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EECS 274 Computer Vision Cameras EECS 274 Computer Vision Cameras

Cameras • Camera models – Pinhole Perspective Projection – Affine Projection – Spherical Perspective Cameras • Camera models – Pinhole Perspective Projection – Affine Projection – Spherical Perspective Projection • • Camera with lenses Sensing Human eye Reading: FP Chapter 1, S Chapter 2

They are formed by the projection of 3 D objects. Figure from US Navy They are formed by the projection of 3 D objects. Figure from US Navy Manual of Basic Optics and Optical Instruments, prepared by Bureau of Naval Personnel. Reprinted by Dover Publications, Inc. , 1969. Images are two-dimensional patterns of brightness values.

Reproduced by permission, the American Society of Photogrammetry and Remote Sensing. A. L. Nowicki, Reproduced by permission, the American Society of Photogrammetry and Remote Sensing. A. L. Nowicki, “Stereoscopy. ” Manual of Photogrammetry, Thompson, Radlinski, and Speert (eds. ), third edition, 1966. Animal eye: a looonnng time ago. Figure from US Navy Manual of Basic Optics and Optical Instruments, prepared by Bureau of Naval Personnel. Reprinted by Dover Publications, Inc. , 1969. Photographic camera: Niepce, 1816. Pinhole perspective projection: Brunelleschi, XVth Century. Camera obscura: XVIth Century.

B’ and C’ have same height A’ is half of B’ From the model B’ and C’ have same height A’ is half of B’ From the model C is half the size of B A is half the size of Bhn Parallel lines: appear to converge on a line formed by the intersection of a plane parallel to π and image plane L in π that is parallel to image plane has no image at all

Vanishing point Vanishing point

Vanishing point The lines all converge in his right eye, drawing the viewers gaze Vanishing point The lines all converge in his right eye, drawing the viewers gaze to this place.

Pinhole Perspective Equation • C’ : image center • OC’: optical axis • π’ Pinhole Perspective Equation • C’ : image center • OC’: optical axis • π’ : image plane is at a positive distance f’ from the pinhole • OP’= λ OP • P: (x, y, z), P’(x’, y’, z’) NOTE: z is always negative

Affine projection models: Weak perspective projection frontal-parallel plane π0 defined by z=z 0 is Affine projection models: Weak perspective projection frontal-parallel plane π0 defined by z=z 0 is the magnification. When the scene relief (depth) is small compared its distance from the camera, m can be taken constant: weak perspective projection.

Affine projection models: Orthographic projection When the camera is always at a (roughly constant) Affine projection models: Orthographic projection When the camera is always at a (roughly constant) distance from the scene, take m=-1

Planar pinhole perspective Orthographic projection Spherical pinhole perspective Planar pinhole perspective Orthographic projection Spherical pinhole perspective

Pinhole camera Pinhole too big many directions are averaged, blurring the image Pinhole too Pinhole camera Pinhole too big many directions are averaged, blurring the image Pinhole too smalldiffraction effects blur the image Generally, pinhole cameras are dark, because a very small set of rays from a particular point hits the screen

Lenses Snell’s law (aka Descartes’ law) Ignoring diffraction, interference n 1 sin a 1 Lenses Snell’s law (aka Descartes’ law) Ignoring diffraction, interference n 1 sin a 1 = n 2 sin a 2 n: index of refraction reflection refraction

Paraxial (or first-order) optics Snell’s law: Small angles: n 1 sin a 1 = Paraxial (or first-order) optics Snell’s law: Small angles: n 1 sin a 1 = n 2 sin a 2 n 1 a 1 ¼ n 2 a 2

Paraxial (or first-order) optics Small angles: n 1 a 1 ¼ n 2 a Paraxial (or first-order) optics Small angles: n 1 a 1 ¼ n 2 a 2

Thin Lenses Thin lenses: n=1 f: focal length F, F’: focal points Thin Lenses Thin lenses: n=1 f: focal length F, F’: focal points

