1. Measuring Bidirectional Texture Reflectance with a Kaleidoscope
Jefferson Y. Han & Ken Perlin
Media Research Laboratory
New York University
Slides by Ingrid Montealegre
34:15 total + 30% = ~45 minutes

2. Introduction
Recent work in realistic image synthesis focuses on use of actual data measurements of surfaces and materials
Want to capture reflectance properties of a surface (exitant and incident angle of light)
High dimensionality makes dense sampling difficult
New technique for measuring the appearance of a textured surface as it is viewed or illuminated from different directions

3. Texture Reflectance
Reflectance of a surface characterized by its Bidirectional Reflectance Distribution Function (BRDF) [Nicodemus et al. 1977]
BRDF is a 4 dimensional function that describes light from it’s incident and exitant angle BRDF(i,i,e,e)
Real objects are not uniform and are not accurately represented by a single BRDF function

4. Texture Reflectance
Dana et al. [1999] introduce Bidirectional Texture Function (BTF) which parameterizes BRDF to allow for spatially varying reflectance
BTF accurately captures surface subtleties (including self-occlusion and self-shadowing)
It is a large 6D function and is difficult to obtain a dense sample - BTF(u,v,i,i,e,e)

5. BTF Measurement
Seminal work by Dana et al. presents a 3DOF robotic arm that incrementally rotates/tilts a sample in front of a light source
Produces 205 total samples w/even distribution
requires sample to be affixed to a device, in situ measurements not possible
Perlin and Han’s approach measures textured surfaces (BTF) in situ as viewed or illuminated from different directions

6. BTF using a Kaleidoscope
Based on the principle of the kaleidoscope [Brewster 1819]
Hollow tube of polygonal cross-section whose inner walls are lined with front surface mirrors
Object at end of kaleidoscope appears to multiply into replicated images of itself

7. View through a Kaleidoscope

8. BTF using a Kaleidoscope
When far end is tapered, sample will look like a faceted virtual sphere since each successive reflection reorients the sample a little further from the perpendicular
Analogous to having an entire array of cameras pointing toward a surface
Optimal for measuring the BTF

9. Optical Schematic
Optical paths of camera and projector are merged using a 45º beam splitter

10. Illumination Also an illumination technique
When projector is pointed down kaleidoscope, different pixels of the image will arrive at the projected sample after having reflected in different ways, approaching the sample from various directions
Different regions of the projected image behave like different light sources
By keeping only certain pixels of projected image bright, can choose direction from which to illuminate the sample

11. Procedure
BTF measurement proceeds by taking a sequence of sub-measurements
At each sub-measure exactly one region of the illumination image is bright
Each region corresponds to a unique sequence of reflections of light off the kaleidoscope walls
Sample will be illuminated from a unique sub-range of incoming light directions
Complete measurement uses all regions to illuminate the sample

12. Advantages
No moving parts guaranteeing registration of sub-measurements & improved accuracy
Can measure in situ
Can be use for skin and loose items such as pebbles
Requires a single camera, lower cost
Richly samples the BTF
Initial prototype captured 484 illuminations (comp. 205)

13. Design Parameters
In general, kaleidoscope can be made as a regular polygon of n sides, for n>=3
Not every virtual facet is complete, # of fragmented facets varies with n
Image processing is most easily performed on rectangular images, for n!=4, use largest inscribable square
Focused on n=3 for simplicity and has largest number of whole facets

14. Simulations of n

15. Choice of Taper Angle
Large taper angle causes reflections to tilt further away from normal, producing fewer facets that are visible
Narrow taper angle causes more visible facets, capturing more facets in a single view results in fewer pixels per view, reducing spatial resolution

16. Choice of Taper Angle Chose taper angle that tilts from vertical by 9º
Provides 4 orders of magnitude of reflections from the horizon, a final effect angle of 76º
Can measure 22 complete views, providing 222 = 484 distinct view/illumination pairs

17. Experimental Setup

18. Calibration
Used a planar 3x3 checkerboard pattern & performed corner detection to id sub-pixel coordinates
Used to compute best homography transform that maps each patch to the unit square
Each transformation applied to the 22 imaging shots and saved to disk
Result is a 22x22 array of images indexed by projector facet and camera facet
Correction for lens distortion of the camera needs to be done once using the technique by Zhang [1999]

19. Full 22x22 BTF Measurements

20. Illumination Alignment
Needed to determine which pixels in the projected image illuminated each kaleidoscopically reflected image of the surface
In current work, done manually
Image from a video camera peering into kaleidoscope as a guide
Ideally done automatically
Needs to be done once

21. 2 Different Illumination Angles

22. BSSTF Trials
For surfaces with appreciable sub-surface scattering measure BSSRDF (Bidirectional Scattering Surface Reflectance Distribution Function)
Illuminate a small spot on the sample and then measure surrounding region [Jensen et al. 2001]
Incrementally moving the spot can measure Bidirectional Scattering Surface Texture Function BSSTF(ui,vi,ue,ve,i,i,e,e)
Uses two dimensions for each of four measures
Entry point of light on sample
Exit point of light on sample
Incoming spherical angle
Outgoing spherical angle

23. Two BSSTF Measurements

24. Future Work
Improve image extraction to utilize the data currently ignored
Add high dynamic range (HDR) capture capability by taking multiple image captures at varying exposure lengths
Adjust lenses and cameras used to make more compact
Make a room sized version to capture movement