Coded Computational Imaging: Light Fields and Applications
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1 Coded Computational Imaging: Light Fields and Applications Ankit Mohan MIT Media Lab
2 Coded Computational Imaging Agrawal, Veeraraghavan, Narasimhan & Mohan Schedule Introduction Assorted Pixels Coding and Modulation in Cameras Break Light Fields and Applications Break Computational Illumination Future Trends Discussion Srinivasa, 10 mins Srinivasa, 20 mins Amit, 45 mins 10 min Ankit, 60 mins 10 min Srinivasa, 45 mins Amit, 15 mins
3 Light Field Basics
4 The Plenoptic Function Figure by Leonard McMillan Q: What is the set of all things that we can ever see? A: The Plenoptic Function [Adelson & Bergen] Let s start with a stationary person and try to parameterize everything that she can see Slide adapted from Michael Cohen and Rick Szeliski
5 Grayscale Snapshot is intensity of light Seen from a single view point At a single time P(θ,φ) Figure by Leonard McMillan Averaged over the wavelengths of the visible spectrum Slide adapted from Michael Cohen and Rick Szeliski
6 Color Snapshot is intensity of light P(θ,φ,λ) Seen from a single view point At a single time As a function of wavelength Figure by Leonard McMillan Slide adapted from Michael Cohen and Rick Szeliski
7 A Movie is intensity of light P(θ,φ,λ, θ,φ,λ,t) Seen from a single view point Over time As a function of wavelength Figure by Leonard McMillan Slide adapted from Michael Cohen and Rick Szeliski
8 A Holographic Movie is intensity of light seen from ANY viewpoint over time as a function of wavelength Figure by Leonard McMillan P(θ,φ,λ,,t,V X,V Y,V Z ) Slide adapted from Michael Cohen and Rick Szeliski
9 The Plenoptic Function Figure by Leonard McMillan P(θ,φ,λ,,t,V X,V Y,V Z ) Can reconstruct every possible view, at every moment, from every position, at every wavelength Slide adapted from Michael Cohen and Rick Szeliski
10 Ray of Light Let s ignore time and color: 5D 3D position 2D direction P(θ,φ, θ,φ,v X,V Y,V Z ) Slide adapted from Michael Cohen and Rick Szeliski
11 Ray of Light in Free Space No Occluding Objects 4D 2D position 2D direction P(θ,φ, θ,φ,v X,V Y,V Z ) Slide adapted from Michael Cohen and Rick Szeliski
12 Light Field [Levoy & Hanrahan 1996] Radiance as a function of position and direction 4D in 3D free space (u, v, s, t) 2D in flatland (u, v, s, t) θ x u s θ θ position-angle parameterization two plane parameterization
13 Light Field Generation
14
15
![Code, Microsoft Tag, ] [IR remote, Sony ID](/docs-images/92/109781587/images/16-1.jpg "CAM] + standard camera focused at infinity")
16 visible light barcodes space time angle [UPC Code, QR Code, Data Matrix Code, Shot Code, Microsoft Tag, ] [IR remote, Sony ID CAM] + standard camera focused at infinity Bokode: Imperceptible Visual Tags for Camera Based Interaction from a Distance, Ankit Mohan, Grace Woo, Shinsaku Hiura, Quinn Smithwick and Ramesh Raskar, in SIGGRAPH Bokode
17 camera Bokode (angle) sensor
18 camera Bokode (angle) sensor ahh circle of confusion circle of information - Kurt Akeley
19 generate directionally encoded information Bokode f b
20 capture directionally encoded information camera Bokode f b f c
21 infinity-corrected microscope camera Bokode f b f c magnification = f c /f b (microscope); focus always at infinity
22 camera Bokode f b less distance more of Bokode imaged f c
23 camera Bokode f b f c less distance more of Bokode imaged
24 MIT Media Lab Camera Culture Bokode image depends on camera angle camera Bokode fb
25 MIT Media Lab Camera Culture Bokode image depends on camera angle camera Bokode fb fc
26 x id=42,x=8,y=5 y id=42 x=7 y=5 camera id=42 x=9 y=5 id=42 x=7 y=6 id=42 x=9 y=6 id=42 x=7 y=7 id=42 x=9 y=7 id=42,x=8,y=7
27 digital angle from Bokode id = (42,10,7)
28 prototype assembled
29 prototype exploded led: 120 view angle, 1350mcd pattern: 15µm resolution lenslet: f=8mm, Φ=3mm cost: ~$5
30 capturing Bokodes focus blur (85mm f/1.8; infinity focus) motion blur (50mm f/8; ~2cm motion)
31 MIT Media Lab Camera Culture street-view tagging
32 capturing Bokodes cell-phone camera close to the Bokode (10,000+ bytes of data)
33
34 traditional AR markers ARToolKit [Kato and Billinghurst 1999] ARTag [Fiala 2005] skew of marker
35 angle estimation robustness
36 wide field of view Bokode via Krill eye compound superposition optics Krill-eye: Superposition Compound Eye for Wide-Angle Imaging via GRIN Lenses, Shinsaku Hiura, Ankit Mohan, Ramesh Raskar, in OMNIVIS 2009.