Depth of field and field of view • Depth of field (field of focus): Depth of field and field of view • Depth of field (field of focus): objects within certain range of distances are in acceptable focus – Depends on focal length and aperture • Field of view: portion of scene space that are actually projected onto camera sensors – Not only defined by focal length – But also depends on effective sensor area

Depth of field f / 5. 6 f / 32 • Changing the aperture Depth of field f / 5. 6 f / 32 • Changing the aperture size affects depth of field – A smaller aperture increases the range in which the object is approximately in focus – f number = f/D (f: focal length, D: diameter or aperature)

Thick lenses • • • Simple lenses suffer from several aberrations First order approximation Thick lenses • • • Simple lenses suffer from several aberrations First order approximation is not sufficient Use 3 rd order Taylor approximation

Orthographic/telecentric lenses Navitar telecentric zoom lens http: //www. lhup. edu/~dsimanek/3 d/telecent. htm Orthographic/telecentric lenses Navitar telecentric zoom lens http: //www. lhup. edu/~dsimanek/3 d/telecent. htm

Correcting radial distortion from Helmut Dersch Correcting radial distortion from Helmut Dersch

Spherical Aberration • • rays do not intersect at one point circle of least Spherical Aberration • • rays do not intersect at one point circle of least confusion Distortion pincushion barrel Chromatic Aberration refracted rays of different wavelengths intersect the optical axis at different points Figure from US Navy Manual of Basic Optics and Optical Instruments, prepared by Bureau of Naval Personnel. Reprinted by Dover Publications, Inc. , 1969.

Vignetting • Aberrations can be minimized by aligning simple lenses with well-chosen shapes and Vignetting • Aberrations can be minimized by aligning simple lenses with well-chosen shapes and refraction indexes, separated by appropriate stops • These compound lenses can still be modeled by thick lenses • However, light rays from object points off-axis are partially blocked by lens configuration vignetting brightness drop in the image periphery

Human eye Corena: transparent highly curved refractive component Pupil: opening at center of iris Human eye Corena: transparent highly curved refractive component Pupil: opening at center of iris in response to illumination Reproduced by permission, the American Society of Photogrammetry and Remote Sensing. A. L. Nowicki, “Stereoscopy. ” Manual of Photogrammetry, Thompson, Radlinski, and Speert (eds. ), third edition, 1966. Helmoltz’s Schematic Eye

Receptive field Retina: thin, layered membrane with two types of photoreceptors • rods: very Receptive field Retina: thin, layered membrane with two types of photoreceptors • rods: very sensitive to light but poor spatial detail • cones: sensitive to spatial details but active at higher light level • generally called receptive field Cones in the fovea Reprinted from Foundations of Vision, by B. Wandell, Sinauer Associates, Inc. , (1995). 1995 Sinauer Associates, Inc. Rods and cones in the periphery Reprinted from Foundations of Vision, by B. Wandell, Sinauer Associates, Inc. , (1995). 1995 Sinauer Associates, Inc.

Sensing Photographs (Niepce, “La Table Servie, ” 1822) Milestones: Daguerreotypes (1839) Photographic Film (Eastman, Sensing Photographs (Niepce, “La Table Servie, ” 1822) Milestones: Daguerreotypes (1839) Photographic Film (Eastman, 1889) Cinema (Lumière Brothers, 1895) Color Photography (Lumière Brothers, 1908) Television (Baird, Farnsworth, Zworykin, 1920 s) CCD Devices (1970) Collection Harlingue-Viollet. .

360 degree field of view… • Basic approach – Take a photo of a 360 degree field of view… • Basic approach – Take a photo of a parabolic mirror with an orthographic lens (Nayar) – Or buy one a lens from a variety of omnicam manufacturers… • See http: //www. cis. upenn. edu/~kostas/omni. html

Digital camera • A digital camera replaces film with a sensor array – Each Digital camera • A digital camera replaces film with a sensor array – Each cell in the array is a Charge Coupled Device • light-sensitive diode that converts photons to electrons • other variants exist: CMOS is becoming more popular • http: //electronics. howstuffworks. com/digital-camera. htm

Image sensing pipeline Image sensing pipeline