Lecture 2: Image Formation and Cameras

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1 #1 Lecture 2: Image Formation and Cameras Saad J Bedros

2 Last Lecture #2 What is Computer vision: deals with the formation, analysis and interpretation of Images Evolving field in Artificial Intelligence Enabler in Robotics as a smart sensor for better decision making.

3 Outline for this Lecture #3 Image Formation Cameras and Lenses Human Visual System Digital Cameras Digital Image representation

4

5 The Electromagnetic Spectrum Radio Waves - communication Microwaves - used to cook Infrared - heat waves Visible Light - detected by your eyes Ultraviolet - causes sunburns X-rays - penetrates tissue Gamma Rays - most energetic

6 The Multi-Wavelength Sun X-Ray UV Visible Infrared Composite Radio

7 Visible Spectrum #7 Light waves extend in wavelength from about 400 to 700 nanometers

8 #8 Image Formation

9 Quantum Theory of Light Newton proposed that light is a stream of particles traveling in a straight line. Each particle is called a quantum and each quantum of light is a photon. Thus the intensity of light is measured in number of photons. the visible spectrum is from 380 nm (violet) to 760 nm (red) refraction occurs when light enters a different medium causing the velocity of the light to change, this change bends the direction of the light Short wavelengths (violet) of light are refracted more than longer wavelengths (red). This is why a spectrum is formed from white light passing through a prism and it also causes the problem of chromatic aberration #9

10 How do we Capture an Image? #10

11 Image formation There are two parts to the image formation process: (1)The geometry, which determines where in the image plane the projection of a point in the scene will be located. (2) The physics of light, which determines the brightness of a point in the image plane. Simple model: f(x,y) = i(x,y) r(x,y) i: illumination, r: reflectance

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

13 Pinhole camera Object Barrier Film 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?

14 Image Formation: Simple Model Digital Camera Film The Eye

15 History of Imaging: Camera Obscura History 1544 Device that led to Photography and the Camera "When images of illuminated objects... penetrate through a small hole into a very dark room... you will see [on the opposite wall] these objects in their proper form and color, reduced in size... in a reversed position, owing to the intersection of the rays". Leonardo da Vinci Slide credit: David Jacobs

16 Camera Obscura The first camera How does the aperture size affect the image? How does the size of the box affect the image?

17 Pinhole camera model The simplest device to form an image of a 3D scene on a 2D surface. Rays of light pass through a "pinhole" and form an inverted image of the object on the image plane. perspective projection: center of projection (X,Y,Z) (x,y) x = fx Z y = fy Z f: focal length, distance from pinhole to image plane

18 Pinhole and the Perspective Projection (x,y) Is an image being formed on the screen? screen image plane scene y YES! But, not a clear one. r = ( x, y, z) optical axis effective focal length, f z x pinhole r' = ( x', y', f ') r ' = f ' r z x' f ' = x z y' f ' = y z

19 What is the effect of aperture size? Large aperture: light from the source spreads across the image (i.e., not properly focused), making it blurry! Small aperture: reduces blurring but (i) it limits the amount of light entering the camera and (ii) causes light diffraction.

20 Shrinking the aperture #20 Why not make the aperture as small as possible? Less light gets through

21 Shrinking more the aperture What happens if we keep decreasing aperture size? When light passes through a small hole, it does not travel in a straight line and is scattered in many directions (i.e., diffraction)

22 Shrinking the aperture #22 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.

23 Problems with Pinholes Pinhole size (aperture) must be very small to obtain a clear image. However, as pinhole size is made smaller, less light is received by image plane. If pinhole is comparable to wavelength of incoming light, DIFFRACTION effects blur the image! Sharpest image is obtained when: pinhole diameter d = 2 f ' λ Example: If f = 50mm, λ = 600nm (red), d = 0.36mm

24 Traditional Photography A chemical process, little changed from 1826 Taken in France on a pewter plate with 8-hour exposure The world's first photograph 24

25 History of Imaging: Adding a Lens Lens Based Camera Obscura, 1568

26 First Camera Design #26

27 The Reason for Lenses #27 Gather more light from each scene point

28 Adding a lens Pinhole replaced by a Lens Lens redirect light rays emanating from the object Lens improve image quality, leading to sharper images.