37 barcode RFID Bokode encoding spatial rf modulation angular decoder camera dedicated reader camera geometry no no yes physical size ~ cm ~ cm ~ mm cost ~ free ~ $0.05 ~ $0.05 (currently $5) range ~ cm ~ cm ~ m (with large aperture lens) line of sight yes no yes
38 tabletop/surface interaction stylus based interaction identity position angle
39 multi-user interaction Bokode laser pointers
40 Bokode next to the eye eye Bokode f e
41 multiple Bokodes next to the eye Bokode A eye Bokode B f e Bokode images overlap
42 relaxed perfect eye focused at infinity Bokode A eye virtual point at infinity A B image points overlap Bokode B f e
43 relaxed eye with myopia Bokode A eye virtual point at infinity A B distinct image points Bokode B f e eye unable to focus at infinity
44 relaxed eye with myopia Bokode A eye virtual point at finite distance A B Bokode B image points overlap f e move points towards each other
45 relaxed eye with hyperopia Bokode A eye virtual point at infinity A B distinct image points Bokode B f e
46 eye with hyperopia Bokode A eye virtual point beyond infinity A B image points overlap Bokode B f e move points away from each other
47 NETRA: interactively measure prescription pinhole or microlens array eye patterns on an LCD f b array of Bokodes f e
48 NETRA: interactively measure prescription pinhole or microlens array eye patterns on an LCD f b array of Bokodes f e user interactio n
49 Shack-Hartmann wave-front sensor laser laser wavefront aberroemter expensive; requires trained professionals
50 interactive self-evaluation of eye s refractive error NETRA: Interactive Display for Estimating Refractive Errors and Focal Range, Vitor Pamplona, Ankit Mohan, Manuel Oliveira, and Ramesh Raskar, in SIGGRAPH 2010.
51 cell phone prototype lcd: 180dpi controls pinhole: a=3mm, Φ~100µm display patterns audio feedback pinhole or microlens array with spacer lenslet: f=20mm, a=3mm resolution: 0.71D cost: ~$2 (pinhole)
52 vs trial lenses Snellen chart NETRA smaller, less bulky, easier to carry phoropter little no training required avoids cycloplegic eye drops allows self-evaluation cheaper (if phone already exists)
53 interaction session with camera displayed patterns camera/subject view
54 patterns displayed subject view alignment accommodation accommodation displayed subject view alignment alignment
55 astigmatism: radially non-symmetric error cross or points may never meet with a 1d search
56 astigmatism lines reduce the problem to a 1d search
57 jittered pinholes reduce crosstalk jittered pinholes -5D 0D +5D display patterns viewmaster inspired prototype +3D to -5D with accommodation
58 interactive self-evaluation of eye s refractive error DEMO at 5PM TODAY in Workshop on cameras for Visually Impaired (Pacific Concourse) NETRA: Interactive Display for Estimating Refractive Errors and Focal Range, Vitor Pamplona, Ankit Mohan, Manuel Oliveira, and Ramesh Raskar, in SIGGRAPH 2010.
59 Light Field Capture
![Camera Arrays [Wilburn 2005] High Performance Imaging](/docs-images/92/109781587/images/60-0.jpg "Using Large Camera Arrays, Bennett Wilburn, Neel Joshi,")
60 Camera Arrays [Wilburn 2005] High Performance Imaging Using Large Camera Arrays, Bennett Wilburn, Neel Joshi, Vaibhav Vaish, Eino-Ville Talvala, Emilio Antunez, Adam Barth, Andrew Adams, Mark Horowitz, Marc Levoy, in SIGGRAPH 2005.
