Soft Morphological Filter

1. Soft Morphological Filter Paper: Simple and Efficient Soft Morphological Filter in Periodic Noise Reduction Authors: Zhen Ji, Huilian Liao, Xinjun Zhang, Q.H. Wu 15 Nov. 2006

2. Outline • Introduction • Mathematical morphology (MM) • Soft morphology • Soft morphological filters (SMF) • Soft morphological filter* (SMF*) • Results • Conclusions • Acknowledgement

3. Introduction to filters • Introduction to filters • 1. Spatial filters (including MM filter) • 2. Frequency filters (including spectral median filter) Fig. 1 Fig. 2

4. Mathematical morphology (MM) • Structuring element (SE) • Two basic operators of morphology: • Erosion • Dilation • Binary morphology & Grey-scale morphology

5. MM – Erosion of Grey-scale morphology The erosion of f by a SE g at a point xis: z = {(1,2),(1,3),(0,2),(0,3)}

6. MM — Dilation of Grey-scale morphology The dilation of f by a SE g at a point xis: z = {(1,2),(1,1),(2,2),(2,1)}

7. Soft morphology • Differences between soft morphology and standard morphology: • The SE g is divided into two parts: the hard αand the soft β= g/α • The min/max operators are substituted by other order statistics • Two basic operators: • Soft erosion & soft dilation

8. Soft morphology — soft erosion Soft erosion of f by SE g (hardα and softβ) at point x is: D[α]={(0,0)}; D[β]={(0,1),(0,2),(1,0),(1,1)}

9. Soft morphology — soft dilation Soft dilation of f by SE g (hardα and softβ) at point x is: D[α]={(0,0)}; D[β]={(0,1),(0,2),(1,0),(1,1)}

10. Soft morphological filter • Soft morphological filter (SMF) • Standard morphological filter (StdMF)

11. Morphological filters — comparison

12. Soft morphological filter* (SMF*) • Design procedure of SMF* • Design of SMF*’s parameters: SE g and hardα are symmetric to its origin

13. Results • Filters: • SMF*; Spectral median filter; median; Standard MM • Experimental image: • Pepper image with periodic noise • Measure of performance: • Peak-Signal-Noise-Ratio (PSNR) • Shape error • Computation time

14. Results — PSNR

15. Results — Shape error

16. Results — Computation time

17. Conclusions About SMF* • Purposes: Reducing the periodic noise • Properties: Preserving details of image • Advantages: Filtering quality & Computation efficiency & Simplicity

18. Acknowledgement • My supervisor: Prof. Ji • All of you

19. Thank you !

20. Dilation expands the image foreground and shrinks its background, whilst erosion shrinks the image foreground and expands its background. • The Erosion filter is a morphological filter that changes the shape of objects in an image by eroding (reducing) the boundaries of bright objects, and enlarging the boundaries of dark ones. It is often used to reduce, or eliminate, small bright objects. • The Dilation filter is a morphological filter that changes the shape of objects in an image by dilating (enlarging) the boundaries of bright objects, and reducing the boundaries of dark ones. The dilation filter can be used to increase the size of small bright objects. • soft erosion is anti-extensive and soft dilation is extensive, provided that the structuring element includes the origin. In particular the smaller the repetition parameter k is the more the input image shrinks or expands. (also 1st property)