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# 06 spatial filtering DIP

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Digital image Processing

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### 06 spatial filtering DIP

1. 1. Spatial Filtering : 1 Spatial FilteringSpatial Filtering
2. 2. Spatial Filtering : 2 Basics of Spatial FilteringBasics of Spatial Filtering Image enhancement operations can also work with the values of the image pixels in the neighborhood and the corresponding values of a subimage that has the same dimensions as the neighborhood. The subimage is called a filter, mask, kernel, template, or window. The values in a filter subimage are referred to as coefficients, rather than pixels. The process consists simply of moving the filter mask from point to point in an image. For linear spatial filtering, the response is given by a sum of products of the filter coefficients and the corresponding image pixels in the area spanned by the filter mask
3. 3. Spatial Filtering : 3 Linear Spatial FilterLinear Spatial Filter
4. 4. Spatial Filtering : 4 Linear Spatial Filter (Cont.)Linear Spatial Filter (Cont.) The result (or response), R, of linear filtering with the filter mask at a point (x, y) in the image is: In general, linear filtering of an image f of size M X N with a filter mask of size m X n is given by the expression: ( 1, 1) ( 1, 1) ( 1,0) ( 1, ) (0,0) ( , ) (1,0) ( 1, ) (1,1) ( 1, 1) R w f x y w f x y w f x y w f x y w f x y = − − − − + − − + + + + + + + + L L ( 1)/2 ( 1)/2 ( 1)/2 ( 1)/2 ( , ) ( , ) ( , ) m n s m t n g x y w s t f x s y t − − =− − =− − = + +∑ ∑
5. 5. Spatial Filtering : 5 Linear Spatial Filter (Cont.)Linear Spatial Filter (Cont.) When interest lies on the response, R, of an m X n mask at any point (x, y), and not on the mechanics of implementing mask convolution 1 1 2 2 1 mn mn mn i i i R w z w z w z w z = = + + + = ∑ L
6. 6. Spatial Filtering : 6 Linear Spatial Filter (Cont.)Linear Spatial Filter (Cont.) 1 1 2 2 9 9 9 1 i i i R w z w z w z w z = = + + + = ∑ L
7. 7. Spatial Filtering : 7 Noise reduction by Spatial FilteringNoise reduction by Spatial Filtering Image averaging takes advantage of information redundancy from the individual images to reduce noise Not always possible to acquire so many images! Alternative option: Take advantage of information redundancy from different pixels within the same image to reduce noise
8. 8. Spatial Filtering : 8 Averaging FilterAveraging Filter Instead of averaging between images, we can average neighboring pixels 9 1 1 9 i i R z = = ∑
9. 9. Spatial Filtering : 9 Averaging FilterAveraging Filter
10. 10. Spatial Filtering : 10 Weighted Average FilterWeighted Average Filter Problem: Simple averaging of neighboring pixels lead to over-smoothing Possible solution: Instead of weighting all neighboring pixels equally, assign higher weights to pixels that are closer to the pixel being convolved
11. 11. Spatial Filtering : 11 Weighted Average FilterWeighted Average Filter
12. 12. Spatial Filtering : 12 Weighted Averaging Filter:Weighted Averaging Filter: ExampleExample
13. 13. Spatial Filtering : 13 Weighted Averaging Filter:Weighted Averaging Filter: ExampleExample
14. 14. Spatial Filtering : 14 Order-Statistic FiltersOrder-Statistic Filters Nonlinear spatial filters Steps Order pixels within an area Replace value of center pixel with value determined by ordering Best known example: median filters ( ) ( ) ( )H af bg aH f bH g+ ≠ +
15. 15. Spatial Filtering : 15 Median FilterMedian Filter Provides good noise reduction for certain types of noise such as impulse noise Considerably less blurring than weighted averaging filter Forces a pixel to be like its neighbors Steps Order pixels within an area Replace value of center pixel with median value (half of all pixels have intensities greater than or equal to the median value)
16. 16. Spatial Filtering : 16 Median Filter: ExampleMedian Filter: Example
