Lecture 12: Cameras and Geometry. CAP 5415 Fall 2010

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1 Lecture 12: Cameras and Geometry CAP 5415 Fall 2010

2 The midterm What does the response of a derivative filter tell me about whether there is an edge or not?

3 Things aren't working Did you look at the filters? Why not? Normalize the filters

4 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

5 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

6 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

7 A little bit of history on building cameras

8 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

9 Camera Obscura Camera Obscura, Gemma Frisius, 1558 The first camera Known to Aristotle Depth of the room is the effective focal length

10 Can also be a box Camera Obscura

11 We ll use the pinhole camera model to describe image formation Notice how the image is inverted (Image from Slides by Forsyth)

12 Projection Effects Pinhole Height of objects depends on the distance from the pinhole (O) (Image from Slides by Forsyth)

13 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)

14 Observe this next time you are driving on a flat road

15 Vanishing points Each set of parallel lines (=direction) meets at a different point The vanishing point for this direction Sets of parallel lines on the same plane lead to collinear vanishing points. The line is called the horizon for that plane Good ways to spot faked images scale and perspective don t work vanishing points behave badly supermarket tabloids are a great source. (From Slides by Forsyth)

16 The equation of projection (Image from Slides by Forsyth)

17 The equation of projection We know: so (Image from Slides by Forsyth)

18 Lenses Why Lenses? For an ideal pinhole, only one ray of light reaches each point Very Dim Image Why not make pinhole bigger?

19 Why not make pinhole bigger? Only one point can generate rays that strike a particular point on the image plane

20 Why not make pinhole bigger? Now add an aperture

21 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. (From Slides by Forsyth)

22 Lenses The lens focuses multiple rays coming from the same point (Image from Slides by Forsyth)

23 Thin Lens Equation

24 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

25 More on Lenses Canon EF mm f/ IS USM Standard Zoom Lens for Canon SLR Cameras

26 28-135mm is the focal length i o P P f Diagram by Shree Nayar

27 What's f/ ? Canon EF mm f/ IS USM Standard Zoom Lens for Canon SLR Cameras

28 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?

29 What's f/ ? This is the widest possible aperture Canon EF mm f/ IS USM Standard Zoom Lens for Canon SLR Cameras

30 Why should I adjust the aperture? Big aperture means more light, shorter exposure time Also affects sharpness and depth of field

31 Here, the rays are focused on the image plane

32 Now, look at a point that is farther way Circle of Confusion

33 It grows as you move farther away Circle of Confusion

34 Circle of Confusion Spot caused by a point that is not in focus You decide the tolerable limits (Diagram from Wikipedia)

35 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

36 Aperture also causes blurring Now add an aperture

37 Depth of Field Increasing the aperture diameter increases the size of the circle of confusion f/22 f/5.6

38 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

39 This leads to a loss of sharpness f/8 f/11 f/16 f/22 From

40 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?

41 Solutions Three sensors One sensor with a color mask Each pixel records one wavelength A common pattern for the mask is the Bayer pattern:

42 Mosaicing So, if I took a picture of this edge My sensor would record this image

43 Demosaicing I have 1 color at each pixel I need three Easy solution: Interpolate +

44 Problem! This smooths across the edge Because the different pixels are used to red and green, the smoothing may be different +

45 Result: Color Fringing

46 Color Fringing (Results from Brainard et al)

47 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

48 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

49 (Slide by Freeman)

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