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MRF and Dempster-Shafer Theory forsimultaneous shadow/vegetation detection on
high resolution aerial color imagesPhD research
Tran-Thanh NGO, Christophe Collet, Vincent Mazet
Université de Strasbourg - CNRS, Laboratoire iCube
Thursday 10th April, 2014
1/18
2/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Outline
1 Introduction
2 DS evidence theory for shadow/vegetation detectionMotivationTheory of Belief functionsApplication to shadow/vegetation detection
3 Contextual InformationMarkov random fieldDS theory in Markovian context
4 Results
Tran-Thanh NGO, Christophe Collet, Vincent Mazet MRF and Dempster-Shafer Theory for simultaneous shadow/vegetation detection on high resolution aerial color images
3/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Process line
Shadow/vegetation detection −→ Building detection −→ Buildingclassification −→ Change detection (updating building database)
At time n At time n+1Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 3/18
3/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Process line
Shadow/vegetation detection −→ Building detection −→ Buildingclassification −→ Change detection (updating building database)
At time n At time n+1Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 3/18
3/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Process line
Shadow/vegetation detection −→ Building detection −→ Buildingclassification −→ Change detection (updating building database)
At time n At time n+1Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 3/18
3/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Process line
Shadow/vegetation detection −→ Building detection −→ Buildingclassification −→ Change detection (updating building database)
At time n At time n+1Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 3/18
3/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Process line
Shadow/vegetation detection −→ Building detection −→ Buildingclassification −→ Change detection (updating building database)
At time n At time n+1Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 3/18
3/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Process line
Shadow/vegetation detection −→ Building detection −→ Buildingclassification −→ Change detection (updating building database)
At time n At time n+1Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 3/18
4/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Motivation
Drawbacks of sequential shadow/vegetation detection:vegetated pixels covered by shadow are wrongly classified.
Represent and handle imprecise and uncertain information.
Combine different sources of information.
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 4/18
5/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Dempster-Shafer Belief Functions
Frame of discernment: Θ = {Hi}, 1 ≤ i ≤ N .
A mass function on Θ is a function m : 2Θ −→ [0, 1] such thatthe following two conditions hold:
m(∅) = 0∑A⊆Θ
m(A) = 1
m(A) measures the degree of belief in the exact proposition.
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 5/18
6/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Dempster-Shafer Belief Functions
Belief (Bel) function:
Bel(A) =∑B⊆A
m(B)
measures the minimum uncertainty value about hypothesis A.
Plausibility (Pls) function:
Pls(A) =∑
B∩A 6=∅
m(B)
measures the maximum uncertainty value about hypothesisA.
The length of belief interval [Bel(A), P ls(A)]: imprecisionabout the uncertainty value.
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 6/18
7/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Combining the evidences
Suppose m1 and m2 are two mass distributions from two sourcesS1, S2, defined over Θ. Then m1 ⊕m2 is given by:
Orthogonal sum
m1 ⊕m2(A) =
0 if A = ∅
1
1−K∑
B⋂
C=A 6=∅
m1(B).m2(C) if ∅ 6= A ⊆ Θ
K =∑
B⋂
C=∅
m1(B).m2(C): normalization constant.
