Basic Principles of Surface Reflectance Lecture #3 Thanks to Shree Nayar, Ravi Ramamoorthi, Pat Hanrahan
Camera Physical Models Computer Computer Vision: Building Machines that See Lighting Scene We need to understand the relation between the lighting, surface reflectance and medium and the image of the scene.
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 viewing direction normal y surface element x Irradiance at Surface in direction Radiance of Surface in direction BRDF :
Important Properties of BRDFs source z incident direction viewing direction normal y surface element x • Rotational Symmetry: • Appearance does not change when surface is rotated about the normal. BRDF is only a function of 3 variables : • Helmholtz Reciprocity: (follows from 2nd Law of Thermodynamics) • Appearance does not change when source and viewing directions are swapped.
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:
Mechanisms of Surface Reflection source incident direction surface reflection body reflection surface Surface Reflection: Specular Reflection Glossy Appearance Highlights Dominant for Metals Body Reflection: Diffuse Reflection Matte Appearance Non-Homogeneous Medium Clay, paper, etc Image Intensity = Body Reflection + Surface Reflection
Mechanisms of Surface Reflection Surface Reflection: Specular Reflection Glossy Appearance Highlights Dominant for Metals Body Reflection: Diffuse Reflection Matte Appearance Non-Homogeneous Medium Clay, paper, etc Many materials exhibit both Reflections:
Diffuse Reflection and Lambertian BRDF source intensity I incident direction normal viewing direction surface element • Surface appears equally bright from ALL directions! (independent of ) albedo • Lambertian BRDF is simply a constant : • Surface Radiance : source intensity • Commonly used in Vision and Graphics!
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 Uniform 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)
Specular Reflection and Mirror BRDF source intensity I specular/mirror direction incident direction normal viewing direction surface element • Very smooth surface. • All incident light energy reflected in a SINGLE direction. (only when = ) • Mirror BRDF is simply a double-delta function : specular albedo • Surface Radiance :
BRDFs of Glossy Surfaces • Delta Function too harsh a BRDF model • (valid only for polished mirrors and metals). • Many glossy surfaces show broader highlights in addition to specular reflection. • Example Models : Phong Model (no physical basis, but sort of works (empirical)) • Torrance Sparrow model (physically based) – Next Class
Phong Model: An Empirical Approximation • An illustration of the angular falloff of highlights: • Very commonly used in Computer Graphics
Phong Examples • These spheres illustrate the Phong model as lighting • direction and nshiny are varied:
A Simple Reflection Model - 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 G Color of Surface (Diffuse/Body Reflection) B
Separating Diffuse and Specular Reflections Observed Image Color = a x Body Color + b x Specular Reflection Color R Color of Source (Specular reflection) G Color of Surface (Diffuse/Body Reflection) B