CS计算机代考程序代写 2/9/2021

2/9/2021
CSE 573/473
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Introduction to Computer Vision and Image Processing
1
Questions from Last Class?
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2
1

2/9/2021
Projection matrix
Extrinsic Assumptions • No rotation
• Camera at (0,0,0)
Intrinsic Assumptions • Optical center at (0,0)
• Unit aspect ratio • No skew
𝐱􏰉𝐊𝐈 𝟎 𝐗
Slide Credit: Savarese
X
x ‘-
u f 0 0 0x wv0 f 0 0y
1 0 0 1 0z   1

3
Remove assumption: known optical center
Extrinsic Assumptions • No rotation
• Camera at (0,0,0)
Intrinsic Assumptions • Optical center at (0,0)
• Unit aspect ratio • No skew
𝐱􏰉𝐊𝐈 𝟎 𝐗
‘-
u f 0 u 0x   0 y
wv  0 f v0 0z
1 0 0 1 0   1

4
2

2/9/2021
Remove assumption: square pixels
Extrinsic Assumptions • No rotation
• Camera at (0,0,0)
Intrinsic Assumptions • Optical center at (0,0)
• Unit aspect ratio • No skew
𝐱􏰉𝐊𝐈 𝟎 𝐗
X
x ‘-
u  0 u 0x   0 y
wv  0  v0 0z
1 0 0 1 0   1

5
Remove assumption: non-skewed pixels
Extrinsic Assumptions • No rotation
• Camera at (0,0,0)
Intrinsic Assumptions • Optical center at (0,0)
• Unit aspect ratio • No skew
𝐱􏰉𝐊𝐈 𝟎 𝐗
Note: different books use different notation for parameters
‘-
u  s u 0x   0 y
wv  0  v0 0z
1 0 0 1 0   1

6
3

2/9/2021
Derive S? Given….
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𝐱􏰉𝐊𝐈 𝟎 𝐗
u  s u 0x   0 y
wv  0  v0 0z
1 0 0 1 0   1

7
Degrees of freedom
xKR tX
3 Extrinsic Rotation
2 Intrinsic Translation 2 Non-square pixels 1 Skew
3 Extrinsic Translation
5 6 ‘-
u  s ur r r tx
  011 12 13 xy wv0  v r r r t 
0 21 22 23 yz
1 0 0 1r r r t   31 32 33 z1