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 7/18
8/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Application to shadow/vegetation detection
Image segmentation with 3 classes:
ω1 : shadow
ω2 : vegetation
ω3 : other
Frame of discernment: Θ = {H1, H2, H3}, Hi = {ωi}
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 8/18
8/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Application to shadow/vegetation detection
Image segmentation with 3 classes:
ω1 : shadow
ω2 : vegetation
ω3 : other
Frame of discernment: Θ = {H1, H2, H3}, Hi = {ωi}
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 8/18
9/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Application to shadow/vegetation detection
RGB color image
Image c3 Image ExG Image L
c3 = arctan
(B
max(R,G)
)ExG =
2×G− R− B
R + G + BL =
R + G + B
3Determine mass function
m1(H1),m1(H2 ∪H3)m2(H2),m2(H1 ∪H3)m3(H1 ∪H2),m3(H3)Calculate the orthogonal sum of mass function
m1 ⊕m2 ⊕m3x̂s = arg max
xs
{Pls(Hxs)
Decision making
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 9/18
9/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Application to shadow/vegetation detection
RGB color image
Image c3 Image ExG Image L
c3 = arctan
(B
max(R,G)
)
ExG =2×G− R− B
R + G + BL =
R + G + B
3Determine mass function
m1(H1),m1(H2 ∪H3)m2(H2),m2(H1 ∪H3)m3(H1 ∪H2),m3(H3)Calculate the orthogonal sum of mass function
m1 ⊕m2 ⊕m3x̂s = arg max
xs
{Pls(Hxs)
Decision making
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 9/18
9/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Application to shadow/vegetation detection
RGB color image
Image c3 Image ExG Image L
c3 = arctan
(B
max(R,G)
)
ExG =2×G− R− B
R + G + B
L =R + G + B
3Determine mass function
m1(H1),m1(H2 ∪H3)m2(H2),m2(H1 ∪H3)m3(H1 ∪H2),m3(H3)Calculate the orthogonal sum of mass function
m1 ⊕m2 ⊕m3x̂s = arg max
xs
{Pls(Hxs)
Decision making
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 9/18
9/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Application to shadow/vegetation detection
RGB color image
Image c3 Image ExG Image L
c3 = arctan
(B
max(R,G)
)ExG =
2×G− R− B
R + G + B
L =R + G + B
3
Determine mass function
m1(H1),m1(H2 ∪H3)m2(H2),m2(H1 ∪H3)m3(H1 ∪H2),m3(H3)Calculate the orthogonal sum of mass function
m1 ⊕m2 ⊕m3x̂s = arg max
xs
{Pls(Hxs)
Decision making
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 9/18
9/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Application to shadow/vegetation detection
RGB color image
Image c3 Image ExG Image L
c3 = arctan
(B
max(R,G)
)ExG =
2×G− R− B
R + G + BL =
R + G + B
3
Determine mass function
m1(H1),m1(H2 ∪H3)
m2(H2),m2(H1 ∪H3)m3(H1 ∪H2),m3(H3)Calculate the orthogonal sum of mass function
m1 ⊕m2 ⊕m3x̂s = arg max
xs
{Pls(Hxs)
Decision making
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 9/18
9/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Application to shadow/vegetation detection
RGB color image
Image c3 Image ExG Image L
c3 = arctan
(B
max(R,G)
)ExG =
2×G− R− B
R + G + BL =
R + G + B
3
Determine mass function
m1(H1),m1(H2 ∪H3)
m2(H2),m2(H1 ∪H3)
m3(H1 ∪H2),m3(H3)Calculate the orthogonal sum of mass function
m1 ⊕m2 ⊕m3x̂s = arg max
xs
{Pls(Hxs)
Decision making
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 9/18
9/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Application to shadow/vegetation detection
RGB color image
Image c3 Image ExG Image L
c3 = arctan
(B
max(R,G)
)ExG =
2×G− R− B
R + G + BL =
R + G + B
3
Determine mass function
m1(H1),m1(H2 ∪H3)m2(H2),m2(H1 ∪H3)
m3(H1 ∪H2),m3(H3)
Calculate the orthogonal sum of mass function
m1 ⊕m2 ⊕m3x̂s = arg max
xs
{Pls(Hxs)
Decision making
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 9/18
9/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Application to shadow/vegetation detection
RGB color image
Image c3 Image ExG Image L
c3 = arctan
(B
max(R,G)
)ExG =
2×G− R− B
R + G + BL =
R + G + B
3
Determine mass function
m1(H1),m1(H2 ∪H3)m2(H2),m2(H1 ∪H3)m3(H1 ∪H2),m3(H3)
Calculate the orthogonal sum of mass function
m1 ⊕m2 ⊕m3
x̂s = arg maxxs
{Pls(Hxs)
Decision making
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 9/18
9/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Application to shadow/vegetation detection
RGB color image
Image c3 Image ExG Image L
c3 = arctan
(B
max(R,G)
)ExG =
2×G− R− B
R + G + BL =
R + G + B
3
Determine mass function
m1(H1),m1(H2 ∪H3)m2(H2),m2(H1 ∪H3)m3(H1 ∪H2),m3(H3)
Calculate the orthogonal sum of mass function
m1 ⊕m2 ⊕m3
x̂s = arg maxxs
{Pls(Hxs)
Decision making
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 9/18
10/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Compute mass function
For each feature image:
Threshold by Otsu∗ method for shadow index c3
Original image Detected shadow mask
(*)Nobuyuki Otsu, A Threshold Selection Method from Gray-Level Histograms, 1984
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 10/18
10/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Compute mass function
For each feature image:
Threshold by Otsu∗ method for vegetation index ExG
Original image Detected vegetation mask
(*)Nobuyuki Otsu, A Threshold Selection Method from Gray-Level Histograms, 1984
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 10/18
10/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Compute mass function
For each feature image:
Threshold by Otsu∗ method for luminance
Original image Detected dark mask
(*)Nobuyuki Otsu, A Threshold Selection Method from Gray-Level Histograms, 1984
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 10/18
10/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Compute mass function
For each feature image:
Threshold by Otsu∗ method for
Compute mass function using assumption of Gaussian distribution:
mj(Ai) =1
σi√
2πexp
(− (y
(j)s − µi)
2
2σ2i
)
where:
j ∈ {1, 2, 3} (3 sources c3, ExG, L).
i ∈ {1, 2} (2 regions).
µi, σi : mean and the variance on the class Ai present in eachfeature to be fused.
(*)Nobuyuki Otsu, A Threshold Selection Method from Gray-Level Histograms, 1984
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 10/18
11/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Combine different sources
m1(H1),m1(H2 ∪H3),m1(Θ)
m2(H2),m2(H1 ∪H3),m2(Θ)
m3(H3),m3(H1 ∪H2),m3(Θ)
m(A), A ⊂ Θ
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 11/18
12/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Decision-making
For each pixel s, xs ∈ {ω1, ω2, ω3}, once the mass function ofsimple hypothesis Hxs is computed:
x̂s = arg maxxs
{Pls(Hxs)}
Original image Detected shadow/vegetation area
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 12/18
12/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Decision-making
For each pixel s, xs ∈ {ω1, ω2, ω3}, once the mass function ofsimple hypothesis Hxs is computed:
x̂s = arg maxxs
{Pls(Hxs)}
Original image Detected shadow/vegetationarea
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 12/18
13/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Markov random field
Classifying image pixels into different regions under theconstraint of both local observations and spatial relationships.
Probabilistic interpretation:
region labels
x̂ = arg maxx
p(x| y , θ )
image pixels
model parameters
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 13/18
13/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Markov random field
Classifying image pixels into different regions under theconstraint of both local observations and spatial relationships.
Probabilistic interpretation:
region labels
x̂ = arg maxx
p(x| y , θ )
image pixels
model parameters
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 13/18
13/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Markov random field
Classifying image pixels into different regions under theconstraint of both local observations and spatial relationships.
Probabilistic interpretation:
region labels
x̂ = arg maxx
p(x| y , θ )
image pixels
model parameters
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 13/18
13/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Markov random field
Classifying image pixels into different regions under theconstraint of both local observations and spatial relationships.
Probabilistic interpretation:
region labels
x̂ = arg maxx
p(x| y , θ )
image pixels
model parameters
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 13/18
13/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Markov random field
Classifying image pixels into different regions under theconstraint of both local observations and spatial relationships.
Probabilistic interpretation:
region labels
x̂ = arg maxx
p(x| y , θ )
image pixels
model parameters
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 13/18
13/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Markov random field
Classifying image pixels into different regions under theconstraint of both local observations and spatial relationships.
Probabilistic interpretation:
region labels
x̂ = arg maxx
p(x| y , θ )
image pixels
model parameters
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 13/18
14/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Iterated conditional modes algorithm (ICM)
P (xs|y, x̂S−{s}) = p(ys|xs)p(xs|x̂Vs)
Conditional probability: Gaussian distributionPrior probability:
p(xs|x̂Vs) =1
Zexp
−β∑l∈Vs
δ(xs − x̂l)
where:δ stands for the Kronecker’s delta function.Vs is the set of sites neighbouring s.
