How do we see the world?

Transcription

1 The Camera 1

2 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? Credit: Steve Seitz 2

3 Pinhole camera Idea 2: 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? Credit: Steve Seitz 3

4 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 Credit: Steve Seitz 4

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

6 ABELARDO MORELL 6

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12 Project 5: a Shoe-box Camera Obscura 12

13 Another way to make pinhole camera Why so blurry? 13

14 Shrinking the aperture Less light gets through Why not make the aperture as small as possible? Less light gets through Diffraction effects Credit: Steve Seitz 14

15 Shrinking the aperture 15

16 3D to 2D Perspective projection 16

17 Dimensionality Reduction Machine (3D to 2D) 3D world 2D image What have we lost? Angles Distances (lengths) Figures Stephen E. Palmer,

18 Funny things happen 18

19 Parallel lines aren t Figure by David Forsyth 19

20 Lengths can t be trusted... Can you find the mistake in this figure? Credit: David Forsyth 20

21 but humans adapt! Müller-Lyer Illusion We don t make measurements in the image plane 21

22 Projecting 3D to 2D (Perspective, Orthographic, Weak Perspective) 22

23 Perspective Projection The coordinate system: Pin-hole model as an approximation Optical center (Center Of Projection) at the origin Put the image plane (Projection Plane) in front of the COP Why? Camera looks down the negative z axis we need this if we want right-handedcoordinates Credit: Steve Seitz 23

24 Projection on the image plane 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: How do we express this in matrix form? Credit: Steve Seitz 24

25 . Y.. X. (x, y) (X, Y, Z) Z Compute intersection Compute projection 1. Divide by w Projection matrix 3D point 2. Drop off last coordinate Projection on the image plane 25

26 Orthographic Projection Special case of perspective projection Distance from the COP to the PP is infinite Image World Also called parallel projection What s the projection matrix? Credit: Steve Seitz 26

27 Weak Perspective Projection average distance divide by w, drop z 27

28 Using lenses 28

29 Credit: Steve Seitz 29

30 Focus and Defocus Object Lens Film 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 Credit: Steve Seitz 30

31 Thin lenses Thin lens equation: Any object point satisfying this equation is in focus What is the shape of the focus region? How can we change the focus region? Credit: Steve Seitz 31

32 The thin lens assumption assumes the lens has no thickness, but this isn t true Object Lens Film Focal point By adding more elements to the lens, the distance at which a scene is in focus can be made roughly planar. Credit: Steve Seitz 32

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34 Depth of Field 34

35 Depth of field Aperture Film 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 But small aperture reduces amount of light need to increase exposure

36 Large aperture = small DOF Small aperture = large DOF 36

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38 Field of View (Zoom) 38

39 Field of View (Zoom) = Cropping 39

40 FOV depends of Focal Length f Smaller FOV = larger Focal Length 40

41 Sigma mm F2.8 EX DG lens What does 1600mm lens look like?

42 Varying focal length and distance Credit: Zisserman & Hartley 42

43 Field of View / Focal Length Large FOV, small f Camera close to car Small FOV, large f Camera far from the car 43

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46 Points to remember Optimal aperture of pinhole camera is between the geometric and diffraction limit 3 projection models (perspective, orthographic, weak perspective) When using a lens: change aperture size ==> change depth of field change focal length ==> change in field of view change focal length and camera distance ==> changes projection effect 46