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Lensless Imaging with A Lensless Imaging with A Controllable ApertureControllable Aperture
Assaf Zomet and Shree K. NayarColumbia University
IEEE CVPR Conference
June 2006, New York, USA
Cameras TodayCameras Today
Lens
Plane in focus
Image Detector
Aperture
AttenuatingAperture
Our Lensless CameraOur Lensless Camera
Image Detector
Volumetric
Multilayer Aperture
Layered ApertureLayered Aperture
Image Detector
Attenuating apertures: Farid&Simoncelli ‘97, Nayar&Branzoi ‘03
ImplementationImplementation
Camera body Aperture: LCD
LCDControl
Image Detector
Attenuating LayerPinhole
Controllable PinholeControllable Pinhole
Image Detector
Pinhole Attenuating Layer
Controllable Pinhole: VideoControllable Pinhole: Video
Limitations of Lensless ImagingLimitations of Lensless Imaging
fa 9.1Optimal pinhole (Raleigh):
Brightness: f-number
ff
f
a
ff
9.1/#
a2
f
a
ff
a
• Sharpness and brightness increase with FOV (image center).
Limitations of Lensless ImagingLimitations of Lensless Imaging
fa 9.1Optimal pinhole (Raleigh):
Brightness: f-number
ff
f
a
ff
9.1/#
• Sharpness and brightness increase with FOV (image center).
• f and detector larger by factor k: Resolution/brightness by .
k
ak
f
f
f
Zand, 1992
Collecting More Light: Coded AperturesCollecting More Light: Coded Apertures
Conventional View Desired View
Split Field of View: ImplementationSplit Field of View: Implementation
Attenuating Layers(2nd layer physical)
Image Detector
Pinhole
Fov 2Fov 1
Fov 3
Split Field of View: ResultsSplit Field of View: Results
Lens camera
Ourcamera
Split Field of View: VideoSplit Field of View: Video
Finding FacesFinding Faces
Wastedpixels
Finding FacesFinding Faces
Pinhole
Attenuating Layers(2nd layer physical)
Split Image: Computational CameraSplit Image: Computational Camera
Correlation pattern
Image Detector
Computations in the OpticsComputations in the Optics
Our cameraLens camera
Correlation Pattern
Normalized correlation:
Image Pattern
vu
vu
vyuxI
vuPvyuxI
yxPId
,
2
,
),(
),(),(
),,,(
Noncoherent optical processing (Rogers 1977)
A Camera as a MappingA Camera as a Mapping
vuS ,
tanu
yxI ,
CameraOptics SMI
dudvvuSvuyxMyxI ),(),,,(,
Imaging Formulation: One LayerImaging Formulation: One Layer
yxI ,
vuS ,
fvyfuxT ,
f
tanu
dudvvuSfvyfuxTyxI ,,,
Imaging Formulation: MultilayerImaging Formulation: Multilayer
vfyufxT jjj ,
yxI ,
vuS ,
fj
tanu
SMI
dudvvuSvfyufxTyxIN
jjjj
1
,,,
Varying ZoomVarying Zoom
Conventional view
Desired view
H
H
L LL
L
Varying Zoom MappingVarying Zoom Mapping
Desired view
Scene
YM TXM
MX and MX are impossible to implement with 3 layers
TXYdesired SMMI
Attenuating Layers
Image Detector
Fov 1 Fov 3
PinholePinhole
Pinhole
Fov 2
Varying Zoom: Imaging (simulation)Varying Zoom: Imaging (simulation)
Captured
Desired
Varying Zoom: ReconstructionVarying Zoom: Reconstruction
TX
TXcapturedYYcomputed MCICMI
Icomputed
TXYcomputed SMMI
Icapturted
TXYcaptured SCCI
SummarySummaryControllable Pinhole
Computational Camera Spatially Varying Zoom
Split Field of View
Programmable cameras, Nayar, Branzoi & Boult 2004
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