全面的图像滤波方面课件

1、,What is noise?,s = 1,3,5,Gaussian filter,s = 2,s = 4,Gaussian smoothing,p1,p2,p1,p1,p1,p2,P2,P1,G,Gx,Gaussian and its 2 derivatives,LOG operator,Local image characteristics based on: Scale Frequency Direction,q,Fourier basis,Spatial domain,Frequency domain,1/s 1/s,s s,Even (Symmetric),Odd (antisymm

2、etic),Gabor Filter Example,High frequency along axis,Lower frequency off-axis,Even lower frequency,Scale small compared to inverse frequency,s = 2 f = 1/6,Odd Gabor filter,First Derivative,Even Gabor filter,Laplacian,Separable, low-pass filter,Not-separable, approximated by A difference of Gaussians

3、. Output of convolution is Laplacian of image: Zero-crossings correspond to edges,Separable, output of convolution is gradient at scale s:,Gaussian,Derivatives of Gaussian,Directional Derivatives,Laplacian,Fourier Transform,F(g)(u,v) = component of image at frequency sqrt(u2+v2) in direction (u,v) T

4、ransform of Gaussian s is Gaussian 1/s,Output of convolution is magnitude of derivative in direction q. Filter is linear combination of derivatives in x and y,Steerability(可操控性),Generalization of property of derivatives: F is steerable if the rotated filter can be expressed as a linear combination o

5、f basis filters.,Gabor Filters,Compute the local contribution of frequency in the direction (kx,ky) at scale s. For s large compared to 1/f, even filters approximate 2nd derivative, odd filters approximate 1st derivative.,Special case of Gabor wavelets if s and f restricted to powers of 2,Gaussian Pyramids,Gaussian smooth image and subsample at each stage,Compute Laplacian by difference of Gaussian at each stage,Laplacian Pyramids,Scale-Space,Convert the image f(x,y) to a continuous funct