Patch-Based Mathematical Morphology for Image Processing ...
Automated Target Recognition Using Mathematical Morphology
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Transcript of Automated Target Recognition Using Mathematical Morphology
Automated Target Recognition Using Mathematical Morphology
Prof. Robert HaralickIlknur IckeJosé Hanchi
Computer Science Dept.The Graduate Center of CUNY
Outline
• Gray Scale Morphology
• Converting Images to Datasets
• Decision Tree Classifier
• Results / Conclusions
Outline
• Gray Scale Morphology
• Converting Images to Datasets
• Decision Tree Classifier
• Results / Conclusions
Mathematical Morphology• Given an image II EN and a structuring element S S EN define the morphological operation of
Dilation
},,|{ sicSsIiEcSI N
},|{)( xicIiEcI Nx
and set translation as
xx SISI )()( Dilation is translation invariant
Mathematical Morphology
I
S
SI
Dilation
Mathematical Morphology• Define the morphological operation of
Erosion
},|{ IsxSsExSI N
Erosion is translation invariant
xx SISI )(
xx SISI )(
Mathematical Morphology
If a structuring element can be decomposed as
YXS
then
YXIYXISI )()(
YXIYXISI )()(
Basic Morphology Operators
Opening
Closing
SSISI )(
SSISI )(
SISSI )(
SISSI )(
Gray Scale Morphology
Dilation of f by k
)}()({max))(( zkzxfxkfFzx
Kz
Erosion of f by k
)}()({min))(( zkzxfxkfKz
Gray Scale Morphology
Opening of f by k
kkfkf )(
kkfkf )(
Closing of f by k
• We have used flat structuring elements
of size { 3,5,7,9,11,13,15,17,19,21 }
Structuring Elements Used
Hw = Horizontal
Vh =Vertical
Bwxh = Box
h = 5
w = 5
… an illustration
Dilation9HI
w = 9
Erosion9HI
w = 9
Opening9HI
w = 9
Closing9HI
w = 9
The van-Herk-Gil-Werman (HGW) Algorithm—dilationSTAGE 1
• Given the input signal stream and a flat structuring element of size = 3 x0 , x1, x2 , x3 , x4 , x5 , x6 , x7 , x8 , x9 , x10 , x11 , x12 , x13 ,…
9 4 5 14 21 18 12 7 8 3 …
• center segments located at x0 , x1, x2 , x3 , x4 , x5 x6 , x7 , x8 x9 , x10 , x11 … example:
… take the first segment and find the max (i.e. dilation)…
The van-Herk-Gil-Werman (HGW) Algorithm—dilation
STAGE 1.a
9 4 5 14 21
5
copy
9
max
R0
5
R1
5
R2
9 4
max
preprocess the prefixesx0 x4x2x1 x3
The van-Herk-Gil-Werman (HGW) Algorithm—dilation
STAGE 1.b
9 4 5 14 21
5
copy
21
max
14
max
preprocess the suffixes
S0
5
S1
14
S2
21
x0 x4x2x1 x3
The van-Herk-Gil-Werman (HGW) Algorithm—dilationSTAGE 2
9 4 5 14 21
R0
5
R1
5
R2
9
merging prefixes and suffixes
S0
5
S1
14
S2
21
max
99
max
1414
max
2121
p
p
p
pp 43)2()1(2
number of max operations per window:
x0 x4x2x1 x3
The van-Herk-Gil-Werman (HGW) Algorithm—dilation
Processing a given input signal for p=3 , segment size=5
x0 , x1, x2 , x3 , x4 , x5 , x6 , x7 , x8 , x9 , x10 , …
9 14 21 21 21 18 12 8 12 …
9 4 5 14 21 18 12 7 8 3 …12
Calculating Morphological Features in 2-D
The HGW algorithm works on 1-D inputTo apply it to 2-D images apply
– Horizontal Structuring Elements
process the image line by line
– Vertical Structuring Elements
transpose the image
process line by line
transpose again
– Box shaped Structuring Elements
horizontal first, then vertical
Efficiency of Flat Structuring Elements
Given the flat structuring elements H and V• Dilation• Erosion• Opening• Closing
Since and given w = h
• Dilation• Erosion• Opening• Closing
HI HI HI HI
VI VI VI VI
hwhw VHB
VHIBI )(VHIBI )(
VHVHIBBIBI )))((()(VHVHIBBIBI )))((()(
Ori
gina
l Im
age
Dilation with H5
ErosionWithH5
OpeningWithH5
Closing With H5
Using V5 Structuring Element
erosiondilation opening closing
Using B5x5 Structuring Element
dilation erosion opening closing
Outline
• Gray Scale Morphology
• Converting Images to Datasets
• Decision Tree Classifier
• Results / Conclusions
Using Morphological Operations As Features for a Pixel
ground truth image
II
(3 structural elements) x (10 sizes) x (4morphological operations) = 120 transformed images
…
5HI 5HI 5HI 5VI 5VI 5VI 55 BI 55 BI
…
55 BI55BI 5VI 5HI
Using Morphological Operations As Features for a Pixel
ground truth image
II
……
5HI 5HI 5HI 5HI 5VI 5VI 5VI 5VI 55 BI 55BI 55 BI55 BI
class label
ff1313 ff1414 ff1515 ff1616 ff1717 ff1818 ff1919 ff2020 ff2121 ff2222 ff2323 ff2424
{t,c}{t,c}={1,0}={1,0}
Given a pixel
Ground Truth Imageof mxnmxn pixelsII
(x(x1,f11,f1, x, x1,f21,f2, x, x1, f31, f3,... , x,... , x1, f1191, f119, x, x1,f1201,f120, , tt))
(x(x2,f12,f1, x, x2,f22,f2, x, x2, f32, f3,..., x,..., x2, f1192, f119, x, x2,f1202,f120, , tt))
(x(x3,f13,f1, x, x3,f23,f2, x, x3, f33, f3,..., x,..., x3, f1193, f119, x, x3,f1203,f120, , cc))
......