61 Synthetic aperture photography Camera array is far away from these bushes, yet it sees
62 Focus Adjustment: Sum of Bundles [Vaish et al. 2004]
63 Light Field Inside a Camera u s Lenslet-based Light Field camera / Integral Photography s u [Lippman 1908, Adelson and Wang, 1992, Ng et al. 2005]
![2005] Contax medium](/docs-images/92/109781587/images/64-1.jpg "format camera Kodak")
64 Stanford Plenoptic Camera [Ng et al 2005] Contax medium format camera Kodak 16-megapixel sensor Adaptive Optics microlens array 125μ square-sided microlenses pixels lenses = pixels per lens
65 Captured Image Behind Microlens 4/2/2010 Slide from Ren Ng and Marc Levoy
66 Digital Refocusing [Ng et al 2005] Light Field Photography with a Hand-Held Plenoptic Camera, Ren Ng, Marc Levoy, Mathieu Bredif, Gene Duval, Mark Horowitz, Pat Hanrahan, in Stanford Tech Report 2005.
67 Extended Depth of Field Light field focal stack extended DOF
68 Light Field Capture with a Programmable Aperture Nikon D70 Liquid crystal array Programmable Aperture Photography: Multiplexed Light Field Acquisition, Chia-Kai Liang, Tai-Hsu Lin, Bing-Yi Wong, Chi Liu, Homer Chen, in SIGGRAPH cm
69 Multiplexing to improve SNR 9 aperture patterns for capturing a light field with 3x3 angular resolution 9 multiplexed aperture patterns O(N) SNR improvement Comparable to previous single-shot light field cameras SNR is a function of W (aperture patterns) The camera noise characteristics
70 Can we capture the Light-Field using a static mask?
71 Mask? Sensor Mask Mask Sensor Full Resolution Digital Refocusing: Coded Aperture Camera 4D Light Field from 2D Photo: Heterodyne Light Field Camera
72 mask based light-field camera lens mask sensor IR filter mask digital back camera body
73 Fourier Slice Theorem θ l(x,θ) 2-D FFT f θ L(f x,f θ ) x f x Line Integral Central Slice 1-D FFT
74 Two-Plane Parameterization of Light Field Object Main Lens 1D Sensor θ -plane x-plane Levoy and Hanrahan 1996 Gortler et al θ 0 x 0 θ x
75 Optical Heterodyning High Freq Carrier 100 MHz Receiver: Demodulation Incoming Signal Baseband Audio Signal 99 MHz Reference Carrier Main Lens Object Mask Sensor Software Demodulation Recovered Light Field Photographic Signal (Light Field) Carrier Incident Modulated Signal Reference Carrier
76 How to Capture 2D Light Field with 1D Sensor? f θ f θ 0 Band-limited Light Field f x0 f x Sensor Slice Fourier Slice Theorem Fourier Light Field Space
77 Extra sensor bandwidth cannot capture extra dimension of the light field f θ f θ 0 Extra sensor bandwidth f x0 f x Sensor Slice
78 ??? f θ????????? f x
79 Solution: Modulation Theorem Make spectral copies of light field f θ f θ0 f x0 f x Modulation Function
80 Sensor Slice captures entire Light Field f θ f θ0 f x0 f x Modulation Function Modulated Light Field
81 Demodulation to recover Light Field 1D Fourier Transform of Sensor Signal f θ f x Rearrange 1D Fourier Transform into 2D
82 Narrowband Cosine Mask Used Mask Tile 1/f 0
83 Where to place the Mask? Sensor Sensor Mask Mask f θ Mask Modulation Function Mask Modulation Function f x
84 Where to place the Mask? Mask Sensor f θ f x Mask Modulation Function
85 Where to place the Mask? Mask Sensor v d Mask Modulation Function α α = (d/v) (π/2)
86 MERL, Northwestern Univ. Captured 2D Photo Mask-Enhanced Cameras: Heterodyned Light Fields & Coded Aperture Veeraraghavan, Raskar, Agrawal, Mohan & Tumblin Encoding due to Cosine Mask
87 Computing 4D Light Field 2D Sensor Photo, 1800*1800 2D Fourier Transform, 1800*1800 2D FFT 9*9=81 spectral copies 4D IFFT Rearrange 2D tiles into 4D planes 200*200*9*9 4D Light Field 200*200*9*9
88 4d light-field capture results Captured Photo Refocusing Changing Views Dappled Photography: Mask Enhanced Cameras for Heterodyned Light Fields and Coded Aperture Refocusing, Ashok Veeraraghavan, Ramesh Raskar, Amit Agrawal, Ankit Mohan, and Jack Tumblin, in SIGGRAPH Non-refractive modulators for encoding and capturing scene appearance and depth, Ashok Veeraraghavan, Ramesh Raskar, Amit Agrawal, Ankit Mohan, and Jack Tumblin, in IEEE CVPR 2008.
