Rendering & Reconstructing Under Complex BRDF ’ s

Rendering & Reconstructing Under Complex BRDF’s Uri Ben-Dor Adi Makmal

AGENDA • Introduction • Motivation • Basic concepts • Photometric Stereo • Image Based Rendering (IBR) • Summary

Introduction In this lecture we will discuss the way light interacts with matter and how to improve realism in CV and in other related areas such as computer graphics, using this knowledge.

Motivation (1) – Constructing Geometry of an Object • Left: no light . • Right: A spot light is pointing down on the object from above and behind, reflecting off the surface of the sphere. • This simple highlight gives the viewer a completely different reading of the scene.

Motivation (2) – Giving Clues To an Object's Material • The objects reflects highlights differently. • Left: soft - as though the object were made of chalk. • Right: glossy - creates the perception of very shiny plastic.

Motivation (3) – Image Based Rendering - Changing View Point

Motivation (4) –Image Based Rendering - Changing Lights Direction • Given 1 object image (face) taken under single lightsource (unknown direction).

Motivation (4) –Image Based Rendering - changing lights • render same faceunder new lighting direction:

Basic Concepts • Radiometry • Solid angle • Radiance • Irradiance • Radiosity & Exitance • BRDF • “Helmholtz” Reciprocity Rule • Isotropic vs. Anisotropic • Special BRDF • Diffuse surface & Lambertian Low • Specular surface & Fong Model • Local vs. Global Illumination

Deals with the following Questions: How do we measure light? How “bright” will surfaces be? How does light interacts with surfaces? Radiometry

L N Radiometry – Some Answers.. Brightness of a surface How much light the surface receives How much of the received light is reflected Surface material

Example Same light source hitting two different surfaces: Light hits the surface directly Light hits the surface at an angle As a result the right surface receives less light per square inch !

reflected Light Behavior Absorbed transmitted

Combination

Fluorescence Absorbing light at one wavelength, and radiate light at different wavelength.

Simplifying Assumptions • The light leaving a point on a surface is due only to light arriving at this point. • No Fluorescence • Surfaces do not generate light internally - treating sources separately.

Radiometry – Formalization N L R (i,i) V (o,  o)

Radiometry – Formalization Around any point there is a hemisphere of directions:

Spherical Coordinates x = r sinq cosf y= r sinq sinf z= r cosq

Basic Concepts • Radiometry • Solid angle • Radiance • Irradiance • Radiosity & Exitance • BRDF • “Helmholtz” Reciprocity Rule • Isotropic vs. Anisotropic • Special BRDF • Diffuse surface & Lambertian Low • Specular surfac & Fong Model • Local vs. Global Illumination

Intro. To Solid Angle Light is form of energy light is measured in terms of flow through an area light coming from a single direction light coming from a small region

Solid Angle - Definition • The solid angle is the area of the projection of the object onto the unit sphere. • Units : steradians, abbreviated sr.

Solid Angle of a Small Patch The solid angle subtended by a small patch area dA is: dA

Basic Concepts • Radiometry • Solid angle • Radiance & Irradiance • Radiosity & Exitance • BRDF • “Helmholtz” Reciprocity Rule • Isotropic vs. Anisotropic • Special BRDF • Diffuse surface & Lambertian Low • Specular surfac & Fong Model • Local vs. Global Illumination

Radiance Amount of energy traveling at some point in a specified direction, per unit time, per unit area perpendicular to the direction of travel, per unit solid angle • Denoted:L(x,,) • Units: Wm-2sr-1 .

Radiance is Constant Along a Straight Line • Assuming light does not interact with the medium through which it travels – i.e. that we are in . vacuum

d cos  d Irradiance • How much light is arriving at a surface. • A surface experiencing radiance L(x,q,f) coming in from dw experiences irradiance: • Note: While the radiance is per area perpendicular to the direction of travel, the Irradiance is not. • Units: W*m -2

Radiosity Total power leaving a surface, per unit area on the surface. To get it, integrate radiance over the hemisphere of outgoing directions: X

Exitance • Light sources emit light, they are sources of radiance • Exitance is the equivalent of radiosity for emitters:

Bidirectional Reflectance Distribution Function Intuition: BRDF is a function that specifies the ratio between the incident light in one direction and the emitted light in a second direction. The function defines properties of the surface (shininess,..)

Outgoing radiance irradiance BRDF – more formally the ratio of the radiance in the outgoing direction to the incident irradiance at a point on the surface Range: [0,infinity] (surprising?) Units: inverse steradians = sr -1

(i,i) (i,i) (r,r) = (r,r) Helmholtz Reciprocity Rule brdf is symmetric:

Isotropic vs. Anisotropic • Isotropic reflection - reflection that does not vary as the surface is rotated about the normal (the  angle). • Isotropic – useful assumption.

Special BRDFs

Diffuse Light • Illumination that a surface reflects equally in all directions. • BRDF is constant: • The brightness is independent of the observer position. • Also called “Lambertian” Reflection.

Ideal Diffuse Surfaces – ALBEDO definition • Albedo - The fraction of the incident radiance in a given direction that is reflected by a point on diffuse surface (in all possible directions). • Denoted d. • Also called diffuse reflectance.

N L radiant Unit normal albedo intensity of light source Light unit vector Lambert’sLaw • The radiant energy I from a diffuse surface:

Specular Surface • Light reflected from the surface unequally to all directions. • These are the bright spots on objects (polished metal, apple ...).

Phong Model – Specular Light • How much reflection light you can see depends on where • you are

Different BRDF  Perfectly Specular “Mirror” n  ∞

Different BRDF Incident LightRay SurfaceNormal ReflectedLight Slightly scattered Specular:

Different BRDF Incident LightRay SurfaceNormal perfectly Diffuse

Different BRDF SurfaceNormal Incident LightRay Combination of Diffuse and Specular

Local vs. Global Illumination Local illumination • Local illuminationEverything is lit only by light sources • Global illumination Everything is lit by everything else global illumination

Rendering & Reconstructing Under Complex BRDF ’ s