Transcript entezari-alireza

Jean Baptiste Joseph Fourier
ALIREZA ENTEZARI ([email protected])
Supervisor: Dr. Torsten Möller
WHAT IS THE PROBLEM?
FOURIER VOLUME RENDERING
LIMITATIONS
 X-ray quality like images (projection)
 Local operations in a global transform are hard:
1. Illumination models like Lambertian model
involve non linear operations, therefore cannot
be represented nicely in frequency domain
2. Occlusion involves spatial ordering, not well
defined in frequency domain
FFT
Slicing
 Scientific Data
 Medical Data
 Data mining
Fourier projection slice theorem
2
3
Fast: O(n logn) vs. O(n ) runtime
Easy filtering effects
Progressive refinement
Interactive rates without help from graphics
3
hardware: 20 fps for 256 dataset on a
common personal computer
Projection
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Interactive visualization of large
volumetric datasets (Terabyte Vis)
IFFT
Lambertian lighting model:
Diffuse light contribution  MAX (0, N  L)
N
L
In Lambertian lighting model the more
normal vector N is aligned with light
direction L, the stronger the diffuse factor is.
SOLUTION
First ten spherical
harmonics basis
functions
 Illumination: Use Spherical coordinates for computing the angle
between the normal and the light direction
 Basis functions: Spherical Harmonics are eigenfunctions of
rotational convolution in spherical domain
 Spherical Harmonics form a closed group under rotation operation
 Occlusion: Use Depth cueing that is Linear ramp in frequency domain
CHALLENGES
RESULTS
FVR
Depth Cueing added
FVR
Lighting added
Lighting added
 Memory considerations: how to compress
spherical harmonic coefficients?
 Working in frequency domain involves floats that
are hard to deal with
 Filtering to remove the ghosting effect
 Using graphics hardware to accelerate the slicing
operation
Collaborators: Randy Scoggins, Mississippi State University
Dr. Raghu Machiraju, Ohio State University
Funding: NSERC, ASI, NSF and US Army Engineering