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Chapter 5 Neighborhood Processing

Chapter 5 Neighborhood Processing. Introduction Filters (LPF, HPF, Gaussian Filter, …) Region of interest processing. Basic Image Processing Operations. Neighborhood processing process the pixel with its neighbors Point operations process according to the pixel’s value alone.

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Chapter 5 Neighborhood Processing

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  1. Chapter 5Neighborhood Processing Introduction Filters (LPF, HPF, Gaussian Filter, …) Region of interest processing SCCS 476

  2. Basic Image Processing Operations • Neighborhood processing • process the pixel with its neighbors • Point operations • process according to the pixel’s value alone. SCCS 476

  3. Neighborhood Processing 3x3 Mask Output derives from multiplying all elements in the mask by corresponding elements in the neighborhood and adding together all these products. SCCS 476

  4. Filter • A rule or procedure for processing an image • Combination of mask and function • Goal: separating/attenuating a desired component of an observed image • Type: • Linear (function), Nonlinear (function) • Low-pass filter (LPF), High-pass filter (HPF), Band-pass filter (BPF) SCCS 476

  5. Steps of Linear Spatial Filtering • Position the mask over the current pixel. • Form all products of filter elements with the corresponding elements of the neighborhood. • Add all products. • Other names for mask: filter, mask, filter mask, kernel, template or window, etc. SCCS 476

  6. 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 Linear Spatial Filter: Example (1) 2 15 10 20 10 Average Filter 10 10 15 10 0 0 10 10 15 5 20 Find the output intensity of the blue pixel. SCCS 476

  7. Linear Spatial Filter: Example (2) 15 10 20 1/9 1/9 1/9 10 15 1/9 1/9 1/9 0 1/9 1/9 1/9 10 10 20 Multiply the number in the filter’s element with the corresponding pixel’s intensity. SCCS 476

  8. 15/9 + 10/9 + 20/9 + 0/9 + 10/9 + 15/9 + 20/9 + 10/9 + 10/9 = 12.22 Linear Spatial Filter: Example (3) 15/9 10/9 20/9 0/9 10/9 15/9 20/9 10/9 10/9 Output intensity of blue pixel = 12.22 Add all products for output. Spatial filtering is spatial convolution. SCCS 476

  9. Correlation • Sum of the product of mask and intensity on each point. SCCS 476

  10. 1 2 3 2 3 4 3 4 5 Example: Correlation (1) 10 20 10 15 5 5 10 15 10 0 Kernel 20 10 20 15 5 20 10 5 0 0 10 10 20 15 0 10 SCCS 476

  11. 101 +152 +103 +102 +203 +154 +53 +04 +05 = 225 Example: Correlation (2) 10 15 10 1 2 3 20 15 2 3 4 10 3 4 5 0 0 5 Multiply and sum all products. SCCS 476

  12. 1 2 3 2 3 4 3 4 5 Exercise: Correlation 0 0 0 0 0 0 0 0 0 0 Kernel 0 0 1 0 0 0 0 0 0 0 0 0 0 0 10 Find the correlation of the green kernel to the above image. SCCS 476

  13. Convolution • Sum of the response on each point SCCS 476

  14. 5 1 2 4 3 3 4 2 3 3 4 2 3 3 2 4 1 5 Example: Convolution (1) 10 20 10 15 5 5 10 15 10 0 Reverse Kernel!! 20 10 20 15 5 20 10 5 0 0 10 10 20 15 0 10 Kernel SCCS 476

  15. 105 +154 +103 +104 +203 +152 +53 +02 +01 = 285 Example: Convolution (2) 10 15 10 5 4 3 20 15 4 3 2 10 3 2 1 0 0 5 Multiply and sum all products. SCCS 476

  16. 1 2 3 2 3 4 3 4 5 Exercise: Convolution 0 0 0 0 0 0 0 0 0 0 Kernel 0 0 1 0 0 0 0 0 0 0 0 0 0 0 10 Find the convolution of the green kernel to the above image. SCCS 476

  17. 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 Notation • A linear filter is represented as a matrix, e.g., the 3 x 3 averaging filter. SCCS 476

