Computational Photography

Transcription

1 Computational Photography Photography and Imaging Michael S. Brown Brown - 1

2 Part 1 Overview Photography Preliminaries Traditional Film Imaging (Camera) Part 2 General Imaging 5D Plenoptic Function (McMillan) 4D Light Fields (Levoy, Gortler) 2

3 Photography Preliminaries 3

4 Photography in a nutshell Focal Length Exposure and Aperture Depth of Field Noise 4

5 Light is coming from all directions Why is there no image on a piece of white paper? paper From Photography, London et al. 5

6 Pinhole From Photography, London et al. We need to focus on some selected rays. One way to do this is to use a pin-hole. Such camera mechanisms have been known for some time: Mozi ( 墨子 ) BC Aristotle 384 BC Abu Ali Al-Hasan Ibn al-haitham 953 AD (book on optics) 6

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8 Focal Length Examples 8

9 Focal length and field of view 9

10 Perspective vs. viewpoint A small change in viewpoint is a big change in background. Telephoto lens can simulate this 10

11 Similar to cropping Sensor size source: canon red book 11

12 Exposure Exposure controls how much light hits the camera sensor Two ways to control this: Aperture: the hole in the optical path for the light Shutter speed: the time the hole is opened Aperture Controllable Shutter 12

13 Shutter speed and aperture Shutter speed Expressed in fraction of a second: 1/30, 1/60, 1/125, 1/250, 1/500 (in reality, 1/32, 1/64, 1/128, 1/256,... ) Aperture Expressed as ratio of aperture size to focal length (f-stop) f/2.0, f/2.8, f/4, f/5.6, f/8, f/11, f/16, f/22, f/32 f/x, means focal length is X times bigger than the aperture Each f-stop reduces the area of the aperture by half So, the larger the f-stop, the smaller the aperture We are going to see how these are related in the following slides. 13

14 Shutter speed and motion Slow shutter speeds can result in motion blur if the scene isn t static or if the camera moves or shakes. 14

15 Sensor/Film Sensor/Film Aperture and depth of field Focus Plane in the scene Points outside the focal plane diverge on the sensor (circle of confusion) Closing the aperture reduces the circle of confusion.. i.e. it expands the depth of field. It also reduces the amount of light. Aperture controls depth of field (dof) 15

16 Main effect of aperture Bigger aperture = shallow depth of field. 16

17 Exposure The play between f-stop and shutter: Aperture (in f stop) Shutter speed (in fraction of a second) Reciprocity The same exposure is obtained with an exposure twice as long and an aperture area half as big 17 Slide from Fredo Durand From Photography, London et al.

18 Reciprocity cont Assume we know how much light we need We have the choice of an infinity of shutter speed/aperture pairs What will guide our choice of a shutter speed? Freeze motion vs. motion blur, camera shake What will guide our choice of an aperture? Depth of field Often we must compromise Open more to enable faster speed (but shallow DoF) 18 Slide from Fredo Durand

19 Note trade-off in DoF for motion blur. From Photography, London et al. 19

20 Note trade-off in DoF for motion blur. 20

21 Note trade-off in DoF for motion blur. 21

22 CCD sensitivity (ISO) and noise One solution to low exposure from a fast shutter speed is to increase the camera s CCD signal (i.e. gain the signal) This is analogous to film ISO sensitivity ISO 100 (slow film), ISO 1600 (fast film, x16 more sensitive) The drawback? Amplifying the CDD signal, amplifies the sensor noise! 22

23 Photography Equation Focal length (and position) Controls view/zoom Finessing motion blur, noise, and dof Trade-off between shutter speed and aperture Camera settings Motion Blur Artifacts DoF Noise fast-shutter speed wide aperture low ISO (gain) slow-shutter speed small aperture low ISO (gain) fast-shutter speed small aperture high ISO (gain) No Narrow No Yes Wide No No Wide Yes 23

24 General Imaging 24

25 Part 2: General Imaging Cameras image are single 2D snap shots Captured at a fixed viewing location Are there better ways to think about 3D scenes in terms of images? Better representations? 25

26 5D Plenoptic Sample All light rays entering a 3D point (Vx, Vy, Vy) can be parameterized by Φ and θ. 26

27 5D Plenoptic Sample A camera image is a good approximation of a portion of a plenoptic sample. We need to somehow know its position and orientation. 27

28 5D Plenoptic Samples So, imagine that you could make dense plenoptic samples over some 3D space y Plenoptic samples z x 28

29 5D Plenoptic Samples Now you want to create a novel view y Plenoptic samples z x Making an image from a new view is a matter of interpolating from the other samples. 29

30 Variations on Plenoptic Samples Sweep, Strip, or Slit cameras Creates a multi-center of projection images Imagine the camera captures only 1 column of pixels 30

31 Surveillance Cameras Slit cameras are used in Satellites and Aerial Photography With a hand-held camera 31

32 From 5D to 4D Light-Field Lumigraph/4D Light-field Assume you are outside the space of 3D objects s,t u,v For each (u,v) there are a bundle of possible rays coming into this point. These rays are parameterized by (s,t). This does not mean there are only 2 images for a light field. There is an full image (s,t) for each pixel (u,v), resulting in a 4D function L(u,v,s,t). Call this a light-slab. 32

33 4D Light-field For a fixed view point, we can calculate which rays to show That is (u,v) and its associated (s,t) for that view We can generate the view for image (x,y) 33

34 From u,v to s,t looks like lots of images from slightly different perspectives. From s,t to u,v looks like the surface of the scene s material as it would scatter light in space. 34

35 Capturing 4D-Light Fields An array of cameras! Data is huge, but highly redundant (compresses well) 35

36 4D Illumination Field Same idea, but to represent illumination falling onto a scene. Light parameterized by (u,v) illuminate in all directions* parameterized by (s,t) * All directions in a half-plane 36

37 4D Illumination field Generating an Illumination field. 37

38 Put them together: 8D Reflectance Field Now, for each possible ray in the 4D Light Field, we have its response to a 4D Illumination Field! Huge amount of data. And this is for a static scene. 38

39 Reflectance Fields 39

40 Summary This lecture covers the preliminaries for Computational Photography Introduction to traditional camera and associated terminology and uses Introduction to some reasonable new ideas on how to think beyond camera for image representation Plenoptic Function, Light Field, Illumination Field Reflectance Fields NEXT? Background on image processing... 40