Adaptive Filtering of Raster Map Images

1. Adaptive Filtering of Raster Map Images Minjie Chen*, MantaoXu and PasiFränti Speech and Image Processing Unit (SIPU)School of Computing University of Eastern Finland, FINLAND

2. Raster Map Images • Topographic or road maps • Few colors • Detailed spatial structures

3. Filtering of Raster Map Images • Requirement • No over-smooth, remain readable • Number of colors does not increase • Preserve spatial structures • Noise Model • Impulsive Noise • Gaussian Noise Scanning Image: 11063 colors Original: 4 colors Quantized Image: 4 colors

4. Existing Methods • Impulsive Noise • Vector Median (VM, AVM) • Peer Group Filtering (PGF,FPGF ) • Morphological Filtering • Context Tree Modelling • Discrete Universal Denoiser (DUDE) • Gaussian Noise • Wavelet denoising using Gaussian scale mixtures (GSM) • Non-local mean (NLM) • Dictionary- based method (K-SVD) • Blocking matching and 3D filtering (BM3D) • Markov random fields/conditional random fields (FoE,ARF) • Non-Local Sparse Models for Image Restoration (NLSM) • Patch-based Locally Optimal Wiener Filtering for Image Denoising (PLOW) • Sparsity-based Image Denoising via Dictionary Learning and Structural Clustering (CSR) • Most algorithms are designed for continuous-tone(photographic) images Complicated spatial structures in the map will be destroyed

5. Multi-Layer Method for Morphological Filtering • Covert multi-dimension image filtering problem into a series of binary image filtering problem using layer seperating • After filtering on each layer, select suitable layer ordering to reconstruct the image Step 1: Divide color image into Multi-Layer binary images Step 2: Filter binary layers separately Step 3: Layer ordering decision Step 4: Merge the filtered layers

6. Example of Multi-Layer Method(Global Color Priority) Layer separating Filter each layer Merging step with global color priority

7. Step 3: Layer ordering (cont.) Global criterion : select colors according to their frequency Same color priority for whole image No difference for different regions Highest Priority 618416 230020 173358 22975 3458 349 Lowest priority is used as background color PRIORITY

8. Step 3: Layer ordering: Local Color Priority (Chen et al. ICIP’09) Segment the image into several regions with different background color, set different ordering criterions for these regions

9. Example of Multi-Layer Method(Local Color Priority) Merging with local color priority

10. Algorithm for color priority decisionStep 3.1: Dilation and fill holes Process each color layer by soft morphological dilation and filling holes operations. Large blocks regions are possible background regions.

11. After dilation and filling holes

12. Algorithm for color priority decisionStep 3.2: Evaluate preliminary segments • Region labeling labels connected pixels • After region labeling, sort segments according to their size • If the size of the segments is larger than a threshold, select as background region candidate • The goal is to extract large connected segments in each layer for later background filling step

13. Example of Step 3.2 Preliminary segments • Six large segments are detected from different layer • 2,5 from black layer, 3 from blue, 1,4 from white, 6 from brown

14. Algorithm for color priority decisionStep 3.3 Background filling Evaluate if those large segments detected in Step 3.2 are real background regions. First create a blank background image Evaluate those segments one by one from large segment to small segment. If it is real background, add to background image, labeling the region with the layer color

15. Algorithm for color priority decisionStep 3.3 Background filling • Two features used for validating if it is background segment • Feature 1: How many change after dilation and image filling operation • Background segment’s size does not change much, have large ratio Region 2: Before 193606 After 662515 Ratio 0.2922(NOT ADDED) Region 1: Before 526337 After 765241 Ratio 0.6878(ADDED)

16. Algorithm for color priority decisionStep 3.3 Background filling (cont.) • Feature 2: Does this segment overlap with background already filled? • In common condition, it should have a small value, this feature can enhance the filling accuracy • If feature 1 is close to 1, this feature can also be large, it will add a background inside one background segment Blank Background Region 1: Overlap percentage 0% (ADDED) Region 2: Overlap percentage 97% (NOT ADDED) Already labeled region 1

17. We can set different threshold in filling step, causing different background images. Classification can be done to decide threshold for different type of images. Blank background image Fill block 1 Fill block 3 Fill block 4

18. Algorithm for color priority decisionStep 3.4 Process unlabeled region Large unfilled regions ---- set as small background region. Small unfilled region ---- merge it to the nearest background. Set as small background region Merge to the nearest background After processing

19. Step 3.5 Calculate the color priority in different background regions For all background region, calculate its corresponding color histogram We then get different color priority for different region

20. More examples of background image

21. Result - impulsive noise

22. Conclusion of Multi-layer method • The current method does not work if color number is large • Priority between small structures not considered • Special local patterns combined with multiple color is missed

23. Statistical Filtering (Chen et al. ICME’10, IEEE TMM’ 11) Context Template Colors with low conditional probability will be replaced by the dominated color Frequency Frequency Frequency Frequency 409 3 4 5 9 2 2 193 3 6 X X

