![http://www.acmi.net.au/AIC/CAMERA_OBSCURA.html (Russell Naughton)
Camera Obscura
"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". Da Vinci
Slide credit: David Jacobs](https://image.slidesharecdn.com/2-basicimagingandradiometry-150527131359-lva1-app6892/85/2-basic-imaging-and-radiometry-20-320.jpg)
![The Equation of Pinhole Projection
• Cartesian coordinates:
– We have, by similar triangles, that
(x, y, z) -> (f x/z, f y/z, f)
[multiply by f/z]
– Ignore the third coordinate, and get
(x,y,z)→(f
x
z
,f
y
z
)
3D object point 2D image point](https://image.slidesharecdn.com/2-basicimagingandradiometry-150527131359-lva1-app6892/85/2-basic-imaging-and-radiometry-38-320.jpg)
2 basic imaging and radiometry
- 1. Basic Principles of Imaging and Lenses
- 2. Light
- 4. These three are the same… • Light * pure energy • Electromagnetic Waves * energy-carrying waves emitted by vibrating electrons • Photons * particles of light
- 6. EM Radiation Travels as a Wave c = 3 x 108 m/s
- 8. EM Radiation Carries Energy • Quantum mechanics tells us that for photons E = hf where E is energy and h is Planck’s constant. • But f = c/λ • Putting these equations together, we see that E = hc/λ
- 9. Electromagnetic Wave VelocityElectromagnetic Wave Velocity • The speed of light is the same for all seven forms of light. • It is 300,000,000 meters per second or 186,000 miles per second.
- 10. The Electromagnetic SpectrumThe 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
- 12. The Multi-Wavelength Sun X-Ray UV Visible Infrared Radio Composite
- 13. EM Spectrum Relative Sizes
- 14. The Visible SpectrumThe Visible Spectrum Light waves extend in wavelength from about 400 to 700 nanometers.
- 15. Transparent MaterialsTransparent Materials Transparent - the term applied to materials through which light can pass in straight lines.
- 16. Opaque MaterialsOpaque Materials Opaque - the term applied to materials that absorb light.
- 17. • Are clouds transparent or opaque to visible light? – Answer: opaque • Are clouds transparent or opaque to ultraviolet light? – Answer: almost transparent
- 18. Special Things About a Light Wave • It does not need a medium through which to travel • It travels with its highest velocity in a vacuum • Its highest velocity is the speed of light, c, equal to 300,000 km/sec • The frequency (or wavelength) of the wave determines whether we call it radio, infrared, visible, ultraviolet, X-ray or gamma-ray.
- 19. Camera Obscura, Gemma Frisius, 1558 1544A Brief History of Images
- 20. http://www.acmi.net.au/AIC/CAMERA_OBSCURA.html (Russell Naughton) Camera Obscura "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". Da Vinci Slide credit: David Jacobs
- 21. Lens Based Camera Obscura, 1568 1558 1568 A Brief History of Images
- 22. http://brightbytes.com/cosite/collection2.html (Jack and Beverly Wilgus) Jetty at Margate England, 1898. Slide credit: David Jacobs
- 23. Still Life, Louis Jaques Mande Daguerre, 1837 1558 1837 1568 A Brief History of Images
- 24. Abraham Lincoln? 1558 1840? 1568 A Brief History of Images
- 25. Silicon Image Detector, 1970 1558 1837 1568 1970 A Brief History of Images
- 26. 1558 1837 1568 1970 1995 A Brief History of Images Digital Cameras
- 27. 1558 1837 1568 1970 1995 A Brief History of Images Hasselblad HD2-39 2006
- 28. Geometric Optics and Image Formation TOPICS TO BE COVERED : 1) Pinhole and Perspective Projection 2) Image Formation using Lenses 3) Lens related issues
- 29. Pinhole Cameras • Pinhole camera - box with a small hole in it • Image is upside down, but not mirrored left-to-right • Question: Why does a mirror reverse left-to-right but not top-to-bottom?
- 30. Pinhole and the Perspective Projection (x,y) screen scene Is an image being formed on the screen? YES! But, not a “clear” one. image plane effective focal length, f’optical axis y x z pinhole ),,( zyx=r z y f y z x f x == ' ' ' ' zf rr = ' ' )',','(' fyx=r
- 31. Magnification image plane f’optical axis y x z Pinhole planar scene A B A’ B’ d d’ z yy f yy z xx f xx z y f y z x f x δδδδ + = ++ = + == ' '' ' '' ' ' ' ' From perspective projection: Magnification: z f yx yx d d m ' )()( )'()'(' 22 22 = + + == δδ δδ ),,( ),,( zyyxxB zyxA δδ ++ )','',''(' )',','(' fyyxxB fyxA δδ ++ 2 m Area Area scene image =
- 32. Properties of Projection • Points project to points • Lines project to lines • Planes project to the whole or half image • Angles are not preserved • Degenerate cases – Line through focal point projects to a point. – Plane through focal point projects to line
- 33. Distant Objects are Smaller Note that B’ and C’ labels should be switched. Size is inversely proportional to distance.
