible source directions: Convert from solid angle to theta-phi representation:

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Mechanisms of Surface Reflection source surface reflection surface incident direction body reflection Body Reflection: Diffuse Reflection Matte Appearance Non-Homogeneous Medium Clay, paper, etc Surface Reflection: Specular Reflection Glossy Appearance Highlights Dominant as long as Metals Image Intensity = Body Reflection + Surface Reflection Mechanisms of Surface Reflection Body Reflection: Diffuse Reflection Matte Appearance Non-Homogeneous Medium Clay, paper, etc Surface Reflection: Specular Reflection Glossy Appearance Highlights Dominant as long as Metals Many materials exhibit both Reflections: Diffuse Reflection in addition to Lambertian BRDF viewing direction surface element normal incident direction Lambertian BRDF is simply a constant : albedo Surface appears equally bright from ALL directions! (independent of ) Surface Radiance : Commonly used in Vision in addition to Graphics! source intensity source intensity I

Diffuse Reflection in addition to Lambertian BRDF White-out Conditions from an Overcast Sky CAN’T perceive the shape of the snow covered terrain! CAN perceive shape in regions lit by the street lamp!! WHY Diffuse Reflection from Uni as long as m Sky Assume Lambertian Surface with Albedo = 1 (no absorption) Assume Sky radiance is constant Substituting in above Equation: Radiance of any patch is the same as Sky radiance !! (white-out condition)

Those Were the Days “In trying to improve the quality of the synthetic images, we do not expect to be able to display the object exactly as it would appear in reality, with texture, overcast shadows, etc. We hope only to display an image that approximates the real object closely enough to provide a certain degree of realism.” – Bui Tuong Phong, 1975

Lewis, Judith Contributing Editor

Lewis, Judith is from United States and they belong to High Country News and they are from  Tuscaloosa, United States got related to this Particular Journal. and Lewis, Judith deal with the subjects like Environment; Regional Interest

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