Basic Principles of Surface Reflectance.pdf

Basic Principles of Surface ReflectanceThanks to Shree Nayar, Ravi Ramamoorthi, Pat Hanrahan Surface Appearance sensor source normal surface element Image intensities = f ( normal, surface reflectance, illumination ) Surface Reflection depends on both the viewing and illumination direction. BRDF: Bidirectional Reflectance Distribution Function source z incident direction  ( i . i ) Lsurface( r . r )  ( r . r ) E surface( i . i ) Irradiance at Surface in direction ( i .  r . r ) BRDF : f Radiance of Surface in direction ( i . i . i ) y viewing direction ( r . i ) . r ) normal  surface element x E surface( i . r ) Lsurface( r .  r . r ) normal y  surface element x • Rotational Symmetry: Appearance does not change when surface is rotated about the normal. i  r ) • Helmholtz Reciprocity: (follows from 2nd Law of Thermodynamics) Appearance does not change when source and viewing directions are swapped. i ) . f (i . r )  f ( r . r .  r . BRDF is only a function of 3 variables : f ( i . i .Important Properties of BRDFs source z incident direction  ( i . i ) viewing direction ( r . i . etc Surface Reflection: Specular Reflection Glossy Appearance Highlights Dominant for Metals Image Intensity = Body Reflection + Surface Reflection .Mechanisms of Surface Reflection source incident direction surface reflection body reflection surface Body Reflection: Diffuse Reflection Matte Appearance Non-Homogeneous Medium Clay. paper. etc Many materials exhibit both Reflections: Surface Reflection: Specular Reflection Glossy Appearance Highlights Dominant for Metals . paper.Mechanisms of Surface Reflection Body Reflection: Diffuse Reflection Matte Appearance Non-Homogeneous Medium Clay. Diffuse Reflection and Lambertian BRDF . i .Diffuse Reflection and Lambertian BRDF source intensity I incident direction s normal n i viewing direction v surface element • Surface appears equally bright from ALL directions! (independent of • Lambertian BRDF is simply a constant : • Surface Radiance : f ( i .  r .s  v) d  source intensity albedo . r )  d L I cos  i  • Commonly used in Vision and Graphics!  d I n. Rendered Sphere with Lambertian BRDF • Edges are dark (N.S = 0) when lit head-on • See shading effects clearly. . 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? . v )   s  (i   v )  (i    v ) • Surface Radiance : L  I  s  (i   v )  (i    v ) v = r ) .Specular Reflection and Mirror BRDF source intensity I incident direction ( i . (only when • Mirror BRDF is simply a double-delta function : specular albedo f (i . i . v ) • Very smooth surface. r ) n viewing direction surface element v ( v . v . i ) s normal specular/mirror direction r ( r . • All incident light energy reflected in a SINGLE direction. • Surfaces are not perfectly smooth – they show micro-surface geometry (roughness). • Example Models : Phong model Torrance Sparrow model .Glossy Surfaces • Delta Function too harsh a BRDF model (valid only for highly polished mirrors and metals). • Many glossy surfaces show broader highlights in addition to mirror reflection. Blurred Highlights and Surface Roughness Roughness . • Very commonly used in computer graphics. easy to compute • But not physically based (no energy conservation and reciprocity). .E ) R   S  2( N .Phong Model: An Empirical Approximation • How to model the angular falloff of highlights: N -S N H R E L  I  s ( R.H ) H  (E  S ) / 2 nshiny Blinn-Phong Model • Sort of works.S ) N nshiny Phong Model L  I  s ( N . Phong Examples • These spheres illustrate the Phong model as lighting direction and nshiny are varied: . with texture. 1975 .” – Bui Tuong Phong. overcast shadows. We hope only to display an image that approximates the real object closely enough to provide a certain degree of realism. we do not expect to be able to display the object exactly as it would appear in reality.Those Were the Days • “In trying to improve the quality of the synthetic images. etc. All components of Surface Reflection . . . Glittering .Reflections on water surfaces . Split off-specular Reflections in Woven Surfaces . . edges of the moon look bright (not close to zero) when illuminated by earth’s radiance.Why does the Full Moon have a flat appearance? • The moon appears matte (or diffuse) • But still. Why does the Full Moon have a flat appearance? Lambertian Spheres and Moon Photos illuminated similarly . Surface Roughness Causes Flat Appearance Actual Vase Lambertian Vase . Surface Roughness Causes Flat Appearance Increasing surface roughness Lambertian model Valid for only SMOOTH MATTE surfaces. Bad for ROUGH MATTE surfaces. . •Based on Geometric Optics. •Roughness represented like in Torrance-Sparrow Model •Lambertian model is simply an extreme case with roughness equal to zero.Oren-Nayar Model – Main Points •Physically Based Model for Diffuse Reflection. . •Explains view dependent appearance in Matte Surfaces •Take into account partial interreflections. Dichromatic Reflection Observed Image Color = a x Body Color + b x Specular Reflection Color Klinker-Shafer-Kanade 1988 R Color of Source (Specular reflection) Does not specify any specific model for Diffuse/specular reflection B G Color of Surface (Diffuse/Body Reflection) .A Simple Reflection Model .