Adaptive Filtering of Raster
Map Images
Minjie Chen*, Mantao Xu and Pasi Fränti
Speech and Image Processing Unit (SIPU)
School of Computing
University of Eastern Finland, FINLAND
Topographic or road maps
Few colors
Detailed spatial structures
Requirement
No over-smooth, remain readable
Number of colors does not increase
Preserve spatial structures
Scanning Image:
11063 colors
Original: 4 colors
Noise Model
Impulsive Noise
Gaussian Noise
Quantized Image:
4 colors
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
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
Layer separating
Filter each layer
Merging step with
global color priority
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
Segment the image into several regions with
different background color, set different ordering
criterions for these regions
Merging with local color priority
Process each color layer by soft morphological dilation
and filling holes operations.
Large blocks regions are possible background regions.
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
Segment
Size
1
765241
2
662515
3
187677
4
83904
5
51170
6
21044
Six large segments are detected from different layer
2,5 from black layer, 3 from blue, 1,4 from white, 6 from brown
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
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)
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
Blank
background
image
S1/S2
Po
ADD(Y/N)
1
0.6878
0
Y
2
0.2922
0.9712
N
3
0.8373
0.0172
Y
4
0.8024
0.0149
Y
5
0.2302
0.9953
N
6
0.1567
1
N
Fill block 1
Fill block 3
Fill block 4
We can set different
threshold in filling step,
causing different
background images.
Classification can be
done to decide
threshold for different
type of images.
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
For all background region, calculate its corresponding
color histogram
We then get different color priority for different region
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
Context Template
Frequency
X
409
3
4
5
9
Frequency
X
2
2
193
3
6
Colors with low conditional probability will be replaced by the dominated color
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)
Root
Threshold Contexts
Children pointer array
1
X
1
X 2
N1=85
N2=16
N3=0
N4=10
1
X 2
N1=220
N2=110
N3=25
N4=35
N1=23
N2=67
N3=25
N4=5
1
X
1
X 2
N1=405
N2=117
N3=238
N4=6
N1=112
N2=27
N3=0
N4=20
1
X
N1=46
N2=810
N3=44
N4=75
1
X
N1=400
N1=58
N1=24
N1=30
N=256
23676
N=128
35847
N=64
54736
N=32
82260
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
Discrete Universal Denoiser(DUDE)
u0  arg max xA P (x|c)
(M  1)2 (1   )
(M  1)
P(x  x0 |c) 
P(x  u0 |c)  1
 ((1   )M  1)
((1   )M  1)
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”:
  1  maxx, p(c)10 p( x | c)
2
This decision rule is designed for the count statistics collected on the noisy image. For a clean image, the decision rule is
P(I (x)  x0 |c)   / ( M  1), x0  1, 2,..., M
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
Definitions:
information fusion.
I ( x)  arg min x (1..M ) ( log 2 f (y x | M x )  log 2 P( x | c))
where M x ~ N (m x ,  2 I),  is the mean variance
(1)
|| y x  mx ||2
f (y x | M x )  exp(
)
2 2
mi (r )  median({rx | x  X, and I ( x)  i})
(2)
1 M

|| y x  m i ||2


3 | X | i 1 xX , I ( x )  i
(3)
X: index image,
Y: corresponding image,
CP=(m1,m2,…mM) color palette where
mi = (mi(r), mi(g), mi(b)) ,
yx = (rx,gx,bx) the color intensity of x in RGB space.
Input: Y
X, CP ← Conduct color quantization based on Y
Σ
← Estimate the quantization variance based on
X, Y,CP according to (3)
For T iterations DO:
Given X, update P(x|c)
Update X , according to (1)
Update CP and σ according to (2) and (3)
End-For
Output: Y, X, CP.
General Scheme for filtering Gaussian noise
Noisy image
Quantized image
Filtering after 1 iteration
Filtering after 5 iterations
5
δ=
0.05
AVM
8.65
4.19
11.8
6.55
9.27
PGF
1.40
1.26
3.26
1.21
6.02
CT
1.04
0.99
2.41
1.42
4.36
DUDE
0.94
0.99
2.09
1.34
2.66
4
ACS
0.65
0.78
1.59
0.82
2.02
Error Rate(%)
Set#1
Set#2
Set#3
Set#4
Set#5
Error rate (%)
AVM
PGF
CT
DUDE
ACS
3
2
1
0
0
5
10
15
20
Impulsive Noise Level(%)
50
σ =25
PSNR
BM3D
NLM
GSM
ARF
ACS
45
Set#1
Set#2
Set#3
Set#4
Set#5
GSM
24.4
24.0
23.7
24.6
25.1
NLM
24.9
23.5
22.4
24.1
24.3
BM3D
26.2
26.5
23.7
25.5
26.1
ARF
24.2
23.3
23.0
23.8
25.1
ACS
47.1
59.2
27.0
33.4
27.7
PSNR
40
35
30
25
20
0
10
20
30
Gaussian Noise()
40
50
Impulsive noise
AVM
PGF
CT
DUDE
ACS
Gaussian noise
BLS-GSM
NLM
BM3D
ARF
ACS
Mixed noise
PGF
BM3D
BM3D+PGF
FPGA
ACS
Statistical filtering for raster map images
Can process images distorted by impulsive noise,
additive Gaussian noise and mixture Gaussianimpulsive noise
Both color distribution in RGB space and the
conditional probabilities of local context are
considered
Pruning?
