CE6451: Introduction to Photogrammetry
Lecture 2-2
Radiometry and Photometric stereo
Acknowledgements: Most of the slides in this lecture come from Ping
Tan. part of the materials of the all the lecture notes are from Cyrill
Stachniss, Marc Pollefey, Wolfgang Foerstner, Bernhard Wrobel,
James Hays, A. Dermanis, Armin Gruen, Alper Yilmaz.
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BRDF
BRDF is a four-parameter function that describes
the reflecting property of the surface material.
𝐿𝑜 𝜃𝑜 , 𝜙𝑜 𝐿𝑜 𝜃𝑜 , 𝜙𝑜
𝐵𝑅𝐷𝐹 = 𝜌 𝜃𝑖 , 𝜙𝑖 , 𝜃𝑜 , 𝜙𝑜 = =
𝐸𝑖 𝜃𝑖 , 𝜙𝑖 𝐿𝑖 𝜃𝑖 , 𝜙𝑖 𝑐𝑜𝑠𝜃𝑖 𝑑𝝎
Once knowing BRDF, the intensity of the pixel
received from the viewing point can be
computed:
𝐿𝑜 𝜃𝑜 , 𝜙𝑜 = 𝜌 𝜃𝑖 , 𝜙𝑖 , 𝜃𝑜 , 𝜙𝑜 𝐿𝑖 𝜃𝑖 , 𝜙𝑖 𝑐𝑜𝑠𝜃𝑖 𝑑𝝎
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Reflection Equation
Single light source
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Reflection Equation - Cont.
Multiple light sources
𝐿𝑜 (𝜃𝑜 , 𝜑𝑜 ) = න 𝜌𝑏𝑑 𝜃𝑜 , 𝜑𝑜 , 𝜃𝑖 , 𝜑𝑖 𝐿𝑖 𝜃𝑖 , 𝜑𝑖 cos 𝜃𝑖 𝑑𝜔𝑖
Ω 𝑖
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Properties of BRDF
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Properties of BRDF - Cont.
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Isotropic vs Anisotropic
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Examples of anisotropic material
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BRDF – Cont.
Energy Conservation
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Typical types of Reflectance
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Diffuse vs. Specular Reflection
Most of the real surfaces have both components
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Diffuse vs. Specular Reflection – Cont.
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Common BRDF Models
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Lambertian Model
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Lambertian Model
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Lambertian Model
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Phong Model
Apparently, we need models for shiny surfaces –
specular reflection. Phong model gives the
mathematical formulation of the specular reflection.
- Assuming light is concentrated on the
“mirrored direction”
- Intensity of light falls off by cosine law
- Observed pixel intensity should be:
Named after Bui Tuong Phong
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Phong Model – Cont.
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Phong Model – Cont.
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Phong Model – Cont.
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Phong Model – Cont.
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Blinn-Phong Model
Formulation similar to Phong model, observed intensity falls off
by cosine law
The computation of H is faster than R
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Measuring BRDF
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Representation of Measured Data
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Acquisition
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Acquisition – Cont.
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Photometric stereo
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Photometric stereo
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Assumptions
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Mathematic Formulation
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Record the lighting directions
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Recall Specular reflection
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Dealing with Shadows
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Dealing with Shadows – Cont.
Take lots of pictures and discard pixels that are
too dark (10% of the darkest pixels)
Similarly we can discard pixels that are too
bright (specular reflections)
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Example Figures
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Recovered reflectance (Kd)
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Recovered normal field
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Depth from Normals (Method I)
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Depth from Normals I – Cont.
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Depth from Normals (Method II)
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Surface Recovered
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Limitations for Lambertian Photometric Stereo
Cannot handle shiny, semi-translucent objects.
Shadows, multiple reflections
Camera and lights have to be distant
Light Calibration requirements
- measure light source detections, intensities
- Camera response function.
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Example-based Photometric Stereo
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Example-based Photometric Stereo – Cont.
Shinny Areas
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Example-based Photometric Stereo – Cont.
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Example-based Photometric Stereo – Cont.
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Example-based Photometric Stereo – Cont.
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Example-based Photometric Stereo – Cont.
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Example-based Photometric Stereo – Cont.
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Example-based Photometric Stereo – Cont.
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Example-based Photometric Stereo – Cont.
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Example-based Photometric Stereo – Cont.
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Example-based Photometric Stereo – Cont.
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Next Class - Features
Questions?
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