- 34. Parallel Lines Meet Common to draw film plane in front of the focal point. Moving the film plane merely scales the image.
- 35. Vanishing Points • Each set of parallel lines 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.
- 37. Model 0: Pinhole Projection
- 38. The Equation of Pinhole Projection • Cartesian coordinates: – We have, by similar triangles, that (x, y, z) -> (f x/z, f y/z, f) [multiply by f/z] – Ignore the third coordinate, and get (x,y,z)→(f x z ,f y z ) 3D object point 2D image point
- 39. Model 1: Weak Perspective Projection • Issue – Perspective effects, but not over the scale of individual objects – Collect points into a group at about the same depth, then divide each point by the depth of its group – Advantage: EASY – Disadvantage: WRONG
- 40. The Equation of Weak Perspective ),(),,( yxszyx → • s is constant for all points. • Parallel lines no longer converge, they remain parallel. Slide credit: David Jacobs
- 41. Model 2: Orthographic Projection image plane optical axis y x z ),,( zyx=r )',','(' fyx=r z z∆ xmx =' ymy ='Magnification: When m = 1, we have orthographic projection This is possible only when zz ∆>> In other words, the range of scene depths is assumed to be much smaller than the average scene depth. But, how do we produce non-inverted images?
- 42. Pros and Cons of These Models • Weak perspective has simpler math. – Accurate when object is small and distant. – Most useful for recognition. • Pinhole perspective much more accurate for scenes. – Used in structure from motion. • When accuracy really matters, we must model the real camera – Use perspective projection with other calibration parameters (e.g., radial lens distortion) Slide credit: David Jacobs
- 43. 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 Example: If f’ = 50mm, = 600nm (red), d = 0.36mm λ'2 fd = λ
- 44. The Reason for Lenses
- 45. Image Formation using (Thin) Lenses • Lenses are used to avoid problems with pinholes. • Ideal Lens: Same projection as pinhole but gathers more light! i o foi 111 =+Gaussian Lens Formula: • f is the focal length of the lens – determines the lens’s ability to bend (refract) light • f different from the effective focal length f’ discussed before! P P’ f
- 46. Focus and Defocus foi 111 =+ Depth of Field: Range of object distances over which image is sufficiently well focused, i.e., range for which blur circle is less than the resolution of the imaging sensor. d aperture diameter aperture foi 1 ' 1 ' 1 =+Gaussian Law: Blur Circle, b )'( )()'( )'( oo fo f fo f ii − −− =− Blur Circle Diameter : )'( ' ii i d b −= i 'i o 'o
- 47. Problems with Lenses Compound (Thick) Lens Vignetting Chromatic Abberation Radial and Tangential Distortion thickness principal planes nodal points α α 1L2L3L B A more light from A than B ! RF BF GF Lens has different refractive indices for different wavelengths. image plane ideal actual ideal actual
- 48. Spherical Aberration Spherical lenses are the only easy shape to manufacture, but are not correct for perfect focus.
- 49. Two Lens System • Rule : Image formed by first lens is the object for the second lens. • Main Rays : Ray passing through focus emerges parallel to optical axis. Ray through optical center passes un-deviated. image plane lens 2 lens 1 object intermediate virtual image 1i 1o 2i 2o2f 1f final image d • Magnification: 1 1 2 2 o i o i m = Exercises: What is the combined focal length of the system? What is the combined focal length if d = 0?
- 50. Lens systems • A good camera lens may contain 15 elements and cost a many thousand dollars • The best modern lenses may contain aspherical elements
- 51. Insect Eye We make cameras that act “similar” to the human eye Fly Mosquito
- 52. http://www.cas.vanderbilt.edu/bsci111b/eye/human-eye.jpg 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
- 53. Human Eye • Rods – Intensity only – Essentially night vision and peripheral vision only – Since we are trying to fool the center of field of view of human eye (under well lit conditions) we ignore rods
- 54. Human Eye • Cones – Three types perceive different portions of the visible light spectrum
- 55. Human Eye • Because there are only 3 types of cones in human eyes, we only need 3 stimulus values to fool the human eye – Note: Chickens have 4 types of cones
- 56. Human Eye vs. the Camera • We make cameras that act “similar” to the human eye
Editor's Notes
- #30: The point to make here is that each point on the image plane sees light from only one direction, the one that passes through the pinhole.