CAP 5415 Computer Vision
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1 CAP 545 Computer Vision Dr. Mubarak Sa Univ. o Central Florida
2 Filtering Lecture-2
3 Contents Filtering/Smooting/Removing Noise Convolution/Correlation Image Derivatives Histogram Some Matlab Functions
4 General Binary Gray Scale Color
5 Binary Images Y Row X q : Black : Wite Row q p
6 Gray Level Image 5 9
7 Gray Scale Image
8 Color Image Red, Green, Blue Cannels
9 Image Histogram
10 Image Noise Ligt Variations Camera Electronics Surace Relectance Lens
11 Image Noise I,y) : te true piel values n,y) : te noise at piel,y) I ˆ,, y I, y n y
12 Gaussian Noise n n 2, y e 2 2 Probability Distribution n is a random variable
13 Image Derivatives & Averages
14 Deinitions Derivative: Rate o cange Speed is a rate o cange o a distance Acceleration is a rate o cange o speed Average Mean) Dividing te sum o N values by N
15 Derivative d d lim ) ) ) v ds dt speed a dv dt acceleration
16 Eamples y dy d y dy d sin cos e ) e
17 Discrete Derivative ) ) ) lim d d ) ) ) d d ) ) ) d d
18 Discrete Derivative Finite Dierence d d ) ) ) Backward dierence d d ) ) ) Forward dierence d d ) ) ) Central dierence
19 Eample ) ) ) Derivative Masks Backward dierence Forward dierence Central dierence [- ] [ -] [- ]
20 Derivatives in 2 Dimensions ), y Given unction y y y y y ), ), ), Gradient vector 2 2 ), y y Gradient magnitude y tan Gradient direction
21 Derivatives o Images 3 Derivative masks 3 y I I
22 Derivatives o Images I y I
23 Correlation k l l k l k,, Kernel Image *
24 Convolution k, l k l *, k l Image X lip Kernel Y lip *
25 Convolution,) ),,) ),,) ),,) ),,) ),,) ), ), ), ), ), ), ), ), y y y y y y y y y y ), ), i j j i i y i -,,, -,,, -,-,-,- Coordinates
26 Correlation and Convolution Convolution is associative F * G * I ) F * G) * I
27 Averages Mean n I n I I I I n i i n 2 Weigted mean n w I n I w I w w I I n i i i n n 2 2
28 Gaussian Filter g ) e g y 2 2, y) e 2 2 g )
29 Properties o Gaussian Most common natural model Smoot unction, it as ininite number o derivatives Fourier Transorm o Gaussian is Gaussian. Convolution o a Gaussian wit itsel is a Gaussian. Tere are cells in eye tat perorm Gaussian iltering.
30 Filtering Modiy piels based on some unction o te neigborood p 5.7 Alper Yilmaz, Mubarak Sa, UCF
31 Linear Filtering Te output is te linear combination o te neigborood piels = Image Kernel Filter Output Alper Yilmaz, Mubarak Sa, UCF
32 Filtering Eamples * Alper Yilmaz, Mubarak Sa, UCF
33 Filtering Eamples * Alper Yilmaz, Mubarak Sa, UCF
34 Filtering Eamples * 9 Alper Yilmaz, Mubarak Sa, UCF
35 Filtering Eamples * 25 Alper Yilmaz, Mubarak Sa, UCF
36 Blurring Eamples original Filter iltered original Filter iltered
37 Filtering Gaussian * Alper Yilmaz, Mubarak Sa, UCF
38 Gaussian vs. Smooting Gaussian Smooting Smooting by Averaging Alper Yilmaz, Mubarak Sa, UCF
39 Noise Filtering Ater Averaging Gaussian Noise Ater Gaussian Smooting Alper Yilmaz, Mubarak Sa, UCF
40 MATLAB Functions conv: -D Convolution. C = conva, B) convolves vectors A and B. conv2: Two dimensional convolution. C = conv2a, B) perorms te 2-D convolution o matrices A and B.
41 MATLAB Functions ilter2: Two-dimensional digital ilter. Y = ilter2b,x) ilters te data in X wit te 2-D ilter in te matri B. Te result, Y, is computed using 2-D correlation and is te same size as X. ilter2 uses CONV2 to do most o te work. 2- D correlation is related to 2-D convolution by a 8 degree rotation o te ilter matri.
42 MATLAB Functions gradient: Approimate gradient. [FX,FY] = gradientf) returns te numerical gradient o te matri F. FX corresponds to df/d, FY corresponds to df/dy. mean: Average or mean value. For vectors, meanx) is te mean value average) o te elements in X.
43 MATLAB Functions special: Create predeined 2-D ilters H = specialtype) creates a two-dimensional ilter H o te speciied type. Possible values or TYPE are: 'average' averaging ilter; 'gaussian' Gaussian lowpass ilter 'laplacian' ilter approimating te 2-D Laplacian operator 'log' Laplacian o Gaussian ilter 'prewitt' Prewitt orizontal edge-empasizing ilter 'sobel' Sobel orizontal edge-empasizing ilter Eample: H=special'gaussian',7,) creates a 77 Gaussian ilter wit variance.
44 Reading Material Mubarak Sa, "Fundamentals o Computer Vision". Capter, 2 Ricard Szeliski, "Computer Vision: Algoritms and Application". Section 3. and 3.2
CAP 5415 Computer Vision Fall 2011
CAP 545 Computer Vision Fall 2 Dr. Mubarak Sa Univ. o Central Florida www.cs.uc.edu/~vision/courses/cap545/all22 Oice 247-F HEC Filtering Lecture-2 General Binary Gray Scale Color Binary Images Y Row X
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