  18. Notation (2) • Edges of the Image • There are a number of different approaches to dealing with this problem. • Ignore the edges: The mask is applied to all pixels except the edges and results in an output image that is smaller than the original. If the mask is very large, a significant amount of information may be lost. • Pad with zeros: We assume that all necessary values outside the image are zero. It will return an output image of the same size as the original, but may have the effect of introducing unwanted artifacts, e.g., edges, around the image. SCCS 476

  19. Filtering in MATLAB • Command: filter2 • Syntax: filter2(filter, image, shape); filter2(filter, image); • shape: • ‘same’: pad edge with zeros. Size unchanged. (default) • ‘valid’: apply mask only to inside pixel. Size smaller. • ‘full’: pad edge with zeros and applying the filter at all places on and around the image where the mask intersects the image matrix. Size larger. SCCS 476

  20. Filter Construction in MATLAB • Command: fspecial • Syntax: fspecial(type, parameter); fspecial(type); • type:type of the filter • ‘average’: average filter • ‘gaussian’ : Gaussian filter • ‘laplacian’ : Laplacian filter … • parameter: parameter of the filter (size, sigma, …). Default varies among filter. Try!!! SCCS 476

  21. Separable Filters • Some filters can be implemented by the successive application of two simple filters. SCCS 476

  22. Separable Filters (2) • Speed up the processing by filtering in one axis at a time. • working with 2D n x n matrix requires n2, O(n2), multiplications, and n2 – 1, O(n2), addition for each pixel. • working with 1D n x 1 matrix twice requires 2n, O(n), multiplications, and 2n – 2, O(n), additions for each pixel. SCCS 476

  23. Examples of Separable Filter • Average filter • Laplacian filter SCCS 476

  24. Filter on Frequency Domain • Low-pass filter (LPF): filter that allows only the low-frequency components and reduces or eliminates the high-frequency components. • E.g. Gaussian, average • High-pass filter (HPF): filter that allows only the high-frequency components and reduces or eliminates the low-frequency components. • E.g. Laplacian, Prewitt, Sobel SCCS 476

  25. Frequency Components • Spatial data (intensity) transformed by Fourier transform. • Simplified version: • high-frequency indicates the abrupt changes in intensity  edges. • low-frequency indicates the intensity smoothness  uniform region. SCCS 476

  26. 1 -2 1 -2 4 -2 1 -2 1 Example: HPF 10 20 10 15 5 5 10 15 10 0 20 10 20 15 5 Kernel 10 5 0 0 10 10 20 15 0 10 Input image SCCS 476

  27. Example: HPF (2) 10 20 10 15 5 5 0 20 -10 0 20 -40 25 15 5 10 5 -35 0 10 10 20 15 0 10 Filtered Image SCCS 476

  28. Computing Consideration • Filter may lead to the value outside [0,255] • Solution 1: Make negative values positive (use absolute value) good when there are few negative values and the negative values are close to zero • Solution 2: Clip values. Values larger than 255 become 255 and values less than 0 become 0.  not good if there are many values outside the range. • Solution 3: Scaling transformation. Rescale the range to [0,255] by pixel transform. Suppose gLand gH are the lowest and the highest values. SCCS 476

  29. Rescaling Intensity Rescaled value (y) 1. Map gL to 0. 255 2. Map gH to 255. 3. Interpolate for the remaining intensity. 0 Filtered value (x) gL gH SCCS 476

  30. Rescaling: MATLAB • Manual: >> gH = max(filtered_image(:)); >> gL = min(filtered_image(:)); >> scaled = (image – gmin)/(gmax – gmin); Note: No need to rescale to 255 because intensity range for double image is [0,1]. SCCS 476

  31. Rescaling: MATLAB (2) • Command: mat2gray • Syntax: mat2gray(double_image); What this command do? • scale the value in double_image to displayable value. Output is double type. • minimum value is mapped to 0. • maximum value is mapped to 1. SCCS 476

  32. Gaussian Filter • 1D Gaussian filter: • 2D Gaussian filter: http://www-mmdb.iai.uni-bonn.de/lehre/BIT/ss03_DSP_Vorlesung/matlab_demos/ http://upload.wikimedia.org/wikipedia/su/thumb/3/38/Gaussian-pdf.png/300px-Gaussian-pdf.png SCCS 476

