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Generalized Mosaics Yoav Y. Schechner, Shree Nayar Department of Computer Science Columbia University
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Mosaics Processing
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Redundant Measurements Generalized Mosaicing: Yoav Schechner and Shree Nayar
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Scanning with Less Redundancy Mantis Shrimp TakataC Different rows = Different optical characteristics
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Generalized Mosaicing Field of View Brightness Dynamic Range Spectrum Depth of Field Polarization camera Spatially varying filter Schechner, Nayar, Generalized mosaics
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Mosaic + High Dynamic Range 88 - 18,794
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Fusion of Measurements Maximum-Likelihood Solution Schechner, Nayar, Generalized mosaics
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8 bit camera Dynamic range as 16 bits Generalized Mosaicing: Yoav Schechner and Shree Nayar 8 bits (almost) (pixels) -2 -4 -6 -8 x log M 2 Log of the mask = 110 -6 110 -2
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M x average row Mask Self-Calibration Unknown filter (vignetting) consistency constraints Consistency, Smoothness A Schechner, Nayar, Generalized mosaics
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Image Registration Schechner, Nayar, Generalized mosaics
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Bias towards “no motion” Schechner, Nayar, Generalized mosaics Image Registration
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Uncertainty Schechner, Nayar, Generalized mosaics Image Registration
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Registration: Standard “Coarse to Fine” 5 pixels 10 pix 9 pix 18 pix 19 pix 4 pixels 2 pixels motion of However, we need: multiscale UNCERTAINTIES Schechner, Nayar, Generalized mosaics
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Maximum-Likelihood Pyramid At each level L, for each pixel estimate 2 Schechner, Nayar, Generalized mosaics
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Max-Likelihood Pyramid Gaussian PyramidML estimation
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log I Intensity range Spatial range x Generalized Mosaic x log I Intensity range Spatial range frame Mosaic Schechner, Nayar, Generalized mosaics
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Generalized Mosaicing: Yoav Schechner and Shree Nayar spectral y x Variable Spectral Filter
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Multi Spectral Multi Spectral Mosaic 500700400600 500700400600 500700400600 Generalized Mosaicing: Yoav Schechner and Shree Nayar
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Rendering : Any Illumination sunset fluorescent
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Halogen y x Illumination at a Glance Fluorescent y x Illuminant spectrum Extra information
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Spatially Varying Polarizer Polarization Mosaicing: Yoav Schechner and Shree Nayar
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0 0.2 0.4 0.6 0.8 1 -30 60 90 30 0 -60 -90 o o o o o o polarizance polarizing angle o Polarization Mosaicing: Yoav Schechner and Shree Nayar transmittance Spatially Varying Polarizer
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Raw images Polarization Mosaicing: Yoav Schechner and Shree Nayar
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Polarization Mosaic Schechner Shamir Kiryati JOSA-A 2000 reflected structure transmitted painting
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= y x Depth Insert a prism behind the lens Spatially Varying Focus Generalized Mosaicing: Yoav Schechner and Shree Nayar
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All Focused All Focused Mosaic Generalized Mosaicing: Yoav Schechner and Shree Nayar … and a Depth Map
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What else? Generalized Mosaicing: Yoav Schechner and Shree Nayar Dynamic Range & Spectrum & Polarization etc. Multi-dimensional Mosaics - Simultaneously
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Signal undergoing LPF “Band limited” signal Minimizing aliasing Nyquist sampling rate 11111111 11111111? 10111001?? Sampling Criteria Generalized Mosaicing: Yoav Schechner and Shree Nayar Number of samples per scene point resolution length L bandwidth B aperture D 1M 1011100101 1011100??? M # samples 1 1/2 2 1/4 3 9 101110????
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MosaicGeneralized Mosaic Spatially varying filter Wide field of view Spectrum I Depth + Focus Dynamic range 88 – 18,794 Polarization
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