Computational Photography. Computational Photography. The Camera. Camera Developments. Yacov Hel-Or and Yossi Rubner
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1 Computational Photography Yacov Hel-Or and Yossi Rubner The Camera A camera is a device that takes photos of images Camera Obscura (Latin = "dark chamber") 9 th century camera Sony s smile recognition camera 2 Camera Developments Computational Photography permanent capturing (wet plates) exposure time and motion capture (dry plates) portability (film-kodak) quality and size (35 mm) optics (SLR) instancy (polaroid) digital cameras computational photography Computational photography refers broadly to computational imaging techniques that enhance or extend the capabilities of digital photography. The output of these techniques is an ordinary photograph, but one that could not have been taken by a traditional camera Earliest surviving photograph. This image required an eight-hour exposure. 4 Steve Mann: The Cyberman
2 Goal: Record a richer, multi-layered layered visual experience. Overcome limitations of today s s cameras 2. Support better post-capture processing 3. Enables new classes of recording the visual signal 4. Synthesize impossible photos 5 Administration Pre-requisites / prior knowledge Course Home Page: What s new Lecture slides and handouts Matlab guides Homework, grades Exercises: Programming in Matlab, ~3 Assignments Final project 6 Administration (Cont.) Schedule Matlab software: Available in PC labs Student version For next week: Run Matlab demo and read Matlab primer until section 3. Grading policy: Final Grade will be based on: Exercises (6%), Final project (4%) Exercises will be weighted Exercises can be submitted in pairs Office Hours: by appointment to toky@idc.ac.il 7 Date Topic Intro and image formation Acquisition and camera model Single exposure enhancement Panoramas and feature-based registration Blending and Composition Appearance-based registration Multi exposure enhancement Multi exposure enhancement Data Driven Synthesis Segmentation and Matting Single View Modeling Light Field Project presentation 8 2
3 Readings Related papers New book: Computational Photography by R. Raskar and J. Tumblin 9 Syllabus Image Formation Image formation HVS pathway Color models Acquisition and camera model Camera model + perspective projections Sensors Noise models & Distortions Sampling (spatial+temporal) and quantization Camera parameters Camera Parameters trade-offs. Single exposure enhancement White Balancing De-mosaicing De-noising De-blurring Geometrical distortion correction Panoramas and feature based registration Image features SIFT Panoramas Feature based registration Panoramas Homography RANSAC Image stitching Syllabus cont. Syllabus cont. Blending and Composition Pyramid blending Optimal cut Seam Carving Graph-cut Gradient domain editing Appearance based registration Similarity measures Lucas Kanade optical flow Multi-modal registration Applications Multi exposure enhancement (2 weeks) HDR Super-resolution multi-exposure fusion Data Driven Synthesis Texture synthesis Video texture Quilting Image analogies Super-Resolution Image Completion Segmentation and Matting Segmentation using Graph cut. mean-shift Spectral clustering Interactive and semi-automatic Matting Single View Modeling Camera Calibration Measurements in affine camera 3D reconstruction Light Field Plenoptic function and the Lumiograph Re-sampling the plenoptic function 2 3
4 . Image Formation 2. Camera Model and Acquisition Taking a picture HVS pathway Color models Cornea Pupil Lens Fovea Vitreous Humor Optic Nerve Perspective projections Camera pipeline and parameters Sensors Sampling and quantization Noise models & Distortions Camera Parameters trade-offs. Iris Optic Disc Retina Ocular Muscle Single Exposure Enhancement White Balancing De-mosaicing De-noising De-blurring Geometrical distortion correction 4. Panoramas and Feature Based Registration Image features SIFT Feature based registration Panoramas Homography RANSAC Image stitching Difference in white point 5 6 4
5 5. Blending and Composition 6. Appearance Based Registration (warping?) Pyramid blending Gradient domain editing Optimal cut Graph-cut Similarity measures Lucas Kanade optical flow Multi-modal registration Applications Multi Exposure Enhancement HDR Super-resolution Different-exposures fusion 8. Data Driven Synthesis Texture synthesis Video texture Quilting Image analogies Super-Resolution Image Completion 9 2 5
6 9. Segmentation and Matting Segmentation using Graph cut. mean-shift Spectral clustering Interactive and semi-automatic Matting. Single View Modeling Camera Calibration 3D reconstruction Metrology Flagellation by Pietro della Francesca (46-92, Italian Renaissance period) Animation by Criminisi et al., ICCV Light Field Plenoptic function and the Lumiograph Re-sampling the plenoptic function Today s s Topic - Image Formation What is an image? What is a color?