(x(xN-1,f1N-1,f1,x,xN-1,f2N-1,f2, x, xN-1, f3N-1, f3,..., x,..., xN-1, f119N-1, f119, x, xN-1,f120N-1,f120, , cc))
(x(xN,f1N,f1, x, xN,f2N,f2, x, xN, f3N, f3,..., x,..., xN, f119N, f119, x, xN,f120N,f120, , tt))
data setrepresentationof I I of sizeN = mxnN = mxn
DD
Morphological Features Data Set From an Image
5HI 5HI 5HI 5HI 5VI 5VI 5VI 5VI 55 BI 55BI 55 BI55 BI
Preparation Of Data Sets to Train and Test the Classifier
DD11
DD22
……
DDkk
DDk+1k+1
……DDKK
Createdatasets
separatevectors
II11
II22
……
IIkk
IIk+1k+1
……IIKK
ground truth images
targetdataset
clutterdataset
trainingdataset
testdataset
Outline
• Gray Scale Morphology
• Converting Images to Datasets
• Decision Tree Classifier
• Results / Conclusions
Creating a Decision Tree Classifier
classify classified classified datasetdataset
evaluate accuracyaccuracy
create decision
treedecision treedecision tree
trainingdataset
parametersparameters
testdataset
decision treedecision tree
testdataset
classified classified datasetdataset
Creating a Decision Tree Classifier
11
1
1
1
1 1
11
0 0
0
0
00
11
22
f1f1
f2f2DDtrainingtraining
f1f1 > 11
true
f2f2 > 22
class 0
true
00
00
0
00
033
44
f2f2 > 33
class 1
true
class 0f1f1 > 44
class 1
true
class 0
• threshold decision rule
• max.entropy = 0.001
• max. depth = 20
Outline
• Gray Scale Morphology
• Converting Images to Datasets
• Decision Tree Classifier
• Results / Conclusions
Decision Tree Classifier resultsfor test dataset derived from
images of resolution = 75mm
Clutter Target
Clutter 1,712,090 15,422
Target 1,419 54,503
train dataset size = 292,831 vectors
test dataset size = 1,783,434 vectors
true
cla
ss
assigned class
accuracy (% correct classification) = 99.046%
Decision Tree Classifier resultsfor images of resolution = 75mm
• 345 images of clutter-only
• 44 images with mostly target
accuracy # clutter images # target images
[0.91 , 0.92) 4 -[0.92 , 0.93) 3 -[0.93 , 0.94) 4 -[0.94 , 0.95) 12 -[0.95 , 0.96) 14 -[0.96 , 0.97) 18 -[0.97 , 0.98) 31 5[0.98 , 0.99) 93 21[0.99 , 1.00) 166 18
Total # images 345 44
Decision Tree Classifier resultsfor test dataset derived from
images of resolution = 200mm
Clutter Target
Clutter 231,495 1,702
Target 254 8,391
train dataset size = 64,127 vectors
test dataset size = 241,842 vectorstr
ue c
lass
assigned class
accuracy (% correct classification) = 99.19%
Decision Tree Classifier forimages with resolution = 200mm
• 689 images with mostly clutter
• 34 images with mostly target
accuracy # clutter images # target images
< 0.90 4 -[0.90 , 0.92) 1 -[0.92 , 0.94) 1 -[0.94 , 0.95) 2 1[0.95 , 0.96) 3 -[0.96 , 0.97) 8 1[0.97 , 0.98) 12 1[0.98 , 0.99) 76 10[0.99 , 1.00] 582 21
Total # images 689 34
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