Cameras and Projection.

Transcription

1 Cameras and Projection Starts at 2:40pm

2 Join Google-groups Project 1 assigned Cameras and Projection

3 Cameras and Projection

4 Müller-Lyer Illusion

5 Image formation Let s design a camera Idea 1: put a piece of film in front of an object Do we get a reasonable image?

6 Pinhole camera Add a barrier to block off most of the rays This reduces blurring The opening is known as the aperture How does this transform the image?

7 Camera Obscura Gemma Frisius, 1558 Basic principle known to Mozi ( BC), Aristotle ( BC) Drawing aid for arcsts: described by Leonardo da Vinci ( )

8 Pinhole camera 8

9 Pinhole camera of light ] 9

10 Student can make a pinhole camera 10

11 Pinhole cameras everywhere Sun shadows during a solar eclipse by Henrik von Wendt

12 Pinhole cameras everywhere Tree shadow during a solar eclipse photo credit: Nils van der Burg

13 Pinhole cameras everywhere 13

14 Camera Obscura The first camera How does the aperture size affect the image?

15 Shrinking the aperture Why not make the aperture as small as possible? Less light gets through Diffraction effects...

16 Shrinking the aperture

17 Diffraction effects 17 [ ]

18 Diffraction effects 18 [ ]

19 Diffraction effects 19

20 Pinhole camera + Actually works + Everything is in focus - Diffraction effects 20

21 Pinhole camera + Actually works + Everything is in focus - Diffraction effects - Either dark image or slow shutter speed 21

22 Questions 22

23 Want to get a Ph.D. from Oxford? Why does a camera have lens? 23

24 Adding a lens 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 Changing the shape of the lens changes this distance

25 Lenses F optical center (Center Of Projection) focal point A lens focuses parallel rays onto a single focal point focal point at a distance f beyond the plane of the lens f is a function of the shape and index of refraction of the lens Aperture of diameter D restricts the range of rays aperture may be on either side of the lens

26 Lenses F optical center (Center Of Projection) focal point A lens focuses parallel rays onto a single focal point focal point at a distance f beyond the plane of the lens f is a function of the shape and index of refraction of the lens Aperture of diameter D restricts the range of rays aperture may be on either side of the lens Lenses are typically spherical (easier to produce) Real cameras use many lenses together

27 Thin lenses

28 Thin lenses

29 Thin lenses

30 Depth of field f / 5.6 Changing the aperture size affects depth of field f / 32 A smaller aperture increases the range in which the object is approximately in focus F-number Flower images from Wikipedia

31 Depth of field Portrait (family photos) Computer vision experiments 31 [ expha.com ]

32 Summary For pinhole Aperture big-> Entire image gets blurry. Aperture small -> Entire image gets sharp. Aperture very small -> Entire image gets blurry For a camera with lens An object at the focus distance is always sharp. An object not at the focus distance follows the pinhole principle. Aperture small -> long exposure -> bad for moving object 32

33 The eye The human eye is a camera Iris - colored annulus with radial muscles Pupil - the hole (aperture) whose size is controlled by the iris What s the film? photoreceptor cells (rods and cones) in the retina How do we refocus? Change the shape of the lens

34 The eye The human eye is a camera Iris - colored annulus with radial muscles Pupil - the hole (aperture) whose size is controlled by the iris What s the film? photoreceptor cells (rods and cones) in the retina How do we refocus? Change the shape of the lens yellow->rods, blue->cones [ blindless.org ]

35 Digital camera A digital camera replaces film with a sensor array Each cell in the array is a Charge Coupled Device (CCD) light-sensitive diode that converts photons to electrons CMOS is becoming more popular (esp. in cell phones)

36 Issues with digital cameras Noise big difference between consumer vs. SLR-style cameras low light is where you most notice noise Compression creates artifacts except in uncompressed formats (tiff, raw) Color color fringing artifacts from Bayer patterns Blooming charge overflowing into neighboring pixels In-camera processing oversharpening can produce halos Interlaced vs. progressive scan video even/odd rows from different exposures Are more megapixels better? requires higher quality lens noise issues Stabilization compensate for camera shake (mechanical vs. electronic) More info online, e.g.,

37 Questions? 37

38 Projection Mapping from the world (3d) to an image (2d) An optical system defines a particular projection

39 Projection Mapping from the world (3d) to an image (2d) An optical system defines a particular projection Three examples: 1. Perspective projection (how we see normally ) 2. Orthographic projection (e.g., telephoto lenses) 3. Weak-perspective (scaled orthographic) projection

40 Projection Mapping from the world (3d) to an image (2d) An optical system defines a particular projection Three examples: 1. Perspective projection (how we see normally ) 2. Orthographic projection (e.g., telephoto lenses) 3. Weak-perspective (scaled orthographic) projection

41 In Computer Vision... Often approximate camera by a pinhole So, we often assume - Everything is sharp and in-focus (no out-of-focus blur) - Lens are thin (no refraction) - No diffraction... 41

42 Modeling projection 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 Why? The camera looks down the negative z axis (optical axis) we need this if we want right-handed-coordinates

43 Modeling projection Projection equations Compute intersection with PP of ray from (x,y,z) to COP Derived using similar triangles (on board) We get the projection by throwing out the last coordinate:

44 Homogeneous coordinates Is this a linear transformation? no division by z is nonlinear Trick: add one more coordinate: homogeneous image coordinates homogeneous scene coordinates Converting from homogeneous coordinates

45 Perspective Projection Projection is a matrix multiply using homogeneous coordinates: divide by third coordinate This is known as perspective projection The matrix is the projection matrix Can also formulate as a 4x4 (today s reading does this) divide by fourth coordinate

46 Perspective Projection Example 1. Object point at (10, 6, 4), d=2 2. Object point at (25, 15, 10) Perspective projection is not 1-to-1!

47 Perspective Projection How does scaling the projection matrix change the transformation?

48 Perspective Projection What happens to parallel lines in 3D? What happens to angles? What happens to distances?

49 Projection Mapping from the world (3d) to an image (2d) Can we have a 1-to-1 mapping? How many possible mappings are there? An optical system defines a particular projection Two examples: 1. Perspective projection (how we see normally ) 2. Orthographic projection (e.g., telephoto lenses) 3. Weak-perspective (scaled orthographic) projection

50 Modeling projection What happens when you - move PP a lot dè - see only distant points zè -

51 Modeling projection What happens when you - move PP a lot dè - see only distant points zè -

52 Modeling projection What happens when you - move PP a lot dè - see only distant points zè -

53 Orthographic projection Special case of perspective projection Distance from the COP to the PP is infinite Image World Good approximation for telephoto optics Also called parallel projection : (x, y, z) (x, y) What s the projection matrix?

54 Orthographic ( telecentric ) lenses Navitar telecentric zoom lens

55 Orthographic Projection What happens to parallel lines in 3D? What happens to angles? What happens to distances?

56 Popular for 3D modeling software 56 [ Maya ]

57 Projection Mapping from the world (3d) to an image (2d) Can we have a 1-to-1 mapping? How many possible mappings are there? An optical system defines a particular projection Two examples: 1. Perspective projection (how we see normally ) 2. Orthographic projection (e.g., telephoto lenses) 3. Weak-perspective (scaled orthographic) projection

58 Perspective projection See the scanned notes. 58

59 Summary Perspective Weak-perspective Scaled-orthographic Orthographic Projection formulae In homogeneous Linear Linear Linear In non-homogeneous Non-linear Linear Linear Notes Exact pin-hole Approximate depths by e Approximate zoom-lens

60 Inverse Pinhole 60

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