7 The Visual Sciences What is an Image? Image/video Processing 2D Images An image is a projection of a 3D scene into a 2D projection plane. An image can be defined as a 2 variable function I(x,y), where for each position (x,y) in the projection plane, I(x,y) defines the light intensity at this point. Computer Vision Rendering 3D Object Geometric Modeling Model The Pinhole Camera Model Funny things happen Image plane COP Focal length Pinhole model: Captures pencil of rays all rays through a single point The point is called Center of Projection (COP) The image is formed on the Image Plane Effective focal length f is distance from COP to Image Plane 27 Slide by Steve Seitz 28 7
8 Parallel lines aren t Lengths can t t be trusted Projection Model (where) The Shading Model (what) The coordinate system We will use the pin-hole model as an approximation Put the optical center (Center Of Projection) at the origin Put the image plane (Projection Plane) in front of the COP The camera looks down the negative z axis Shading Model: Given the illumination incident at a point on a surface, what is reflected? 3 Slide by Steve Seitz 32 8
9 Shading Model Parameters Light and the Visible Spectrum The factors determining the shading effects are: The light source properties: Positions, Electromagnetic Spectrum, Shape. The surface properties: Position, orientation, Reflectance properties. The eye (camera) properties: Position, orientation, Sensor spectrum sensitivities. Newton s Experiment, 665 Cambridge. Discovering the fundamental spectral components of light The light Spectrum Electromagnetic Radiation - Spectrum Ultraviolet Short- Gamma X rays Infrared Radar FM TV wave AM AC electricity Monochromators Monochromators measure the power or energy at different wavelengths Wavelength in meters (m) Visible light 4 nm 5 nm 6 nm 7 nm Wavelength in nanometers (nm)
10 Light Parameters Examples of Spectral Power Distributions The Spectral Power Distribution (SPD) of a light is a function e(λ) which defines the energy at each wavelength..5.5 Relative Power Blue Skylight Tungsten bulb Wavelength (λ) Red monitor phosphor Monochromatic light Surface Parameters Incident light normal Specular reflection Diffuse reflection Diffuse (lambertian) reflection reflected randomly between color particles reflection is equal in all directions Specular reflection mirror like reflection at the surface Different Types of Surfaces 39 4
11 Spectral Property of Lambertian Surfaces Yellow Red Blue Wavelength (nm) Surface Body Reflectances (albedo) 4 Gray R V Ambient reflection: I amb = K(λ) e a (λ) Diffuse reflection: N 42 θ L Surface properties Light properties I diff = K(λ) e p (λ) (N L) Specular reflection: I spec = K s (λ)e p (λ) (R V) n e p e a - the ambient and point light intensities. K, K s [,] - the surface ambient / diffuse / specular reflectivity. N - the surface normal, L - the light direction, V viewing direction geometry R V N θ L Ambient reflection: I amb = K(λ) e a (λ) Diffuse reflection: I diff = K(λ) e p (λ) (N L) Specular reflection: I spec = K s (λ)e p (λ) (R V) n e p e a - the ambient and point light intensities. K, K s [,] - the surface ambient / diffuse / specular reflectivity. N - the surface normal, L - the light direction, V viewing direction Ambient surface Diffuse surface Diffuse + Specular 43 44
12 The final illumination equation: Composition of Light Sources I(λ) = I amb +I diff +I spec If several light sources are placed in the scene: I(λ)= I amb +Σ k (I k diff+i k spec) The Human Visual System Lens Cornea Pupil Iris Fovea Vitreous Humor Optic Disc Optic Nerve קרנית - Cornea איש ון - Pupil קשתית - Iris רשתית - Retina Ocular Muscle Retina
