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  1. DISPLAY SUPERSAMPLING Niranjan Damera-Venkata Nelson Chang HP Labs, Palo Alto, CA

  2. Display Super-sampling Scene samples are computationally combined Anti-aliased screen resolution image Conventional super-sampling Display super-sampling • Multiple display samples are physically combined • How to produce alias-free images? • Resolution Limits? • Practical algorithms?

  3. Dual of camera super-resolution The rendering problem for DSS is the computational dual of camera super-resolution!

  4. Relation to previous work Super-sampling/Texture mapping Successive refinement [Fuchs et. al., 1985] Jittered sampling [Deering et. al., 1988] Multi-viewpoint texturing [Wang et. al., 2001] Capture Super-resolution [Irani and Peleg, 1990] Jittered camera [Ben-Ezra et. al., 2004] Display Jittered Display (“Wobulation”) [Allen and Ulichney, 2005] Projector super-resolution [Jaynes and Ramakrishnan, 2003] Resolution analysis [Majumder, 2005] [Said 2006]

  5. Sampling Geometries Recurrent non-uniform Critical uniform General non-uniform

  6. 1-D DSS model • Input is bandlimited • Subframes are shifted and superimposed PSF

  7. Single sub-frame model (Nyquist view) Aliased edges Alias-free but blurred

  8. Multiple sub-frame model Each channel is under-sampled Sub-frames are shifted and superimposed

  9. Analysis of point sampling NN sampling perfectly cancels aliasing when Aliased results for all other values of

  10. Nearest neighbor point sampling NN sampling is alias free for critical uniform sampling! Recurrent non-uniform Critical uniform

  11. Analysis of anti-aliased rendering Anti-alias filtering chops off high sub-frame frequencies

  12. Ideal anti-alias filtering Chops off Super-Nyquist frequencies Recurrent non-uniform Critical uniform

  13. Optimal sub-frame generation • Optimal rendering requires alias generation!!

  14. Optimal sub-frame generation filters • Closed form solution follows from proving a dual of the generalized sampling theorem!

  15. Alias-cancellation

  16. Discrete alias-cancellation example

  17. Optimal sub-frame generation Alias cancellation leads to super-Nyquist rendering Recurrent non-uniform Critical uniform

  18. Ideal anti-alias filtering Chops off Super-Nyquist frequencies Recurrent non-uniform Critical uniform

  19. Sampling geometry limits Sub-frame clipping leads to distortion Can be relaxed via oversampling

  20. Pixel PSF limits • Cannot de-blur without exceeding [0,1] signal range • Can be relaxed by using smaller duty cycle

  21. Analysis of resolution gain • Not all super-Nyquist signals can be perfectly reconstructed • Sinusoidal analysis can produce a curve of amplitude vs. frequency of sinusoids that can be perfectly reconstructed! • Suggestions for best resolution • Low duty-cycle pixels • Increase super-sample factor

  22. General 2-D image formation model Warped Pre-filter Reconstruction filter Low-res space Hi-res space

  23. Iterative sub-frame generation algorithm

  24. Optimal resample filters for real-time processing WxW neighborhood around [k,l] Pixel center of pixel at location [m,n] low-res subframe generation result Hi-res impulse training images Relationship between subframe outputs for different impulse inputs and filter coefficients low-res subframe generation result

  25. Example filters

  26. Experimental platforms 4 xp7030s 10 xp8020s camera Firewire camera 10 xw8000s 1 xw9300w/dual pci-e • Fast geometric calibration by coded light patterns • Real-time 1080p/2K rendering on 16’x9’ screen 10-Projector(33 klumens*) 4-Projector(12 klumens*) *peak ANSI lumens from specs

  27. 10 projector simulation Input Image Single Projector Multi-Projector Courtesy: Robert Ulichney and A. Gajharnia

  28. Experimental results Multi-projector (10 superimposed) • Alias generation is needed to cancel aliasing in the display superimposition process • Filter bank algorithm generated appropriate aliased sub-frames Single projector (aliased, anti-aliased)

  29. Conclusions Optimal rendering for super-sampled displays requires alias generation! Super-Nyquist resolution gain is feasible! Resolution gain is limited by pixel PSF and sampling geometry Practical algorithm for subframe-generation Based on filter-bank model for alias cancellation Optimal filters derived by computing impulse response of linearized iterative algorithm Verified by experiments on real multi-projector system