29 Lenses #29 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)

30 Properties of thin lens (i.e., ideal lens) focal point f Light rays passing through the center are not deviated. Light rays passing through a point far away from the center are deviated more.

31 Properties of thin lens (i.e., ideal lens) focal point f All parallel rays converge to a single point. When rays are perpendicular to the lens, it is called focal point.

32 Properties of thin lens focal point f The plane parallel to the lens at the focal point is called the focal plane. The distance between the lens and the focal plane is called the focal length (i.e., f) of the lens.

33 Thin lenses Object Lens Film Focal point Thin lens equation: Not quite right Any object point satisfying this equation is in focus What is the shape of the focus region? How can we change the focus region? Thin lens applet: (by Fu-Kwun Hwang )

34 Thin lens equation Assume an object at distance u from the lens plane: v f u object image

35 Thin lens equation (cont d) Using similar triangles: y v f image u y y /y = v/u

36 Thin lens equation (cont d) Using similar triangles: y v f image u y y /y = (v-f)/f

37 Thin lens equation (cont d) Combining the equations: v f u image u + v = f

38 Lens Aperture #38

39 Adding a lens Object Lens Film 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 circle of confusion

40 depth of field The size of blur circle is proportional to aperture size.

41 Controlling depth of field 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

42 Depth of Field Changing the aperture of a camera also changes the amount of the image that is in focus this amount is called the depth of field

43 depth of field trade off Changing aperture size (controlled by diaphragm) affects depth of field. A smaller aperture increases the range in which an object is approximately in focus (but need to increase exposure time). A larger aperture decreases the depth of field (but need to decrease exposure time).

44 Depth of field trade off Aperture Film 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

45 Depth of Field The range of depths over which the world is approximately sharp (i.e., in focus).

46 Another Example Large aperture = small DOF

47 Varying aperture size Large aperture = small DOF Small aperture = large DOF DOF is Depth of Field

48 Aperture Small Apertures (e.g. f11, f16, f22) only let a small amount of light through Large Apertures (e.g. f4, f5.6, f8) let through a lot of light So for a sunny day you might need to use a small aperture to get the correct exposure

49 Thin lens assumption 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.

50 Field of View (Zoom) The cone of viewing directions of the camera. Inversely proportional to focal length. f f

51 Field of View (Zoom)

52 Lens Flaws: Chromatic Aberration Lens has different refractive indices for different wavelengths. Could cause color fringing: i.e., lens cannot focus all the colors at the same point.

53 Chromatic Aberration - Example

54 Lens Flaws: Radial Distortion Straight lines become distorted as we move further away from the center of the image. Deviations are most noticeable for rays that pass through the edge of the lens.

55 Lens Flaws: Radial Distortion No distortion Pin cushion Barrel

56 Lens Flaws: Tangential Distortion Lens is not exactly parallel to the imaging plane!

57 Now the test! Under or over exposure?

58 Now the test! Which is the largest aperture?

59 Now the test! Under, or over exposed?

60 Now the test! Small or large aperture?

61 Human Eye #62 Cameras are a Copy of the Human Eye!

62 Human Eye vs. the Camera We make cameras that act similar to the human eye

63 Image formation in the eye 64 Light receptor Brain radiant energy electrical impulses

64 Human Eye The eye has an iris like a camera Focusing is done by changing shape of lens Retina contains cones (mostly used) and rods (for low light) The fovea is small region of high resolution containing mostly cones Optic nerve: 1 million flexible fibers Slide credit: David Jacobs

65 Human Eye: Pupil Hole or opening where light enters Or, the diameter of that hole or opening Pupil of the human eye Bright light: 1.5 mm diameter Average light: 3-4 mm diameter Dim light: 8 mm diameter Camera Wider aperture admits more light Though leads to blurriness in the objects away from point of focus 66

66 Human Eye : Lens Focusing is achieved by varying the shape of the lens (i.e., flattening of thickening).

67 Human Eye: Retina Retina contains light sensitive cells that convert light energy into electrical impulses that travel through nerves to the brain. Brain interprets the electrical signals to form images.

