Lecture 7
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This document discusses sharpening filters used in digital image processing. It describes two types of sharpening filters: high-pass filters that enhance high frequencies and frequency correcting filters that enhance high and medium frequencies. Unsharp masking is presented as a classical frequency correcting filter that subtracts a blurred version of an image from the original to highlight transitions. Practical implementations of linear and nonlinear unsharp masking filters are shown for local and global frequency correction. Parameters for controlling the level of sharpening and frequency enhancement are also discussed.
Lecture 7
- 1. SPATIAL DOMAIN FILTERING SHARPENING FILTERS CS-467 Digital Image Processing 1
- 2. Sharpening • The principal objective of sharpening is to highlight transitions in intensity • While image smoothing can be achieved by averaging (integration) in a local neighborhood, which leads to suppression of high frequencies, image sharpening can be accomplished by differentiation in a local neighborhood, which leads to the high and possibly medium frequencies enhancement 2
- 3. Sharpening • There are two types of sharpening : • Using high-pass filters – these filters suppress or eliminate low and medium frequencies, passing and possibly enhancing high frequencies. This is resulted in edge detection and edge enhancement • Using frequency correcting filters – these filters enhance high and possibly medium frequencies, which leads to image sharpening and distinguishing of the details whose area is about a half by a half of the filtering window size 3
- 4. Frequency Correcting Filters • Frequency correcting filters enhance high and possibly medium frequencies, which leads to visual image sharpening and visual distinguishing of the details whose area is about a half by a half of the filtering window size • It is important to understand that these filters improve visual perception, but they cannot restore missing frequencies. Thus, they cannot be used for image deblurring • These filters are also called image preparation filters 4
- 5. Unsharp Masking • Unsharp masking is a classical frequency corrector • High frequencies enhancement is utilized through a filter, which adds the “unsharp mask” to an image • The unsharp mask corresponding to the filtering window is a pixel-wise difference between the original image and its smoothed (averaged) version • Depending on the method of averaging this filter can be linear or nonlinear 5
- 6. Unsharp Masking • Mask where is taken from the averaged version of the image. • Averaging is applied to a local window • Filter • where k is a weight (parameter) 6 ( ) ( ) ( ), , ,maskg x y f x y f x y= − ( ),f x y ( ) ( ) ( ), , ,maskg x y f x y k g x y= + ⋅
- 7. Unsharp Masking • Unsharp masking leads to the enhancement of high frequencies • It is the most efficient for 3x3 and 5x5 windows • Averaging can be linear (arithmetic mean over a filtering window) or nonlinear (median over a filtering window) • Unsharp masking enhances image details whose area is about a half by a half of the filtering window size 7
- 8. Unsharp Masking: Practical Implementation • Unsharp masking linear filter • Filter kernel (mask) for a 3 x 3 window 8 ( ) ( ) ( ) ( )( ), , , xyg x y f x y k f x y MEAN S= + − 9 9 9 1 9 9 9 9 9 9 k k k k k k k k k k − − − − + − − − − −
- 9. Unsharp Masking: Practical Implementation • The larger is k, the higher is a level of sharpening • k=1 regular unsharp masking • k>1 highboost filtering • k<1 slight enhancement of edges 9 ( ) ( ) ( ) ( )( ), , , ,g x y f x y k f x y f x y= + −
- 10. Unsharp Masking: Practical Implementation • Unsharp masking nonlinear filter 10 ( ) ( ) ( ) ( )( ), , , xyg x y f x y k f x y MED S= + −
- 11. Unsharp Masking: Global Frequency Correction • Unsharp masking can also be used to enhance simultaneously high and medium frequencies. • This global frequency correction not only leads to image sharpening, but also can enhance details whose area is a half by a half of the filtering window size • Again, depending on the method of averaging this filter can be linear or nonlinear 11 ( ) ( ) ( ) ( )( ) ( )1 2 3, , , , ,g x y k f x y k f x y f x y k f x y= + − +
- 12. Unsharp Masking: Global Frequency Correction • Global frequency correction linear • Filter kernel (mask) for an m x n window 12 ( ) ( ) ( ) ( )( ) ( )1 2 3, , , xy xyg x y k f x y k f x y MEAN S k MEAN S= + − + 3 2 3 2 3 2 3 2 3 2 3 2 1 2 3 2 3 2 3 2 ... ... ... ... ... ... ... ... ... ... ... ... k k k k k k mn mn mn k k k k k k k k mn mn mn k k k k k k mn mn mn − − − − − − + + − − −
- 13. Unsharp Masking: Global Frequency Correction • Global frequency correction - nonlinear 13 ( ) ( ) ( ) ( )( ) ( )1 2 3, , , xy xyg x y k f x y k f x y MED S k MED S= + − +
- 14. Unsharp Masking: Global Frequency Correction • The larger is k2, the higher is a level of medium frequencies enhancement (the best choice is ) • are responsible for a level of high frequencies enhancement, they should be taken such that 14 ( ) ( ) ( ) ( )( ) ( )1 2 3, , , , ,g x y k f x y k f x y f x y k f x y= + − + 23 7k≤ ≤ 1 3,k k 1 3 1k k+ =