Michael Oren’s Thesis

Damian Gordon

Reflectance Analysis for Image Understanding

How do we model these surfaces ??????????

Reflectance Mechanisms

• Diffuse Reflection (Body Reflection) Lamertian Model• Specular Reflection Specular Spike (smooth) Specular Lobe (rough)

Reflectance Components

Diffuse Reflectance

Lambertian Model

• Essentially, surface brightness is independent of viewer direction and is determined solely by enery flux of the incident light.

Surface Roughness

Surface Roughness

• Assume Surface is a collection of planar facets

=> At high magnification, each pixel images one facet

=> At low magnification, each pixel images many facets

Surface Roughness

Surface Roughness

• Modelled as a series of V-cavities whose upper edges are in the same plane.

• The width of each facet is assumed to be small compared to its length.

• Torrance-Sparrow Model (1967)

Geometric Attenuation Factor (GAF)

• If surface not illuminated from normal direction, suffers from shadowing and masking

• SHADOWING : Facet partially illuminated, adjacent facet casts shadow

• MASKING : Facet partially visible, adjacent facet occludes.

Geometric Attenuation Factor (GAF)

Interreflection Factor

• Experiments suggest too important to be ignored in model

• But, energy in incident light ray diminishes after each bounce

• So, only two-bounce interreflections modelled

Interreflection Factor

Surface Types Modelled

• Uni-directional Single-Slope Distribution• Isotropic Single-Slope Distribution• Gaussian Distribution

Gaussian Distribution

Qualitative Model

• Model is being used to calculate surface orientation, reflectance and roughness, etc.

• To be tractable, model must use maths that can be easily inverted

• This is why Lambertian is so popular after 240 years

• Must sacrifice accuracy

Qualitative Model

Experiments

Wall Plaster

Sand Paper

Wood Shaving

Conclusions

• Rough surfaces are inherently non-Lambertian in reflectance

• New model could be used in graphics for realistic rendering

• Model can be used to measure surface roughness

• If rough object can appear flat

Future Work

• Simultaneous recovery of shape and roughness

Specular Reflectance

Two Main Problems

• Detecting specularitiesReal FeaturesVirtual Features• Shape recovery of specular surfacesMany pitfalls

Result not on Surface !!!!!

Real & Virtual Features

Approach

• Use virtual features to help recover shape• Model in 2D domain first • And generalize to 3D domain

Recovery of 2D Surface Profile

• Curve Representation• Important to simplify analysis• Cartesian Coordinates - represents curve as

series of points (but no local slope)• Legendre Transform – represents curve as

an envelope of tangents

Curve Representation

Caustics

• Virtual feature travels on a surface producing a family of reflection rays

• The envelope defined by the family is called the caustic

• Use caustic compactness to distinguish real from virtual feature

Caustics

2D Surface Recovery

• Develop equations to recover profile to one parameter family of equations

• May determine correct profile by tracks two virtual features

Results

Results

3D Motion

• Generalizes 2D concepts of caustics & equations

3D Motion

3D Caustics

Results

Conclusions & Future Work

• Closed-form relationship between image trajectory of a virtual feature and surface profile

• New technique for detecting virtual featuresFuture Work• Fusion of real & virtual feaure• Shape recovery of rough surfaces