  33. Benefits of Gaussian Filter • They are mathematically very well behaved. The Fourier transform of a Gaussian filter is another Gaussian. • There are rotationally symmetric, so are very good starting points for some edge-detection algorithms. • They are separable in x and y axes. This can lead to very fast implementations. • The convolution of two Gaussians is another Gaussian. SCCS 476

  34. Gaussian Filter (2) • Effect of Gaussian filter = blurring • larger leads to more blur. •  average filter • Construction of Gaussian filter: • command: fspecial(‘gaussian’, size, gamma); size : size of the filter [row column], default [3 3] gamma : , default 0.5. SCCS 476

  35. Gaussian Filter: MATLAB >>gaussian1 = fspecial(‘gaussian’, [5 5], 5); • Create the 55 Gaussian filter with the  value of 5. >>gaussian2 = fspecial(‘gaussian’, 3, 0.75);  Create the 33 Gaussian filter with the  value of 0.75. SCCS 476

  36. Effect of Gaussian Filter  = 0.5  = 2  = 5 Filter size = 5  5 SCCS 476

  37. Effect of Gaussian Filter (2) Filter size = 3  3 Filter size = 5  5  = 5 SCCS 476

  38. Edge Sharpening • Also known as edge enhancement, edge crispening, unsharp masking. • Process to make the edge slightly sharper and crisper. • E.g. linear edge sharpening, unsharp masking, high boost filtering SCCS 476

  39. Linear Edge Sharpening • High pass filter (HPF) • Increase the edge power • Example: SCCS 476

  40. Unsharp Masking Original Image Scale for Display Blurred with LPF Scale with a < 1 SCCS 476

  41. Unsharp Masking: MALAB >> f = fspecial(‘average’);  Create LPF (E.g. average filter) >> xf = filter2(f,x);  Filter input image x by average filter. >> xu = double(x) – xf/1.5;  Substract the low passed components. >> imshow (xu/70)  Scale intensity for better viewing. SCCS 476

  42. Unsharp Filter [unsharp_image] = [input] – (a[filter][input]) = (I*– a[filter])[input] = [unsharp_filter]  [input] I* : matrix whose center member is 1 and the others are zero. E.g. for 3  3 matrix I* = SCCS 476

  43. Unsharp Filter (2) • For 33 matrix, after some rearranging term: [unsharp_filter] = MATLAB use this format for the unsharp filter with the default  of 0.2. SCCS 476

  44. Unsharp Filter: MATLAB • Command: fspecial • Syntax: fspecial(‘unsharp’, alpha); • alpha: alpha value for unsharp filter • Size of the filter is fixed to 3  3 SCCS 476

  45. Effect of Unsharp Masking BEFORE AFTER http://ise.hansung.ac.kr/jun/DI/Chapter-5.htm SCCS 476

  46. High-Boost Filtering Original Image Scale with A>1 Scale for Display Blurred with LPF Amplification factor. A=1, high boost = HPF [high_boost] = A [input] – [low_passed] SCCS 476

  47. High Boost Filter (2) high_boost = A input – low_pass = Ainput – (input - high_pass) = (A – 1) input + high_pass Rescale high_boost by w. whigh_boost = w (A – 1) input + w high_pass Best result when w (A – 1) = 1.  w = 1/(A – 1) SCCS 476

  48. High Boost Filter (3) • General high boost filter: Another version: Best result when 3/5  A  5/6 • Used in dark image. • Boost the intensity of the original image. SCCS 476

  49. Effect of High Boost Filter AFTER BEFORE A = 5/6 SCCS 476

  50. Non-linear Filter • A non-linear filter is obtained by a nonlinear function of the grayscale values in the mask. • E.g. rank-order filters (minimum filter, maximum filter, median filter); the elements under the mask are ordered. • MATLAB command: nlfilter • A faster alternative: colfilt (rearranges the image into column) • Good for removing impulse-like noise • Better tradeoff between smoothing and retention of fine image details. SCCS 476

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