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Image Enhancement

Image Enhancement. Antal Nagy Department of Image Processing and Computer Graphics University of Szeged. Syllabus. Human perception Image degradation Convolution, Furier Transform Noise Image operations Frequency filters Spatial filtering Inverse filtering Wiener filtering.

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Image Enhancement

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  1. Image Enhancement Antal Nagy Department of Image Processing and Computer Graphics University of Szeged 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  2. Syllabus • Human perception • Image degradation • Convolution, Furier Transform • Noise • Image operations • Frequency filters • Spatial filtering • Inverse filtering • Wiener filtering 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  3. Image Enhancement • Aim • to improve the perception of information images • for human viewers • to provide ‘better’ input • for other automated image processing techniques 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  4. Human perception • No general theory for determining what is good image enhancement • If it looks good, it is good!? 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  5. Mach Band Effect 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  6. Optical Dissillusion 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  7. Photoshopretouch • http://www.youtube.com/watch?v=_d_l5nsnIvM 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  8. Pre-processing tool • Focus • Noise reduction techniques • Quantitative measures can determine which techniques are most appropriate • How does it improve e.g. the result of the next automated image processing step? • E.g. image segmentation 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  9. Image acquisition • The first stage of any vision system • Can we do it in perfect way? • Sometimes yes • Industrial applications • Ideal background • Ideal lighting • Faultless camera • Sometimes not • Industrial applications • Despite of supreme conditions we got degraded image • Accumulation of the faults of the electrical components • Physical phenomena • E.t.c. • Medical image acqusition 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  10. Image Degradation • Non-linear mapping • E.g., non-linear sensitivity, image of the straight line is not straight e.t.c. • Blurring • Image of a point is blob • Moving during the image acquisition • Probabilistic noise 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  11. Image Degradation/RestorationModel Spatial domain Frequency domain 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  12. Convolution Theorem • Multiplication point by point 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  13. ExampleforConvolutionTheorem Convolution = * Inverse Fourier transf. Fourier transf. · = Multiplication 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  14. Spatial Domain - Convolution Definition 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  15. Properties of theConvolution 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  16. x x x ExampleforConvolution - Smoothing 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  17. FrequencyAnalysis • Even functions that are not periodic can be expressed as the integrals of sines and/or cosines multiplied by a weighting function. • The formulation in this case is the Fourier transform. ∑ = 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  18. Jean-Baptiste Joseph Fourier1768-1830 Taught mathematics in Paris Eventually traveled to Egypt with Napoleon to become the secretary of the Institute of Egypt After fall of Napoleon worked at Bureau of Statistics Elected to National Academy of Sciences in 1817 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  19. Fourier Transform (1D) (continous) (inverstransform) base-functions 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  20. Fourier Transform (2D) (inverstransform) base-functions 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  21. BaseFunctions u=-2, v=2 u=-1, v=2 u=0, v=2 u=1, v=2 u=2, v=2 u=-2, v=1 u=-1, v=1 u=0, v=1 u=1, v=1 u=2, v=1 u u=0, v=0 u=-2, v=0 u=-1, v=0 u=1, v=0 u=2, v=0 wavelength: u=-2, v=-1 u=-1, v=-1 u=0, v=-1 u=1, v=-1 u=2, v=-1 u=-2, v=-2 u=-1, v=-2 u=0, v=-2 u=1, v=-2 u=2, v=-2 v 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  22. Properties of the Fourier Transform • F(0,0) -value is by far the largest component of the image, • Other frequency components are usually much smaller, • The magnitude of F(X,Y) decreases quickly • Instead of displaying the |F(u,v)| we displaylog( 1 + |F(u,v)| )real function usually 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  23. Examplefor Fourier Transform y u v x 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  24. Properties of the Fourier Transform • The 2D Fourier transform can be separated • The edges on the image appears as point series in perpendicular direction in Fourier transform of the image and vice versa. 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  25. Properties of the Fourier Transform Image-space Frequencyspace original rotation linearity shift scale 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  26. Noiseonly • Noise unknown  subtraction not possible • Periodic noise • N(u,v) can be estimated from G(u,v) 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  27. SomeImportantNoiseModels • Exponential and gamma • Laser imaging • Impulse • Faulty switching • Uniform density • Practical situations 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary • Gaussian • In an image due to factors • Electronic circuit noise • Sensor noise due to • poor illumination • High temperature • Rayleigh • Range imaging

  28. ProbabilityDensityFunctions 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  29. ProbabilityDensityFunctions 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  30. ProbabilityDensityFunctions 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  31. Examples 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  32. Examples 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  33. PeriodicNoise • Electrical and electromechanical interference • Spatial dependent noise • Can be reduced via frequency domain filtering • Pair of impulses 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  34. Image Operation T: A=[a(i,j)] → B=[b(i,j)] b(i,j)=T{a(i,j), S(i,j), i, j} enviroment position intensity 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  35. Classification of the Image Operations • Global:b(i,j)=T{A} (S(i,j)=A)(e.g. Fourier-transformation) • Local: T{a(i,j), S} given size of S and independent from the position (e.g. convolution with a mask) • Local, adaptive:T{a(i,j), S(i,j), i, j} the size of S(i,j) is independent from the size of image (e.g. adaptive thresholding) • Point operation: T{a(i,j)} (e.g. gamma-correction, histogram-equalization) 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  36. Frequency Filtering – SmoothingIdealLowpass Filter D0: cutoff frequency All frequencies less thanD0 will be passed, Other frequencies will be filtered out. Bluring and ringing properties Scope: noise filtering 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  37. Example of IdealLowPass Filter F . Input image F-1 Frequency-mask 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  38. Example of IdealLowPass Filter Cutoff frequencies 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  39. Frequency Filtering – SmoothingButterworthLowpass Filter • n: order of the filter • Properties: • Smooth transition in blurring • No ring effect (continouos filter) • Smoothed edges 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  40. Example of Butterworth Filter Cutofffrequencies 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  41. Frequency Filtering – SmoothingGaussian Lowpass Filter 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  42. Example of Gaussian Lowpass Filter Cutofffrequencies 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  43. Low and Highpass Filter Pairs 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  44. Example of IdealHighpass Filter 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  45. SelectiveFiltering • Bandreject and Bandpass Filters • Notch Filters • Rejects or passes frequencies in a predefined neighborhood about the frequency rectangle • Zero-phase-shift filters • Symmetric about the origin • (u0,v0)  (-u0,-v0) • Product of highpass filters whose centers have been translated to the centers of the notches. 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  46. Example of IdealBandreject Filter noisyimage frequencyimage 0 frequencymask filteredimage 1 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  47. Example of Notch Filter 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  48. SpatialFiltering • Mean Filter where g input image, S(x,y)neighborhood of (s,t) point, mnnumber of pixels in neighborhood. 3x3 neighborhood 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  49. MeanFilteringbyConvolution 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

  50. FilteringwithWeightedAverage of Neighborhood • Averaging • same weight for every pixels in neighborhood, • Weighted average • weights for pixels in the neighborhood (generally decreasing with the distance). • The sum of the Noise Filtering/smoothing masks elements is 1! 17th SSIP 2009, 2 - 11 July, Debrecen, Hungary

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