Coded Computational Photography!
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1 Coded Computational Photography! EE367/CS448I: Computational Imaging and Display! stanford.edu/class/ee367! Lecture 9! Gordon Wetzstein! Stanford University!
2 Coded Computational Photography - Overview!! coded apertures!! extended depth of field!! wavefront coding!! lattice lens!! diffusion coding!! focal sweep!! motion deblurring!! flutter shutter!! motion invariance! [Raskar et al. 2006]! [Cossairt et al., 2010]!
3 Remember Apertures?!! out of focus blur! focal plane! circle of confusion!
4 What makes Defocus Deblurring Hard?! 1.! depth-dependent PSF scale (depth unknown)! 2.! circular / Airy PSF is not (well) invertible! focal plane! circle of confusion!
5 Coded Computational Imaging - Motivation! 1. depth-dependent PSF scale (depth unknown)! engineer PSF to be depth invariant! resulting shift-invariant deconvolution is much easier!! 2. circular / Airy PSF is not (well) invertible: ill-posed problem! engineer PSF to be broadband (flat Fourier magnitudes)! resulting inverse problem becomes well-posed!
6 Computational Imaging! 1.! optically encode scene information! 2.! computationally recover information!?!!!! new optics! new sensors! new illumination! new algorithms!???
7 Coded Computational Imaging (for this Class)! 1.! optically encode scene information using! new optics! invertible (and possibly invariant) PSF!! easier algorithms! 2.! computationally recover information (easy because of engineered PSF)!??
8 Coded Computational Imaging (for this Class)! idea applies to!! new optics!! coded apertures!! easier algorithms!! extended depth of field / DOF deblurring!! extended motion / motion deblurring!??
9 Before going to Advanced Techniques for DOF Deblurring, let s take a look at! Coded Apertures!
10 ! two important parts:! Apertures Revisited! 1.! aperture stop attenuating pattern! 2.! refractive element (lens or compound lens system)! 1. attenuating coded aperture: e.g., MURA pattern! 2. refractive coded! aperture: e.g., cubic phase plate!
![Coded Aperture Changes PSF! [Veeraragharavan et al. 2007]!](/docs-images/78/77833156/images/11-3.jpg "in-focus photo! out-of-focus, circular aperture!")
11 Coded Aperture Changes PSF! [Veeraragharavan et al. 2007]! in-focus photo! out-of-focus, circular aperture! out-of-focus, coded aperture!
12 Coded Aperture Changes PSF! [Veeraragharavan et al. 2007]! in-focus photo! out-of-focus, circular aperture! out-of-focus, coded aperture!
13 Coded Aperture Changes PSF! [Veeraragharavan et al. 2007]!! preserves high frequencies!! deconvolution well-posed! conventional! FFT! coded!
14 Coded Aperture Allows for Depth Estimation!! introduce zeros in Fourier domain!! better depth discimination!! worse invertibility! conventional aperture! coded aperture! PSF! [Levin et al. 2007]!
15 Coded Aperture Allows for Depth Estimation!! deconvolution with strong prior necessary! input! local depth estimate! regularized depth! [Levin et al. 2007]!
16 In Astronomy!! some wavelengths are difficult to focus!! no lenses available!! coded apertures for x-rays and gamma rays! ESA SPI / INTEGRAL! NASA Swift!
17 In Microscopy!! for low-light, coding of refraction is better (less light loss)! e.g., rotating double helix PSF Stanford Moerner lab! e.g., cubic phase plate for depth-invariant imaging!
18 Extended Depth of Field!
19 Depth Invariant PSFs - Overview!! two general approaches:! 1.! move sensor / object! (known as focal sweep)! 2. change optics! (e.g., wavefront coding)!
20 Focal Sweep! exposure! linear motion:! distance! sensor-lens! time! nonlinear motion:! distance! sensor-lens! time! nonlinear motion:! distance! sensor-lens! [Nagahara et al. 2008]! time!
21 Focal Sweep! [Nagahara et al. 2008]! distance! sensor-lens! time! time! two points at different distance!
22 Focal Sweep! [Nagahara et al. 2008]! PSF 1!! t 1 t 2 distance! sensor-lens! PSF 2!! time! instantaneous PSF! integrated PSF! time! two points at different distance!
![Focal Sweep! [Nagahara et al. 2008]! PSF 1!! t 1 t 2 distance!](/docs-images/78/77833156/images/23-3.jpg "sensor-lens! PSF 2!! time! instantaneous PSF! time! two points at different distance!")
23 Focal Sweep! [Nagahara et al. 2008]! PSF 1!! t 1 t 2 distance! sensor-lens! PSF 2!! time! instantaneous PSF! time! two points at different distance!
24 Focal Sweep! [Nagahara et al. 2008]! PSF 1!! t 1 t 2 t 3 distance! sensor-lens! PSF 2!! time! instantaneous PSF! integrated PSF! time! two points at different distance!
