Lecture 12: Cameras and Geometry CAP 5415 Fall 2010 The midterm • What does the response of a derivative filter tell me about whether there is an edge or not? Things aren't working • Did you look at the filters? • Why not? • Normalize the filters How do we see the world? Let’s design a camera – Idea 1: put a piece of film in front of an object – Do we get a reasonable image? Slide by Steve Seitz Pinhole camera Add a barrier to block off most of the rays – This reduces blurring – The opening known as the aperture – How does this transform the image? Slide by Steve Seitz Pinhole camera model 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 Slide by Steve Seitz A little bit of history on building cameras Camera Obscura • Latin for “Dark Box” • Dark room with a pinhole in wall • Projects image onto wall • Allows artists to get perspective right Image from Wikipedia Camera Obscura Camera Obscura, Gemma Frisius, 1558 The first camera – Known to Aristotle – Depth of the room is the effective focal length Camera Obscura • Can also be a box We’ll use the pinhole camera model to describe image formation Notice how the image is inverted (Image from Slides by Forsyth) Projection Effects Pinhole • Height of objects depends on the distance from the pinhole (O) (Image from Slides by Forsyth) Projection Effects: Horizon Line • Consider two parallel lines that lie in a plane (Π) • Will converge to a point on the horizon line(H) Pinhole (Image from Slides by Forsyth) • Observe this next time you are driving on a flat road Vanishing points • Each set of parallel • Good ways to spot lines (=direction) faked images meets at a different – scale and perspective point don’t work – The vanishing point for – vanishing points this direction behave badly • Sets of parallel lines – supermarket tabloids on the same plane are a great source. lead to collinear vanishing points. – The line is called the horizon for that plane (From Slides by Forsyth) The equation of projection (Image from Slides by Forsyth) The equation of projection We know: so (Image from Slides by Forsyth) Lenses • Why Lenses? • For an ideal pinhole, only one ray of light reaches each point – Very Dim Image • Why not make pinhole bigger? Why not make pinhole bigger? • Only one point can generate rays that strike a particular point on the image plane Why not make pinhole bigger? • Now add an aperture Pinhole too big - many directions are averaged, blurring the image Pinhole too small- diffraction effects blur the image Generally, pinhole cameras are dark, because a very small set of rays from a particular point hits the screen. (From Slides by Forsyth) Lenses • The lens focuses multiple rays coming from the same point (Image from Slides by Forsyth) Thin Lens Equation Focus and Defocus “circle of confusion” A lens focuses light onto the film – There is a specific distance at which objects are “in focus” • other points project to a “circle of confusion” in the image – How can we change focus distance? Slide by Steve Seitz More on Lenses Canon EF 28-135mm f/3.5-5.6 IS USM Standard Zoom Lens for Canon SLR Cameras 28-135mm is the focal length i o P P’ f Diagram by Shree Nayar What's f/3.5-5.6? Canon EF 28-135mm f/3.5-5.6 IS USM Standard Zoom Lens for Canon SLR Cameras f-number • f is the focal length • D is the diameter of the pupil or aperture • f/2 is the same as N=2 • f/16 is the same as N=16 • Which has the bigger aperture? What's f/3.5-5.6? • This is the widest possible aperture Canon EF 28-135mm f/3.5-5.6 IS USM Standard Zoom Lens for Canon SLR Cameras Why should I adjust the aperture? • Big aperture means more light, shorter exposure time • Also affects sharpness and depth of field Here, the rays are focused on the image plane Now, look at a point that is farther way Circle of Confusion It grows as you move farther away Circle of Confusion Circle of Confusion • Spot caused by a point that is not in focus • You decide the tolerable limits (Diagram from Wikipedia) Aperture also causes blurring • Go back to pinhole camera model • Only one point can generate rays that strike a particular point on the image plane Aperture also causes blurring • Now add an aperture Depth of Field • Increasing the aperture diameter increases the size of the circle of confusion f/22 f/5.6 Diffraction • When light passes through a small aperture the rays begin to interfere with each other • For a perfectly circular aperture this leads to the airy disc pattern Image from http://www.cambridgeincolour.com/tutorials/diffraction-photography.htm# This leads to a loss of sharpness f/8 f/11 f/16 f/22 From http://www.cambridgeincolour.com/tutorials/diffraction-photography.htm# After Light Strikes the sensor • Engineering problem: – I have sensor that records the amount of light at different pixels – How do I get a color image instead of a black and white image? Solutions • Three sensors • One sensor with a color mask – Each pixel records one wavelength • A common pattern for the mask is the Bayer pattern: Mosaicing • So, if I took a • My sensor would picture of this edge record this image Demosaicing • I have 1 color at each pixel • I need three • Easy solution: Interpolate + Problem! This smooths across the edge • Because the different pixels are used to red and green, the smoothing may be different + Result: Color Fringing Color Fringing (Results from Brainard et al) Fast Solution • The fringing occurs when the correlation between the color channels is incorrectly estimated • One measure of this correlation is the color difference • Can fix errors using median filtering Simple Demosaicing Algorithm (Freeman) • Use linear interpolation to get first estimate • Compute difference images between color channels • Median filter these difference images • Use filtered difference images to reconstruct (Slide by Freeman).