17. 17. Spatial Filtering : 17 Median Filter: ExampleMedian Filter: Example
18. 18. Spatial Filtering : 18 Spatial Filtering: SharpeningSpatial Filtering: Sharpening Goal: highlight or enhance details in images Some applications: Photo enhancement Medical image visualization Industrial defect detection
19. 19. Spatial Filtering : 19 Sharpening Spatial FilteringSharpening Spatial Filtering Goal: highlight or enhance details in images Some applications: Photo enhancement Medical image visualization Industrial defect detection Basic principle: Averaging (blurring) is analogous to integration Therefore, logically, sharpening accomplished by differentiation
20. 20. Spatial Filtering : 20 Derivatives of digital functionDerivatives of digital function First-order derivative Second-order derivative ( 1) ( ) f f x f x x ∂ = + − ∂ 2 2 ( 1) ( 1) 2 ( ) f f x f x f x x ∂ = + + − − ∂
21. 21. Spatial Filtering : 21 Derivatives of digital functionDerivatives of digital function First-order derivatives generally produce thicker edges Second-order derivatives have stronger response to fine detail (e.g., thin lines and points) First-order derivatives have stronger response to step changes Second-order derivatives produce double response at step changes
22. 22. Spatial Filtering : 22 Derivatives of digital function:Derivatives of digital function: ExampleExample
23. 23. Spatial Filtering : 23 Derivatives of digital function:Derivatives of digital function: ExampleExample
24. 24. Spatial Filtering : 24 Sharpening using LaplacianSharpening using Laplacian Second-order derivatives is better suited for most applications for sharpening How? By constructing a filter based on discrete formulation of second- order derivatives Simplest isotropic derivative operator: Laplacian 2 2 2 2 2 f f f x y ∂ ∂ ∇ = + ∂ ∂
25. 25. Spatial Filtering : 25 How to create Laplacian filterHow to create Laplacian filter 2 2 2 2 2 f f f x y ∂ ∂ ∇ = + ∂ ∂ 2 2 ( 1, ) ( 1, ) 2 ( , ) f f x y f x y f x y x ∂ = + + − − ∂ 2 2 ( , 1) ( , 1) 2 ( , ) f f x y f x y f x y y ∂ = + + − − ∂ [ ]2 ( 1, ) ( 1, ) ( , 1) ( , 1) 4 ( , )f f x y f x y f x y f x y f x y∇ = + + − + + + − −
26. 26. Spatial Filtering : 26 Laplacian FilterLaplacian Filter
27. 27. Spatial Filtering : 27 Sharpening using LaplacianSharpening using Laplacian Problem: While applying Laplacian highlights fine detail, it de-emphasizes smooth regions (e.g., background features) Results in featureless background with grayish fine details Solution: Add original image to recover background features 2 2 ( , ) ( , ), negative filter center ( , ) ( , ) ( , ), positive filter center f x y f x y g x y f x y f x y  −∇ =  +∇
28. 28. Spatial Filtering : 28 ExampleExample
29. 29. Spatial Filtering : 29 Sharpening using Unsharp MaskingSharpening using Unsharp Masking Subtract blurred version of image from the image itself to produce sharp image ( , ) ( , ) ( , )g x y f x y f x y= −
30. 30. Spatial Filtering : 30 ExampleExample
31. 31. Spatial Filtering : 31 Sharpening using High-boostSharpening using High-boost FilteringFiltering Generalization of unsharp masking As A increases, contribution of sharpening decreases ( , ) ( , ) ( , )g x y Af x y f x y= −
32. 32. Spatial Filtering : 32 Sharpening using High-boostSharpening using High-boost FilteringFiltering
33. 33. Spatial Filtering : 33 Example
34. 34. Spatial Filtering : 34 First Derivatives for EnhancementFirst Derivatives for Enhancement Implemented as magnitude of gradient in image processing f x f f y ∂   ∂  ∇ = ∂   ∂  1/222 f f f x y   ∂ ∂  ∇ = +  ÷ ÷ ∂ ∂    
35. 35. Spatial Filtering : 35 ImplementationImplementation Problem: Expensive to implement directly Solution: Approximate using absolute values Can be implemented using two 2x2 filters Even filters difficult to implement, so 3x3 filters are used for approximation 9 5 8 6f z z z z∇ ≈ − + − 7 8 9 1 2 3 3 6 9 1 4 7 ( 2 ) ( 2 ) ( 2 ) ( 2 ) f z z z z z z z z z z z z ∇ ≈ + + − + + + + + − + +