68 Retina up-close Light

69 Two types of light-sensitive receptors Cones cone-shaped less sensitive operate in high light color vision Rods rod-shaped highly sensitive operate at night gray-scale vision Stephen E. Palmer, 2002

70 Rod / Cone sensitivity ME5286 The Lecture famous 2 (Theory) sock-matching problem

71 Human Eye - Color Three different types of cones; each type has a special pigment that is sensitive to wavelengths of light in a certain range: Short (S) corresponds to blue Medium (M) corresponds to green Long (L) corresponds to red Ratio of L to M to S cones: approx. 10:5:1 Almost no S cones in the center of the fovea RELATIVE ABSORBANCE (%) S nm. M L WAVELENGTH (nm.)

72 Visual Cortex #73

73 Visual Perception #74 Modern view is that visual transformation is a creative process Vision transforms light stimuli on the retina into mental constructs of a stable 3D world Visual perception is a 3D perception of the world that is invariant to a wide range of changes in illumination, size, shape, and brightness of the image

74 Digital Image Formation

75 First digitally scanned photograph 1957, 176x176 pixels

76 Digital cameras A digital camera replaces film with a sensor array. Each cell in the array is light-sensitive diode that converts photons to electrons Two common types Charge Coupled Device (CCD) Complementary metal oxide semiconductor (CMOS)

77 What is a digital image? 8 bits/pixel 0 255

78 Spatial Sampling #79

79 Quantization #80

80 Image Acquisition Pipeline Lens Shutter scene radiance sensor irradiance sensor exposure 2 (W/sr/m ) t CCD ADC Remapping analog voltages digital values pixel values

81 Digital Camera: Properties Focus Shifts the depth that is in focus. Focal length Adjusts the zoom, i.e., wide angle or telephoto lens. Aperture Adjusts the depth of field and amount of light let into the sensor. Exposure time How long an image is exposed. The longer an image is exposed the more light, but could result in motion blur. ISO Adjusts the sensitivity of the film. Basically a gain function for digital cameras. Increasing ISO also increases noise.

82 Camera exposure ISO number Sensitivity of the film or the sensor Can go as high as 1,600 and 3,200 Shutter speed How fast the shutter is opened and closed f/stop The size of aperture 1.0 ~ 32 83

83 Illumination #84 1 Lux = 1 Lumen/m 2 = ft-candles Office = 100-1,000 Lux Sunlight = 50, ,000 Lux Cloudy day = 1,1000 Lux Twilight = 1-10 Lux Full moon = Lux Night sky =

84 Exposure #85

85 Exposure Time #86

86 Aperture & Shutter control Exposure #87

87 Aperture vs. Shutter #88

88 Long Exposure Real world 10-6 High dynamic range 10 6 Picture to 255

89 Short Exposure Real world 10-6 High dynamic range 10 6 Picture to 255

90 Varying Exposure

91 Image file formats Many image formats adhere to the simple model shown below (line by line, no breaks between lines). The header contains at least the width and height of the image. Most headers begin with a signature or magic number (i.e., a short sequence of bytes for identifying the file format)

92 Common image file formats GIF (Graphic Interchange Format) - PNG (Portable Network Graphics) JPEG (Joint Photographic Experts Group) TIFF (Tagged Image File Format) PGM (Portable Gray Map) FITS (Flexible Image Transport System)

93 PBM/PGM/PPM format A popular format for grayscale images (8 bits/pixel) Closely-related formats are: PBM (Portable Bitmap), for binary images (1 bit/pixel) PPM (Portable Pixelmap), for color images (24 bits/pixel)» ASCII or binary (raw) storage ASCI Binary

94 Chromatic Aberration #95

95 Spherical Aberration #96

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