![Focal Sweep! [Nagahara et al. 2008]! PSF 1!! t 1 t 2 t 3 t 4 distance!](/docs-images/78/77833156/images/25-4.jpg "sensor-lens! time! PSF 2!! instantaneous PSF! time! two points at different distance!")
25 Focal Sweep! [Nagahara et al. 2008]! PSF 1!! t 1 t 2 t 3 t 4 distance! sensor-lens! time! PSF 2!! instantaneous PSF! time! two points at different distance!
![Focal Sweep! [Nagahara et al. 2008]! PSF 1! PSF 2! t! 1 t 2 t 3 t 4 t 5 dt =! dt =! distance!](/docs-images/78/77833156/images/26-5.jpg "sensor-lens! time! instantaneous PSF! integrated PSF! time! two points at different distance!")
26 Focal Sweep! [Nagahara et al. 2008]! PSF 1! PSF 2! t! 1 t 2 t 3 t 4 t 5 dt =! dt =! distance! sensor-lens! time! instantaneous PSF! integrated PSF! time! two points at different distance!
27 Focal Sweep! [Nagahara et al. 2008]! PSF 1! PSF 2! t! 1 t 2 t 3 t 4 t 5 dt =! dt =! distance! sensor-lens! time! instantaneous PSF! integrated PSF! time! two points at different distance!
![! Focal Sweep! [Nagahara et al. 2008]!](/docs-images/78/77833156/images/28-1.jpg "! spend equal amount of time at each depth to make depth invariant!!! distance! sensor-lens!")
28 ! Focal Sweep! [Nagahara et al. 2008]!! spend equal amount of time at each depth to make depth invariant!!! distance! sensor-lens! time! integrated PSF! time! two points at different distance!
29 Focal Sweep! [Nagahara et al. 2008]! conventional photo (small DOF)! conventional photo (large DOF, noisy)! captured focal sweep! always blurry!! EDOF image!
30 ! Focal Sweep!! noise characteristics are main! benefit of EDOF! may change for different sensor EDOF image! noise characteristics! [Nagahara et al. 2008]! SNR should be! evaluation metric! conventional photo (large DOF, noisy)!
31 Focal Sweep for Moving Objects! motion! motion! defocus! conventional camera PSF! focal sweep camera PSF! [Bando et al. 2013]!
32 Focal Sweep for Moving Objects! motion! motion! defocus! conventional camera PSF! focal sweep camera PSF! [Bando et al. 2013]!
33 Focal Sweep for Moving Objects! motion! motion! defocus! conventional camera PSF! focal sweep camera PSF! [Bando et al. 2013]!
34 Focal Sweep for Moving Objects! conventional camera! focal sweep! focal sweep deblurred! [Bando et al. 2013]!
35 ! Wavefront Coding! [Dowski and Cathey 1995]!! how to obtain a depth invariant PSF without mechanically moving parts!! change the lens!! for many, this is the dawn of computational imaging! cubic phase plate!! tricky to understand intuitively, so let s try to understand what it does by looking at something else!
36 Lattice Focal Lens! superimpose array of lenses with different focal lengths! time! [Levin et al. 2009]!
37 Lattice Focal Lens! conventional camera! lattice focal lens! all-in-focus image from lattice focal lens! [Levin et al. 2009]!
38 Extended Depth of Field (EDOF)! remember focal sweep: move sensor s.t. same time for each depth! lattice focal lens: same idea, but no sweeping (optical overlay) optimal in 4D! cubic phase plate: same idea (optimal in 2D, not optimal in 4D)! (can look at this in more detail if we have time)!
39 Diffusion Coded Photography!! can also do EDOF with diffuser as coded aperture, has better inversion! characteristics than lattice focal lens! [Cossairt et al. 2010]!
40 Back to Coding Motion!
41 Flutter Shutter! [Raskar et al. 2006]! engineer motion PSF (coding exposure time) so it becomes invertible!!
42 photo with coded motion! [Raskar et al. 2006]!
43 deblurred!
![[Raskar et al. 2006]!](/docs-images/78/77833156/images/44-1.jpg "Input Photo!")
44 [Raskar et al. 2006]! Input Photo! Deblurred Result!
45 ! Traditional Camera! Shutter is OPEN! [Raskar et al. 2006]!
46 [Raskar et al. 2006]!! Flutter Shutter!
47 !! [Raskar et al. 2006]! Shutter is OPEN and CLOSED!
48 Harold Doc Edgerton H
49 [Raskar et al. 2006]!
50 Lab Setup [Raskar et al. 2006]!
51 [Raskar et al. 2006]! spatial convolution! sinc Function! Blurring! =! Convolution! Fourier magnitudes! Traditional Camera: Box Filter!
52 [Raskar et al. 2006]! spatial convolution! Preserves High Frequencies!!!! Fourier magnitudes! Flutter Shutter: Coded Filter!