12
4

2/9/2021
Weak perspective
• Approximation: treat magnification as constant • Assumes scene depth << average distance to camera Image plane ‘- World points: 13 Orthographic projection • Given camera at constant distance from scene • World points projected along rays parallel to optical access ‘- 14 5 2/9/2021 2D Planer Transformation ‘- 15 2D ‘- 16 6 2/9/2021 3D ‘- 17 line Things to remember Vanishing Vertical vanishing point (at infinity) Vanishing point • Vanishing points and vanishing lines • Pinhole camera model and camera projection matrix • Homogeneous coordinates Vanishing point ‘- xKR tX 18 7 2/9/2021 Other types of projection • Lots of intriguing variants... ‘- S. Seitz 19 360 degree field of view... • Basic approach • Takeaphotoofaparabolicmirrorwithanorthographiclens(Nayar) • Orbuyonealensfromavarietyofomnicammanufacturers... ‐ See http://www.cis.upenn.edu/~kostas/omni.html ‘- 20 S. Seitz 8 2/9/2021 Tilt-shift http://www.northlight-images.co.uk/article_pages/tilt_and_shift_ts-e.html ‘- Titlt-shift images from Olivo Barbieri and Photoshop imitations 21 S. Seitz tilt, shift ‘- http://en.wikipedia.org/wiki/Tilt-shift_photography 22 9 2/9/2021 Tilt-shift perspective correction ‘- http://en.wikipedia.org/wiki/Tilt-shift_photography 23 normal lens tilt-shift lens ‘- http://www.northlight-images.co.uk/article_pages/tilt_and_shift_ts- e.html 24 10 2/9/2021 Rotating sensor (or object) ‘- Rollout Photographs © Justin Kerr http://research.famsi.org/kerrmaya.html Also known as “cyclographs”, “peripheral images” 25 S. Seitz Photofinish ‘- 26 S. Seitz 11 2/9/2021 IMAGE FORMATION IMAGE PROCESSING ‘- 27 Creating an Image... Lets Drill Down... Digital Camera Image Processing Image Processing ‘- SCENE 28 12 2/9/2021 Physical parameters of image formation • Geometric • Type of projection • Camera pose • Optical ‘- • Sensor’s lens type • focal length, field of view, aperture • Photometric • Type, direction, intensity of light reaching sensor • Surfaces’ reflectance properties • Sensor • sampling, etc. 29 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’sthe“film”? – photoreceptor cells (rods and cones) in the retina ‘- 30 Slide by Steve Seitz 13 2/9/2021 Electromagnetic Spectrum ‘- Human Luminance Sensitivity Function 31 http://www.yorku.ca/eye/photopik.htm Visible Light Why do we see light of these wavelengths? 10000 C . ...because that’s where the ‘- 5000 C Sun radiates EM energy 0 400 700 1000 700 C 2000 3000 2000 C Visible Wavelength (nm) Region © Stephen E. Palmer, 2002 32 14 Energy 2/9/2021 Pinhole size / aperture How does the size of the aperture affect the image we’d get? ‘- Larger Smaller 33 K. Grauman Adding a lens focal point ‘- f • A lens focuses light onto the film – Rays passing through the center are not deviated – All parallel rays converge to one point on a plane located at the focal length f 34 Slide by Steve Seitz 15 2/9/2021 What are the physical benefits or challenges of adding lens? • Light Concentration • Change the Focus • Change the Depth of Field • Change of the Field of View • Vignetting • Aberration ‘- 35 Light Concentration ‘- focal point f 36 Slide by Steve Seitz 16 2/9/2021 Cameras with lenses optical center (Center Of Projection) F ‘- focal point • A lens focuses parallel rays onto a single focal point • Gather more light, while keeping focus; make pinhole perspective projection practical Thin lens Thin lens Left focus Lens diameter d 37 K. Grauman Right focus Focal length f Rays entering parallel on one side go through focus on other, and vice versa. In ideal case – all rays from P imaged at P’. 38 K. Grauman ‘- 17 2/9/2021 Thin lens equation uv 111 ‘- fuv • Any object point satisfying this equation is in focus 39 K. Grauman Focus and depth of field ‘- 40 Image credit: cambridgeincolour.com 18 2/9/2021 Focus and depth of field • Depth of field: distance between image planes where blur is tolerable Thin lens: scene points at distinct depths come ‘- (Real camera lens systems have greater depth of field.) 41 “circles of confusion” in focus at different image planes. Shapiro and Stockman Focus and depth of field • How does the aperture affect the depth of field? ‘- • A smaller aperture increases the range in which the object is approximately in focus Flower images from Wikipedia http://en.wikipedia.org/wiki/Depth_of_field Slide from S. Seitz 42 19 2/9/2021 Depth from focus ‘- Images from same point of view, different camera parameters 3d shape / depth estimates [figs from H. Jin and P. Favaro, 2002] 43 Field of view • Angular measure of portion of 3D space seen by the camera ‘- http://en.wikipedia.org/wiki/Angle_of_view 44 K. Grauman 20 2/9/2021 Field of view depends on focal length • As f gets smaller, image becomes more wide angle • more world points project onto the finite image plane • As f gets larger, image becomes more telescopic • smaller part of the world projects onto the finite image plane ‘- 45 from R. Duraiswami Field of view depends on focal length ‘- Smaller FOV = larger Focal Length 46 Slide by A. Efros 21 2/9/2021 Vignetting http://www.ptgui.com/examples/vigntutorial.html ‘- http://www.tlucretius.net/Photo/eHolga.html 47 Vignetting • “natural”: • “mechanical”: intrusion on optical path ‘- 48 22 2/9/2021 Chromatic aberration ‘- 49 Chromatic aberration ‘- 50 23 2/9/2021 Other Distortions ‘- 51 24