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 14/18
14/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Iterated conditional modes algorithm (ICM)
P (xs|y, x̂S−{s}) = p(ys|xs)p(xs|x̂Vs)
Conditional probability: Gaussian distributionPrior probability:
p(xs|x̂Vs) =1
Zexp
−β∑l∈Vs
δ(xs − x̂l)
where:δ stands for the Kronecker’s delta function.Vs is the set of sites neighbouring s.
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 14/18
14/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Iterated conditional modes algorithm (ICM)
P (xs|y, x̂S−{s}) = p(ys|xs)p(xs|x̂Vs)
Conditional probability: Gaussian distributionPrior probability:
p(xs|x̂Vs) =1
Zexp
−β∑l∈Vs
δ(xs − x̂l)
where:δ stands for the Kronecker’s delta function.Vs is the set of sites neighbouring s.
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 14/18
14/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Iterated conditional modes algorithm (ICM)
P (xs|y, x̂S−{s}) = p(ys|xs)p(xs|x̂Vs)
Conditional probability: Gaussian distribution
Prior probability:
p(xs|x̂Vs) =1
Zexp
−β∑l∈Vs
δ(xs − x̂l)
where:δ stands for the Kronecker’s delta function.Vs is the set of sites neighbouring s.
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 14/18
14/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Iterated conditional modes algorithm (ICM)
P (xs|y, x̂S−{s}) = p(ys|xs)p(xs|x̂Vs)
Conditional probability: Gaussian distributionPrior probability:
p(xs|x̂Vs) =1
Zexp
−β∑l∈Vs
δ(xs − x̂l)
where:δ stands for the Kronecker’s delta function.Vs is the set of sites neighbouring s.
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 14/18
14/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Iterated conditional modes algorithm (ICM)
P (xs|y, x̂S−{s}) = p(ys|xs)p(xs|x̂Vs)
Conditional probability: Gaussian distributionPrior probability:
p(xs|x̂Vs) =1
Zexp
−β∑l∈Vs
δ(xs − x̂l)
where:δ stands for the Kronecker’s delta function.Vs is the set of sites neighbouring s.
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 14/18
14/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Iterated conditional modes algorithm (ICM)
P (xs|y, x̂S−{s}) = p(ys|xs)p(xs|x̂Vs)
Conditional probability: Gaussian distributionPrior probability:
p(xs|x̂Vs) =1
Zexp
−β∑l∈Vs
δ(xs − x̂l)
where:δ stands for the Kronecker’s delta function.Vs is the set of sites neighbouring s.
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 14/18
15/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
DS evidence theory in Markovian context
Probabilistic framework Evidential framework
p(xs) [Bel(Hxs),Pls(Hxs
)]
Likelihood p(ys|xs) ms(A), Hxs⊆ A
m1 ⊕m2 ⊕m3
Conditionalprobability
p(xs|x̂Vs) ms(A|x̂Vs), Hxs ⊆ A
Posteriorprobability
p(xs|y, x̂S−{s}) Ms(A) = ms(A)⊕ms(A|x̂Vs)
Decisionmaking
x̂s =
arg maxxsp(xs|y, x̂S−{s})
x̂s = arg maxxsPls(Hxs)
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 15/18
15/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
DS evidence theory in Markovian context
Probabilistic framework Evidential framework
p(xs) [Bel(Hxs),Pls(Hxs
)]
Likelihood p(ys|xs) ms(A), Hxs⊆ A
m1 ⊕m2 ⊕m3
Conditionalprobability
p(xs|x̂Vs) ms(A|x̂Vs), Hxs ⊆ A
Posteriorprobability
p(xs|y, x̂S−{s}) Ms(A) = ms(A)⊕ms(A|x̂Vs)
Decisionmaking
x̂s =
arg maxxsp(xs|y, x̂S−{s})
x̂s = arg maxxsPls(Hxs)
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 15/18
15/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
DS evidence theory in Markovian context
Probabilistic framework Evidential framework
p(xs) [Bel(Hxs),Pls(Hxs
)]
Likelihood p(ys|xs) ms(A), Hxs⊆ A
m1 ⊕m2 ⊕m3
Conditionalprobability
p(xs|x̂Vs) ms(A|x̂Vs), Hxs ⊆ A
Posteriorprobability
p(xs|y, x̂S−{s}) Ms(A) = ms(A)⊕ms(A|x̂Vs)
Decisionmaking
x̂s =
arg maxxsp(xs|y, x̂S−{s})
x̂s = arg maxxsPls(Hxs)