53 Comparison! [Raskar et al. 2006]!
![[Raskar et al. 2006]!](/docs-images/78/77833156/images/54-3.jpg "Inverse Filter stable!")
54 [Raskar et al. 2006]! Inverse Filter stable! Inverse Filter Unstable!
55 Short Exposure Long Exposure Coded Exposure Our result Matlab Richardson-Lucy Ground Truth
![2006]!](/docs-images/78/77833156/images/56-5.jpg "All ones!")
56 Our Code! Are all codes good?! [Raskar et al. 2006]! All ones! Alternate! Random!
57 License Plate Retrieval! [Raskar et al. 2006]!
58 License Plate Retrieval! [Raskar et al. 2006]!
59 ! Motion Invariant Photography! making motion PSFs invariant is great, BUT need to know motion direction and velocity!! we have already seen that focal sweep makes the PSF almost depth invariant! how about making motion PSFs motion invariant?!
60 title!! text! Jacques Henri Lartigue, 1912!
61 text! animation by largeformatphotography.info user Lindolfi!
62 Controlling Motion Blur! [Levin et al. 2008]!
63 Controlling Motion Blur! [Levin et al. 2008]! Can we control motion blur?!
64 Controlling Motion Blur! [Levin et al. 2008]!
65 Controlling Motion Blur! [Levin et al. 2008]!
66 Controlling Motion Blur! [Levin et al. 2008]! Motion invariant blur?!
67 !! Sensor position x(t)=a t 2! start by moving very fast to the right! continuously slow down until stop! continuously accelerate to the left! Intuition:! for any velocity, there is one instant where we track perfectly! all velocities captured same amount of time! Parabolic Sweep! Time t! [Levin et al. 2008]! Sensor position x!
68 Motion Invariant Blur! [Levin et al. 2008]!
![!!! [Levin et al. 2008]! Static camera!](/docs-images/78/77833156/images/69-0.jpg "Unknown and variable blur kernels!")
69 !!! [Levin et al. 2008]! Static camera! Unknown and variable blur kernels! Our parabolic input! Blur kernel is invariant to velocity! Our output after deblurring! NON-BLIND deconvolution!
![2008]! Objects!! x x!](/docs-images/78/77833156/images/70-1.jpg "sensor integration!")
70 t! Primal Domain! Frequency Domain! Frequency Domain!! t [Levin et al. 2008]! Objects!! x x! sensor integration! Camera integration curve! t! Parabolic sweep! x!! t Velocity 1!! x Static! Velocity 2! Equal high response in all range!
71 Next: Noise!!!! Gaussian noise! Poissonian noise! Denoising!
72 References and Further Reading! Extended Depth of Field (EDOF)! DOWSKI, E. R., AND CATHEY, W. T Extended depth of field through wave-front coding. Appl. Opt. 34, 11, ! Levin, Hasinoff, Green, Durand, Freeman, 4D Frequency Analysis of Computational Cameras for Depth of Field Extension, ACM SIGGRAPH 2009! Cossairt, Zhou, Nayar, Diffusion-Coded Photography, ACM SIGGRAPH 2012! overview and analysis in light field space: Zhang, Levoy, Wigner Distributions and How They Relate to the Light Field, ICCP 2009! A. Isaksen, L. McMillan, and S. J. Gortler. Dynamically reparameterized light fields. In Proc. ACM SIGGRAPH, 2000! EDOF through Focal Sweep! HAUSLER, G A method to increase the depth of focus by two step image processing. Optics Communications 6 (Sep), ! NAGAHARA, H., KUTHIRUMMAL, S., ZHOU, C., AND NAYAR, S Flexible Depth of Field Photography. In ECCV 08, 73! Cossairt, Nayar Spectral Focal Sweep for Extending Depth of Field, Proc. ICCP 2010! Coded Apertures! LEVIN, A., FERGUS, R., DURAND, F., AND FREEMAN, W. T Image and depth from a conventional camera with a coded aperture. In SIGGRAPH 07, 70.! VEERARAGHAVAN, A., RASKAR, R., AGRAWAL, A., MOHAN, A., AND TUMBLIN, J Dappled photography: mask enhanced cameras for heterodyned light fields and coded aperture refocusing. In SIGGRAPH 07, 69! ZHOU, C., AND NAYAR, S What are Good Apertures for Defocus Deblurring? In ICCP 09! Coding Motion! Raskar, Agrawal, Tumblin, Coded Exposure Photography: Motion Deblurring using Fluttered Shutter, ACM SIGGRAPH 2006! Levin, Sand, Cho, Durand, Freeman, Motion-Invariant Photography, ACM SIGGRAPH 2008! Motion and Depth Invariance! Bando, Holtzman, Raskar, Near-Invariant Blur for Depth and 2D Motion via Time-Varying Light Field Analysis, ACM Trans. Graph. 2013! Bando, An Analysis of Focus Sweep for Improved 2D Motion Invariance, IEEE CVPR CCD Workshop 2013!!
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