13 The Visual Pathway Eye v.s.. Camera Retina Optic Nerve Optic Chiasm Lateral Geniculate Nucleus (LGN) Visual Cortex 49 5 Yaho Wang s slides The Human Retina rods cones Retina contains 2 types of photo-receptors Cones: Day vision, can perceive color tone Rods: Night vision, perceive brightness only bipolar horizontal amacrine ganglion light
14 Relative sensitivity Cones: High illumination levels (Photopic vision) Sensitive to color (there are three cone types: L,M,S) Produces high-resolution vision 6-7 million cone receptors, located primarily in the central portion of the retina Cone Spectral Sensitivity Wavelength (nm) 53 L S M A side note: Humans and some monkeys have three types of cones (trichromatic vision); most other mammals have two types of cones (dichromatic vision). Marine mammals have one type of cone. Most birds and fish have four types. Lacking one or more type of cones result in color blindness. Rods: Low illumination levels (Scotopic vision). Highly sensitive (respond to a single photon). Produces lower-resolution vision million rods in each eye. No rods in fovea. Relative sensitivity Rod Spectral Sensitivity Wavelength (nm) 54 Photoreceptor Distribution Foveal Periphery photoreceptors Cone Receptor Mosaic (Roorda and Williams, 999) rods S - Cones 55 L/M - Cones L-cones M-cones S-cones 56 4
15 Cone s Distribution: L-cones (Red) occur at about ~65% of the cones throughout the retina. M-cones (green) occur at about ~3% of the cones. S-cones (blue) occur at about ~2-5% of the cones (Why so few?). Receptors per square mm 8 x 4 rods cones Distribution of rod and cone photoreceptors fovea Degrees of Visual Angle 57 The Cone Responses Assuming Lambertian Surfaces Output Sensors I(λ) Fixed, point source illuminant l(λ),m(λ),s(λ) Cone responsivities Illuminant L = l( λ) I( λ) M = m( λ) I( λ) S = s( λ) I( λ) 58 Metamer - two lights that appear the same visually. They might have different SPDs (spectral power distributions). The Trichromatic Color Theory Trichromatic: tri =three chroma =color color vision is based on three primaries (i.e., it is 3D). Power 2 Tungsten light Wavelength (nm) 59 Monitor emission The phosphors of the monitor were set to match the tungsten light. Thomas Young ( ) - A few different retinal receptors operating with different wavelength sensitivities will allow humans to perceive the number of colors that they do. Suggested 3 receptors. Helmholtz & Maxwell (85) - Color matching with 3 primaries. 6 5
16 Color Matching Experiment Given a set of 3 primaries, one can determine for every spectral distribution, the intensity of the guns required to match the color of that spectral distribution. Color matching experiment for Monochromatic lights The 3 numbers can serve as a color representation. test match + - R(λ) T(λ) + - G(λ) Primary Intensities Primaries + - B(λ) ( λ ) rr ( λ ) + gg ( λ ) bb ( λ ) T Primary Intensity 3 r(λ) 2 b(λ) g(λ) Wavelength (nm) Observation - Color matching is linear: if (S P) then (S+N P+N) if (S P) then (α S α P) Outcome : Any T(λ) can be matched: r = T λ r λ dλ ; g = T λ g λ dλ ; b = ( ) ( ) ( ) ( ) T( λ) b ( λ) dλ Outcome 2: CMF can be calculated for any chosen primaries U(λ), V(λ), W(λ): Stiles & Burch (959) Color matching functions. Primaries are: and Problems: Some perceived colors cannot be generated. This is true for any choice of visible primaries. u c v = c w c ru rv rw c c c gu gv gw c c c bu bv bw r g b