Merging?
Reorder the context pixel-wise?
Our solution: An voting-based method to optimize the context selection
PX |C (x|c)
P(c)
F(c)  log 2 (
)  k  PX |C ( x|c) log(
)
PE (c)
P( x)
x
k
PE (c)   P( yi )
i 1
P(c) is probability of context c, P( yi ) is the probability of color yi
identify good or bad context by top-down tracing from the root of tree.
Original
Original
Noisy
Noisy
Noisy pixel with bad context
Noisy pixel with bad context can not filter correctly.
Can we use bad context for noise estimation?
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:
zi  c /{xi }, i  1..k
R(xi ) = R(xi ) + F(zi ) - F(c)
when F(zi ) - F(c)  0
xi is the pixel position of ith context element
-0.39
2.29
5.41
-0.38 F(z)- F(c)
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2.29
0
0
0
0
2.29
0
0
0
0
0
0
0
0
5.41
0
0
0
0
5.41
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
+
Voting image
1.39
-1.24
-1.33
3.58
F(z)- F(c)
Voting image
0
0
0
0
0
0
0
0
1.39
0
0
0
0
1.39
0
0
0
0
2.29
0
0
0
3.58
0
0
0
0
3.58
2.29
0
0
0
5.41
0
0
0
0
0
0
0
0
0
5.41
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
+
-0.62
5.69
1.96
-0.40 F(z)- F(c)
Voting image
0
0
0
1.39
0
0
0
0
0
0
0
0
0
1.39
0
0
0
3.58
2.29
0
0
0
0
0
0
0
0
3.58
2.29
0
0
0
5.41
0
0
0
0
5.69
0
0
0
0
11.0
0
0
0
0
0
0
0
0
1.96
0
0
0
0
1.96
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
+
4.15 -2.86 -2.32
2.24
-0.65 F(z)- F(c)
Voting image
0
0
0
1.39
0
0
0
0
0
0
0
0
0
1.39
0
0
0
3.58
2.29
0
0
0
4.15
0
0
0
0
7.73
2.29
0
0
0
11.0
0
0
0
2.24
0
0
0
0
2.24
11.0
0
0
0
1.96
0
0
0
0
0
0
0
0
0
1.96
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
+
-2.02 3.23
-1.40
-1.63 5.51
F(z)- F(c)
Voting image
0
0
0
1.39
0
0
0
0
0
0
0
0
0
1.39
0
0
0
7.73
2.29
0
0
0
0
0
0
0
0
7.73
2.29
0
0
2.24
11.0
0
0
0
0
5.51
0
0
0
2.24
16.5
0
0
0
1.96
0
0
0
0
0
3.23
0
0
0
1.96
3.23
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
+
1.79 1.38
-1.43
-1.16 2.35
F(z)- F(c)
Voting image
0
0
0
1.39
0
0
0
0
0
0
0
0
0
1.39
0
0
0
7.73
2.29
0
0
0
0
0
0
0
0
7.73
2.29
0
0
2.24
16.5
0
0
0
0
1.79
2.35
0
0
2.24
18.3
2.35
0
0
1.96
3.23
0
0
0
0
0
1.38
0
0
1.96
3.23
1.38
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
+
Noisy pixel have a high
voting value
Bad context include black noisy pixel
south
east
reduced
context
F(z)- F(c)
4.15
Voting value
7.73
3.58
Bad context include white noisy pixel
north
south
west
west
south
reduced
context
F(z)- F(c)
5.41
5.69
5.51
1.79
Voting value
18.30
Original
Noisy
voting image
noisy image
voting image
If contexts are not good context, pixels with low voting value are selected to
construct new adaptive context.
Original
Iteration 1
Noisy
DUDE
Proposed
Iteration 2
Noisy pixels with
contaminated contexts are filtered
correctly by optimal context selection
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.
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)