89 4/2/2010
90 Which Heterodyne Mask to Use? Conditions for heterodyne light field detection Mask spectrum must be a (windowed) 2D impulse train Can be achieved (approximately) with a pinhole array y fy fx m pinhole (x,y) x M pinhole (f x,f y )
91 y Which Heterodyne Mask to Use? Conditions for heterodyne light field detection Mask spectrum must be a (windowed) 2D impulse train Can be achieved exactly by Sum-of-Sinusoids (SoS) [Veeraraghavan et al. 2007] fy fx m SoS (x,y) M SoS (f x,f y ) x
92 y Which Heterodyne Mask to Use? Conditions for heterodyne light field detection Both pinhole array and SoS are periodic functions What other tiles lead to impulse trains????????????????????????????????????????????????????????????????????????????????????????????????? m general (x,y) M general (f x,f y ) x fy fx
93 General Tiled-broadband Masks Conditions for heterodyne light field detection (Almost) any 2D tile can be used (tiling impulse train) Amplitude of impulses given by Fourier series of tile y fy fx m general (x,y) M general (f x,f y ) x
94 y Specific Choice: Tiled-MURA Conditions for optimal heterodyne light field detection Modified Uniformly Redundant Array (MURA) Shield Fields: Modeling and Capturing 3D Occluders, Douglas Lanman, Ramesh Raskar, Amit Agrawal, Gabriel Taubin, in SIGGRAPH Asia fy fx M MURA (x,y) M MURA (f x,f y ) x
95 Benefits of New Heterodyne Codes Tiled-Broadband Code MURA Sum-of-Sinusoids Pinholes Average Transmission (%) Pinholes Sum-of-Sinusoids MURA 11x11 23x23 43x43 Angular Resolution Benefits and Limitations Angular Resolution Sum-of-Sinusoids converges to 18% transmission Tiled-MURA near 50% (but only for prime-lengths) Binary vs. continuous-tone process (quantization)
96 Prototype Implementation LED Array Mask + Diffuser Camera Subject Components 8.0 megapixel Canon EOS Digital Rebel XT 6x6 array of Philips Luxeon Rebel LEDs [1.2x1.2 m] 5,080 DPI mask and a paper vellum diffuser [75x55 cm]
97 Tiled-MURA Results: Sensor Image High-Resolution Sensor Image (0.25 sec. Exposure)
98 Tiled-MURA Results: Shadowgrams Light Field Reconstruction
99 Reconstruction Light Field Reconstruction Visual Hull Reconstruction
100 Tiled-MURA Results: Dynamic Scene Components and Limitations 1600x fps Point Grey Grasshopper camera 6x6 array of Philips Luxeon Rebel LEDs [1.2x1.2 m] 5,080 DPI mask and a paper vellum diffuser [75x55 cm] Light Field Reconstruction Individual shadowgrams only 75x50 pixels
101 Bi-Di Screen: Light Field capture with a flat display for User Interaction BiDi Screen: A Thin, Depth-Sensing LCD for 3D Interaction using Light Fields, Matthew Hirsch, Douglas Lanman, Henry Holtzman, Ramesh Raskar, in SIGGRAPH Asia 2009.
102 BiDi Screen Sharp Microelectronics Optical Multi-touch Prototype Display with embedded optical sensors
103 BiDi Screen: Design Overview ~50 cm ~2.5 cm Display with embedded optical sensors Optical sensor array LCD, displaying mask
104 BiDi Screen: Design Vision Spatial Light Modulator Bare Sensor Object Collocated Capture and Display
105 Reinterpretable Imaging Coded Aperture Static Aperture Mask Sensor Optical Heterodyning Static Mask Sensor Veeraraghavan et al. SIGGRAPH 2007 Digital Refocusing Veeraraghavan et al. SIGGRAPH 2007 Light Field Capture
106 Reinterpretable Imager Coded Aperture Static Aperture Mask Sensor Optical Heterodyning Static Mask Sensor Reinterpretable Imager Dynamic Aperture Mask Static Mask Sensor Veeraraghavan et al. SIGGRAPH 2007 Veeraraghavan et al. SIGGRAPH 2007 Agrawal et al. Eurographics 2009 Digital Refocusing Light Field Capture Post-Capture Resolution Control Reinterpretable Imager: Towards Variable Post-Capture Space, Angle and Time Resolution in Photography, Amit Agrawal, Ashok Veeraraghavan, Ramesh Raskar, in Eurographics 2010.
