像素和过滤

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#信息技术

本章节主要介绍了计算机视觉的像素以及过滤方面的有关知识，图像包含了各种不连续的像素，介绍了像素的过滤，什么是计算机视觉的过滤，怎么进行图像的过滤，以及通过视觉的过滤我们可以得到什么，与原来的视觉图形有什么区别等。

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1 . Lecture 4: Pixels and Filters Professor Fei-‐Fei Li Stanford Vision Lab Fei-Fei Li! Lecture 4- ! 1 30-‐Sep-‐14

2 . What we will learn today? •  Images as funcEons •  Linear systems (ﬁlters) •  ConvoluEon and correlaEon Some background reading: Forsyth and Ponce, Computer Vision, Chapter 7 Fei-Fei Li! Lecture 4- ! 2 30-‐Sep-‐14

3 . Images as func,ons •  An image contains discrete number of pixels –  A simple example 75 –  Pixel value: •  “grayscale” (or “intensity”): [0,255] 231 148 Fei-Fei Li! Lecture 4- ! 3 2010.12.18

4 . Images as func,ons •  An image contains discrete number of pixels –  A simple example [90, 0, 53] –  Pixel value: •  “grayscale” (or “intensity”): [0,255] •  “color” –  RGB: [R, G, B] [249, 215, 203] –  Lab: [L, a, b] –  HSV: [H, S, V] [213, 60, 67] Fei-Fei Li! Lecture 4- ! 4 2010.12.18

5 . Images as func,ons •  An Image as a funcEon f from R2 to RM: •  f( x, y ) gives the intensity at posiEon ( x, y ) •  Deﬁned over a rectangle, with a ﬁnite range: f: [a,b] x [c,d ] à [0,255] Domain range support Fei-Fei Li! Lecture 4- ! 5 30-‐Sep-‐14

6 . Images as func,ons •  An Image as a funcEon f from R2 to RM: •  f( x, y ) gives the intensity at posiEon ( x, y ) •  Deﬁned over a rectangle, with a ﬁnite range: f: [a,b] x [c,d ] à [0,255] Domain range support ⎡ r ( x, y ) ⎤ •  A color image: f ( x, y ) = ⎢⎢ g ( x, y ) ⎥⎥ ⎢⎣ b( x, y ) ⎥⎦ Fei-Fei Li! Lecture 4- ! 6 30-‐Sep-‐14

7 . Images as discrete func,ons •  Images are usually digital (discrete): –  Sample the 2D space on a regular grid •  Represented as a matrix of integer values pixel Fei-Fei Li! Lecture 4- ! 7 30-‐Sep-‐14

8 . Images as discrete func,ons Cartesian coordinates NotaEon for discrete funcEons Fei-Fei Li! Lecture 4- ! 8 30-‐Sep-‐14

9 . What we will learn today? •  Images as funcEons •  Linear systems (ﬁlters) •  ConvoluEon and correlaEon Some background reading: Forsyth and Ponce, Computer Vision, Chapter 7 Fei-Fei Li! Lecture 4- ! 9 30-‐Sep-‐14

10 . Systems and Filters •  Filtering: –  Form a new image whose pixels are a combinaEon original pixel values Goals: -‐ Extract useful informaEon from the images •  Features (edges, corners, blobs…) -‐ Modify or enhance image properEes: •  super-‐resoluEon; in-‐painEng; de-‐noising Fei-Fei Li! Lecture 4- ! 10 30-‐Sep-‐14

11 . Super-‐resoluEon De-‐noising In-‐painEng Bertamio et al Fei-Fei Li! Lecture 4- ! 11 30-‐Sep-‐14

12 . 2D discrete-‐space systems (ﬁlters) Fei-Fei Li! Lecture 4- ! 12 30-‐Sep-‐14

13 . Filter example #1: Moving Average •  2D DS moving average over a 3 × 3 window of neighborhood h 1 1 1 1 1 1 1 1 1 1 ( f ∗ h)[m, n] = ∑ f [k , l ] h[m − k , n − l ] 9 k ,l Fei-Fei Li! Lecture 4- ! 13 30-‐Sep-‐14

14 . Filter example #1: Moving Average 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 0 0 0 90 90 0 0 90 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 90 90 90 90 90 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Courtesy of S. Seitz 0 0 0 0 90 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ( f ∗ h)[m, n] = ∑ f [k, l] h[m − k, n − l] k,l Fei-Fei Li! Lecture 4- ! 14 30-‐Sep-‐14

15 . Filter example #1: Moving Average 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 0 0 0 90 90 90 90 90 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 90 0 90 90 90 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ( f ∗ h)[m, n] = ∑ f [k, l] h[m − k, n − l] k,l 15 Fei-Fei Li! Lecture 4- ! 15 1-‐Oct-‐14