24. Example of Context Tree Modeling • Context Dilution • 6-color, 20-pixel template has 620 = 3,656,158,440,062,976 contexts • Most contexts has rare appearance, cause inaccurate conditional probability estimation. • Context Tree Modeling • Only appeared contexts are allocated in memory • Time complexity O(N), where N is the length of a data sequence. • Tree spanning is terminated once the frequency of the context on a given node is less than a predefined value(N) Threshold Contexts N=256 23676 N=128 35847 N=64 54736 N=32 82260

25. Context Merging • Including noise pixels in the surrounding contexts makes good conditional probability estimation difficult. • For contexts with rare appearance, a merging process is done to collect the statistics of all similar contexts. • Time complexity is O(kNM2), where M is the number of colors, k is the depth of the context tree, N is the number of contexts with rare appearance. Most consistent sub-context Noisy pixel Example of context merging

26. Filtering Threshold • Discrete Universal Denoiser(DUDE) • M is the number of colors, δ is the noise level, u0 is the color with highest conditional probability. • DUDE has a so-called “asymptotic optimality” property for M-ary symmetric noise. • Estimation of δ • Estimated by the minimum conditional probability occurred for contexts with “sufficient frequency”: This decision rule is designed for the count statistics collected on the noisy image. For a clean image, the decision rule is

27. Extension for Gaussian Noise • Iterative algorithm to optimize both the estimation of the indexed image and its color palette. • The distance between RGB color vector to its corresponding component in the color palette, and its conditional probability of local context are taken into account as an information fusion. (1) (2) (3)

28. Filtering Example Noisy image Quantized image Filtering after 1 iteration Filtering after 5 iterations

29. Experiments under Different Noise Level

30. Visual Examples

31. Summary • Statistical filtering for raster map images • Can process images distorted by impulsive noise, additive Gaussian noise and mixture Gaussian-impulsive noise • Both color distribution in RGB space and the conditional probabilities of local context are considered

32. Optimize the Context Selection (Chen et al. ICIP’11) Pruning? Merging? Reorder the context pixel-wise? • Our solution: An voting-based method to optimize the context selection

33. Measuring Goodness Score of Context identify good or bad context by top-down tracing from the root of tree.

34. Example of pixel with good Context and bad Context in the Map Original Noisy Original Noisy Noisy pixel with bad context Noisy pixel with bad context can not filter correctly. Can we use bad context for noise estimation?

35. Detect Noisy Pixel by bad Context Bad contexts will have higher score difference after the noisy pixel is removed. Include noisy pixel may cause bad context. We can accumulated these score difference for bad context to find noisy pixel, which is the voting image R:

36. Voting Image (cont.) -0.39 2.29 5.41 -0.38 F(z)- F(c) + Voting image

37. Voting Image (cont.) 1.39 -1.24 -1.33 3.58 F(z)- F(c) Voting image +

38. Voting Image (cont.) -0.62 5.69 1.96 -0.40 F(z)- F(c) Voting image +

39. Voting Image (cont.) 4.15 -2.86 -2.32 2.24 -0.65 F(z)- F(c) Voting image +

40. Voting Image (cont.) -2.02 3.23 -1.40 -1.63 5.51 F(z)- F(c) Voting image +

41. Voting Image (cont.) 1.79 1.38 -1.43 -1.16 2.35 F(z)- F(c) Voting image + Noisy pixel have a high voting value

42. Voting Image (cont.) Bad contextinclude black noisy pixel south east reduced context Voting value 7.73 F(z)- F(c) 4.15 3.58 Bad contextinclude white noisy pixel south west north west south reduced context Voting value 18.30 F(z)- F(c) 5.41 5.69 5.51 1.79

43. Voting Image (cont.) Original Noisy voting image

44. Voting Image (cont.) noisy image voting image

45. Adaptive Context Selection If contexts are not good context, pixels with low voting value are selected to construct new adaptive context.

46. Filtering Result for Impulsive Noise Original Noisy DUDE Proposed Iteration 1 Iteration 2 Noisy pixels with contaminated contexts are filtered correctly by optimal context selection

47. Conclusions • Adaptive context selection via a voting-based noise estimation scheme • Can process raster map images distorted by impulsive noise, additive Gaussian noise or mixture Gaussian-impulsive noise • Extension for optimizing the context selection for denoising gray-scale image, e.g. voting-based method to optimize the weighting coefficient in NLM, PLOW, K-SVD.

48. Related Paper • M. Chen, M. Xu and P. Fränti, "Multi-layer filtering approach for map images", IEEE Int. Conf. on Image Processing (ICIP'09), Cairo, Egypt, 3953-3956, 2009. • M. Chen, M. Xu and P. Fränti, "Statistical filtering of raster map images", IEEE Int. Conf. on Multimedia & Expo (ICME'10), Singapore, 394-399, 2010. (oral) • M. Chen, M. Xu, P. Fränti, "Adaptive Context-tree based Statistical Filtering of Raster Map Images Denoising", IEEE Trans. on Multimedia, 16(3), 1195-1207, 2011. • M. Chen, M. Xu, P. Fränti, "Adaptive Filtering of Raster Map Images Using Optimal Context Selection", IEEE Int. Conf. on Image Processing (ICIP’11), 77-80, Brussels, Belgium, 2011.(oral)