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 15/18
15/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
DS evidence theory in Markovian context
Probabilistic framework Evidential framework
p(xs) [Bel(Hxs),Pls(Hxs
)]
Likelihood p(ys|xs) ms(A), Hxs⊆ A
m1 ⊕m2 ⊕m3
Conditionalprobability
p(xs|x̂Vs) ms(A|x̂Vs), Hxs ⊆ A
Posteriorprobability
p(xs|y, x̂S−{s}) Ms(A) = ms(A)⊕ms(A|x̂Vs)
Decisionmaking
x̂s =
arg maxxsp(xs|y, x̂S−{s})
x̂s = arg maxxsPls(Hxs)
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 15/18
15/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
DS evidence theory in Markovian context
Probabilistic framework Evidential framework
p(xs) [Bel(Hxs),Pls(Hxs
)]
Likelihood p(ys|xs) ms(A), Hxs⊆ A
m1 ⊕m2 ⊕m3
Conditionalprobability
p(xs|x̂Vs) ms(A|x̂Vs), Hxs ⊆ A
Posteriorprobability
p(xs|y, x̂S−{s}) Ms(A) = ms(A)⊕ms(A|x̂Vs)
Decisionmaking
x̂s =
arg maxxsp(xs|y, x̂S−{s})
x̂s = arg maxxsPls(Hxs)
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 15/18
15/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
DS evidence theory in Markovian context
Probabilistic framework Evidential framework
p(xs) [Bel(Hxs),Pls(Hxs
)]
Likelihood p(ys|xs) ms(A), Hxs⊆ A
m1 ⊕m2 ⊕m3
Conditionalprobability
p(xs|x̂Vs) ms(A|x̂Vs), Hxs ⊆ A
Posteriorprobability
p(xs|y, x̂S−{s}) Ms(A) = ms(A)⊕ms(A|x̂Vs)
Decisionmaking
x̂s =
arg maxxsp(xs|y, x̂S−{s})
x̂s = arg maxxsPls(Hxs)
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 15/18
15/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
DS evidence theory in Markovian context
Probabilistic framework Evidential framework
p(xs) [Bel(Hxs),Pls(Hxs
)]
Likelihood p(ys|xs) ms(A), Hxs⊆ A
m1 ⊕m2 ⊕m3
Conditionalprobability
p(xs|x̂Vs) ms(A|x̂Vs), Hxs ⊆ A
Posteriorprobability
p(xs|y, x̂S−{s}) Ms(A) = ms(A)⊕ms(A|x̂Vs)
Decisionmaking
x̂s =
arg maxxsp(xs|y, x̂S−{s})
x̂s = arg maxxsPls(Hxs)
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 15/18
16/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Qualitative evaluation
Original image DS fusion DS fusion + MRF
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 16/18
16/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Qualitative evaluation
Original image DS fusion DS fusion + MRF
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 16/18
16/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Qualitative evaluation
Original image DS fusion DS fusion + MRF
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 16/18
16/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Qualitative evaluation
Original image DS fusion DS fusion + MRF
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 16/18
16/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Qualitative evaluation
Original image DS fusion DS fusion + MRF
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 16/18
16/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Qualitative evaluation
Original image DS fusion DS fusion + MRF
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 16/18
17/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Conclusion
Introduces a new scheme to simultaneously detect shadowregions and vegetation regions.
DS evidence theory combine different shadow indices andvegetation indices and estimate the imprecision anduncertainty of information.
Contextual information is taken into account using MRF.
Applied successfully on color aerial images with differentscenes: urbain and rural.
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 17/18
18/18
Introduction DS evidence theory for shadow/vegetation detection Contextual Information Results
Thank you for your attention!Question?
Tran-Thanh NGO, Christophe Collet, Vincent Mazet ICube UMR 7357, Group MIV 18/18
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