107 Temporally changing mask in Aperture
108 Captured 2D Photo Static Scene Parts Dynamic Scene Parts In-Focus Out of Focus In-Focus Out of Focus High Resolution 2D Image 4D Light Field Video 1D Parallax + Motion
109 Captured Photo
110 Video from Single-Shot (Temporal Frames)
111 Reconstructed Sub-Aperture Views (3 by 3 Light Field)
112 Time Time For Rotating Doll
113 Angle Angle For Static Scene Parts
114 Light Field Modulation
115 Agile Spectrum Imaging I A B C x I x 400nm 550nm 700nm λ Arbitrary white 1D signal Agile Spectrum Imaging: Programmable Wavelength Modulation for Cameras and Projectors, Ankit Mohan, Ramesh Raskar and Jack Tumblin, in Eurographics 2008.
116 Pinhole Camera x C A I B B I A Object C Image x Pinhole
117 x C A B B I A Object Lens L 1 C Prism Pinhole
118 Spectral Light-Field Prism A λ x B λ λ C λ x
119 Prism I A λ B λ λ C λ x Screen I x p
120 Prism t = I A λ p B λ λ x C λ x I t
121 I Prism A λ Lens L 2 C B λ B x C λ x A t S
122 C B A
123 Sensor plane (t=t s ) C B λ A x t t S I p
124 Rainbow plane (t=t R ) C p B λ A x I t t R
125 Rainbow plane (t=t R ) C B A λ position t t R
126 Mask in the Rainbow plane C 0 B λ 0 A x t t R t S I p
127 Rainbow plane (t=t R ) C Control the spectral sensitivity of the B A sensor by placing an appropriate grayscale masks in the R-plane. t t R t S
128 Lens L 1 Diffraction R-plane Grating Lens L 2 mask Sensor
129 m(λ ) 400nm 550nm 700nm λ
130 m(λ ) 400nm 550nm 700nm λ
131 Pinhole multi-spectral camera Pinhole x Scene C B A θ 2 θ 0 θ 1 x Lens L 1 x A B C Prism λ λ λ Light field camera
132 Mask based multi-spectral camera x Scene C A Lens L 1 x θ x Mask, m(θ) Prism Light field camera
133 Glare separation camera Glare Aware Photography: 4D Ray Sampling for Reducing Glare Effects of Camera Lenses, Ramesh Raskar, Amit Agrawal, Cyrus Wilson and Ashok Veeraraghavan, in SIGGRAPH 2008.
134 Effects of Glare on Image Hard to model, Low Frequency in 2D But reflection glare is outlier in 4D ray-space Glare coherence to recover full resolution Sensor b a Angular Variation at pixel a
135
136
137 Reducing Glare Conventional Photo After removing outliers Glare Reduced Image
138 Enhancing Glare Conventional Photo Glare Enhanced Image
139 Conclusions Light Field Capture Heterodyne Camera Shield Fields BiDi Screen Reinterpretable Imager Light Field Modulation Spectral Light Fields Glare Camera Light Field Generation Bokode NETRA
140
141 camera barcode (spatial) sensor
142 camera barcode (space) sensor
143 camera barcode (space) sensor image much smaller; refocus if distance changes
144 limitations overlapping Bokodes auto-exposure / motion blur angular range (+/-20 ) thickness holographic Bokode 20 25
145 retro-reflector for passive Bokode
146 focusing range and refractive errors perfect vision eye ~25mm myopia hyperopia presbyopia infinity ~10cm cornea (~40D) crystalline lens (0~10D)
147 accommodation eye ~25mm infinity ~10cm focusing at infinity cornea (~40D) crystalline lens (~0D)
148 accommodation eye ~25mm infinity ~10cm focusing close to eye cornea (~40D) crystalline lens (~10D)
149 Impact / PerfectSight sending 4 prototypes over the summer MIT IDEAS award to deploy in Mwanda, Malawi local testing
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