Sebastian Thrun & Jana Kosecka CS223B Computer Vision, Winter 2007 Stanford CS223B Computer Vision, Winter 2006 Lecture 2: Lenses and Vision Software.

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Sebastian Thrun & Jana Kosecka CS223B Computer Vision, Winter 2007 Stanford CS223B Computer Vision, Winter 2006 Lecture 2: Lenses and Vision Software Professors Sebastian Thrun and Jana Kosecka CAs: Vaibhav Vaish and David Stavens

Sebastian Thrun & Jana Kosecka CS223B Computer Vision, Winter 2007 Today’s Goals Thin Lens Aberrations Vision Software

Sebastian Thrun & Jana Kosecka CS223B Computer Vision, Winter 2007 Pinhole Camera (last Wednesday) Marc Pollefeys comp256, Lect 2 -- Brunelleschi, XVth Century

Sebastian Thrun & Jana Kosecka CS223B Computer Vision, Winter 2007 Snell’s Law Snell’s law n 1 sin  1 = n 2 sin  2

Sebastian Thrun & Jana Kosecka CS223B Computer Vision, Winter 2007 Thin Lens: Definition optical axis focus f Spherical lense surface: Parallel rays are refracted to single point

Sebastian Thrun & Jana Kosecka CS223B Computer Vision, Winter 2007 Thin Lens: Projection optical axis z Spherical lense surface: Parallel rays are refracted to single point Image plane f

Sebastian Thrun & Jana Kosecka CS223B Computer Vision, Winter 2007 Thin Lens: Projection optical axis z Spherical lense surface: Parallel rays are refracted to single point Image plane ff

Sebastian Thrun & Jana Kosecka CS223B Computer Vision, Winter 2007 Thin Lens: Properties 1.Any ray entering a thin lens parallel to the optical axis must go through the focus on other side 2.Any ray entering through the focus on one side will be parallel to the optical axis on the other side

Sebastian Thrun & Jana Kosecka CS223B Computer Vision, Winter 2007 Thin Lens: Model Zff O P Q R FrFr FlFl p z

Sebastian Thrun & Jana Kosecka CS223B Computer Vision, Winter 2007 Thin Lens: Model Zff O P Q R FrFr FlFl p z

Sebastian Thrun & Jana Kosecka CS223B Computer Vision, Winter 2007 A Transformation

Sebastian Thrun & Jana Kosecka CS223B Computer Vision, Winter 2007 The Thin Lens Law Zff O P Q R FrFr FlFl p z

Sebastian Thrun & Jana Kosecka CS223B Computer Vision, Winter 2007 The Thin Lens Law

Sebastian Thrun & Jana Kosecka CS223B Computer Vision, Winter 2007 Limits of the Thin Lens Model 3 assumptions : 1.all rays from a point are focused onto 1 image point Remember thin lens small angle assumption 2. all image points in a single plane 3. magnification is constant Deviations from this ideal are aberrations

Sebastian Thrun & Jana Kosecka CS223B Computer Vision, Winter 2007 Today’s Goals Thin Lens Aberrations Vision Software

Sebastian Thrun & Jana Kosecka CS223B Computer Vision, Winter 2007 Aberrations chromatic : refractive index function of wavelength 2 types : geometrical : geometry of the lense, small for paraxial rays Marc Pollefeys

Sebastian Thrun & Jana Kosecka CS223B Computer Vision, Winter 2007 Geometrical Aberrations q spherical aberration q astigmatism q distortion q coma aberrations are reduced by combining lenses

Sebastian Thrun & Jana Kosecka CS223B Computer Vision, Winter 2007 Astigmatism Different focal length for inclined rays Marc Pollefeys

Sebastian Thrun & Jana Kosecka CS223B Computer Vision, Winter 2007 Astigmatism Different focal length for inclined rays Marc Pollefeys

Sebastian Thrun & Jana Kosecka CS223B Computer Vision, Winter 2007 Spherical Aberration rays parallel to the axis do not converge outer portions of the lens yield smaller focal lenghts

Sebastian Thrun & Jana Kosecka CS223B Computer Vision, Winter 2007 Distortion Can be corrected! (if parameters are know) pincushion (tele-photo) barrel (wide-angle) Marc Pollefeys magnification/focal length different for different angles of inclination

Sebastian Thrun & Jana Kosecka CS223B Computer Vision, Winter 2007 Coma point off the axis depicted as comet shaped blob Marc Pollefeys

Sebastian Thrun & Jana Kosecka CS223B Computer Vision, Winter 2007 Chromatic Aberration rays of different wavelengths focused in different planes cannot be removed completely Marc Pollefeys

Sebastian Thrun & Jana Kosecka CS223B Computer Vision, Winter 2007 Vignetting Effect: Darkens pixels near the image boundary

Sebastian Thrun & Jana Kosecka CS223B Computer Vision, Winter 2007 Vignetting Effect: Darkens pixels near the image boundary

Sebastian Thrun & Jana Kosecka CS223B Computer Vision, Winter 2007 CCD vs. CMOS Mature technology Specific technology High production cost High power consumption Higher fill rate Blooming Sequential readout Recent technology Standard IC technology Cheap Low power Less sensitive Per pixel amplification Random pixel access Smart pixels On chip integration with other components Marc Pollefeys

Sebastian Thrun & Jana Kosecka CS223B Computer Vision, Winter 2007 Today’s Goals Thin Lens Aberrations Vision Software

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