16 . Filter example #1: Moving Average 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 20 0 0 0 90 90 90 90 90 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 90 0 90 90 90 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ( f ∗ h)[m, n] = ∑ f [k, l] h[m − k, n − l] k,l Fei-Fei Li! Lecture 4- ! 16 1-‐Oct-‐14

17 . Filter example #1: Moving Average 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 20 30 0 0 0 90 90 90 90 90 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 90 0 90 90 90 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ( f ∗ h)[m, n] = ∑ f [k, l] h[m − k, n − l] k,l Fei-Fei Li! Lecture 4- ! 17 1-‐Oct-‐14

18 . Filter example #1: Moving Average 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 20 30 30 0 0 0 90 90 90 90 90 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 90 0 90 90 90 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ( f ∗ h)[m, n] = ∑ f [k, l] h[m − k, n − l] k,l Fei-Fei Li! Lecture 4- ! 18 1-‐Oct-‐14

19 . Filter example #1: Moving Average 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 20 30 30 30 20 10 0 0 0 90 90 90 90 90 0 0 0 20 40 60 60 60 40 20 0 0 0 90 90 90 90 90 0 0 0 30 60 90 90 90 60 30 0 0 0 90 90 90 90 90 0 0 0 30 50 80 80 90 60 30 0 0 0 90 0 90 90 90 0 0 0 30 50 80 80 90 60 30 0 0 0 90 90 90 90 90 0 0 0 20 30 50 50 60 40 20 0 0 0 0 0 0 0 0 0 0 10 20 30 30 30 30 20 10 0 0 90 0 0 0 0 0 0 0 10 10 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ( f ∗ h)[m, n] = ∑ f [k, l] h[m − k, n − l] k,l Source: S. Seitz Fei-Fei Li! Lecture 4- ! 19 1-‐Oct-‐14

20 . Filter example #1: Moving Average h[⋅ ,⋅ ] In summary: •  Replaces each pixel 1 1 1 with an average of its 1 1 1 neighborhood. 1 1 1 •  Achieve smoothing eﬀect (remove sharp features) Fei-Fei Li! Lecture 4- ! 20 30-‐Sep-‐14

21 . Filter example #1: Moving Average Fei-Fei Li! Lecture 4- ! 21 30-‐Sep-‐14

22 . Filter example #2: Image SegmentaEon •  Image segmentaEon based on a simple threshold: 255, Fei-Fei Li! Lecture 4- ! 22 30-‐Sep-‐14

23 . ClassiﬁcaEon of systems • Amplitude properEes • Linearity • Stability • InverEbility • SpaEal properEes • Causality • Separability • Memory • Shii invariance • RotaEon invariance Fei-Fei Li! Lecture 4- ! 23 30-‐Sep-‐14

24 . Shii-‐invariance If then for every input image f[n,m] and shiis n0,m0 Fei-Fei Li! Lecture 4- ! 24 30-‐Sep-‐14

25 . Is the moving average system is shii invariant? 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 20 30 30 30 20 10 0 0 0 90 90 90 90 90 0 0 0 20 40 60 60 60 40 20 0 0 0 90 90 90 90 90 0 0 0 30 60 90 90 90 60 30 0 0 0 90 90 90 90 90 0 0 0 30 50 80 80 90 60 30 0 0 0 90 0 90 90 90 0 0 0 30 50 80 80 90 60 30 0 0 0 90 90 90 90 90 0 0 0 20 30 50 50 60 40 20 0 0 0 0 0 0 0 0 0 0 10 20 30 30 30 30 20 10 0 0 90 0 0 0 0 0 0 0 10 10 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Fei-Fei Li! Lecture 4- ! 25 30-‐Sep-‐14

26 . Is the moving average system is shii invariant? Yes! Fei-Fei Li! Lecture 4- ! 26 30-‐Sep-‐14

27 . Linear Systems (ﬁlters) •  Linear ﬁltering: –  Form a new image whose pixels are a weighted sum of original pixel values –  Use the same set of weights at each point •  S is a linear system (funcEon) iﬀ it S sa&sﬁes superposiEon property Fei-Fei Li! Lecture 4- ! 27 30-‐Sep-‐14

28 . Linear Systems (ﬁlters) •  Is the moving average a linear system? •  Is thresholding a linear system? –  f1[n,m] + f2[n,m] > T –  f1[n,m] < T –  f2[n,m]<T No! Fei-Fei Li! Lecture 4- ! 28 30-‐Sep-‐14

29 . LSI (linear shi$ invariant) systems Impulse response Fei-Fei Li! Lecture 4- ! 29 30-‐Sep-‐14

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