17 The CIE Color Standard The CIE (Commission Internationale d Eclairage) defined in 93 three hypothetical lights X, Y, and Z whose matching functions are positive everywhere: Tristimulus Let X, Y, and Z be the tristimulus values. A color can be specified by its trichromatic coefficients, defined as X x = X + Y + Z Y y = X + Y + Z Z z = X + Y + Z X ratio Y ratio Z ratio Two trichromatic coefficients are enough to specify a color. (x + y + z = ) 65 From: Bahadir Gunturk 66 CIE Chromaticity Diagram Input light spectrum CIE Chromaticity Diagram Input light spectrum y y x x From: Bahadir Gunturk 67 From: Bahadir Gunturk 68 7
18 CIE Chromaticity Diagram Input light spectrum CIE Chromaticity Diagram Input light spectrum y y 7nm Boundary 38nm x x From: Bahadir Gunturk 69 From: Bahadir Gunturk 7 CIE Chromaticity Diagram Input light spectrum CIE Chromaticity Diagram Light composition Boundary From: Bahadir Gunturk 7 From: Bahadir Gunturk 72 8
19 CIE Chromaticity Diagram Light composition CIE Chromaticity Diagram The CIE chromaticity diagram is helpful to determine the range of colors that can be obtained from any given colors in the diagram. Gamut: The range of colors that can be produced by the given primaries. Light composition From: Bahadir Gunturk 73 Source: The srgb Color Standard Color matching predicts matches, not appearance The srgb is a device-independent color space. It was created in 996 by HP and Microsoft for use on monitors and printers. It is the most commonly used color space. It is defined by a transformation from the xyz color space
20 Color Appearance Color Appearance Color Appearance Color Spaces
21 RGB Color Space (additive) Define colors with (r, g, b) ; amounts of red, green, and blue CMY Color Space (subtractive) Cyan, magenta, and yellow are the complements of red, green, and blue We can use them as filters to subtract from white The space is the same as RGB except the origin is white instead of black 8 82 HSV color space HSV - a more intuitive color space Hue - the color we see (red, green, purple). Saturation - how pure is the color (how far the color from gray ). Value (brightness) - how bright is the color. Saturation Value Hue
22 Opponent Color Space Observation: Color bands are highly correlated in high spatial frequencies h( x, y) Green derivative A joint Histogram of r x v.s. g x Red derivative A joint Histogram of g x v.s. b x A joint Histogram of r x v.s. b x Blue derivative Blue derivative Green derivative Red derivative
23 Joint histograms of R v.s. G for a low pass images Define a new color basis (l,c,c 2 ): l R c = T G c2 B T = where n Green derivative A joint Histogram of r x v.s. g x L c 2 l luminance C - red/green C 2 blue/yellow l luminance value C Red-Green C 2 Blue-Yellow Comments: l channel encodes the color luminance. C and C 2 encodes the chrominance. In the chrominance channels high freq. are attenuated. It the luminance channel high freq. are maintained. The 3 opponent channels are uncorrelated in the high freq. Efficient for encoding Red derivative
24 Original Image High freq. details Low freq. details Low freq. details Claim: The HVS high spatial sensitivity in the luminance domain and low spatial sensitivity in the chrominance domains is a direct outcome of the statistical properties of color images! After blurring C and C 2 bands After blurring l band as well
25 Opponent Color Spaces The standard representation used in TV broadcasting Backwards compatibility with B/W TV Low bit rate is needed in the chrominance channels There are various opponent representations: YIQ - used for NTSC color TV YUV (also called YC b C r ) - used for PAL TV and video Question: why S cones are sparsely populated? T H E E N D
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