a l2-norm regularized pseudo-code for change analysis...

Motivation & AimTraditional Change Analysis Techniques

Pseudo-code for Change Analysis in SITSExperimentsConclusions

A L2-Norm Regularized Pseudo-Code for ChangeAnalysis in Satellite Image Time Series

A. Radoi1 M. Datcu2

1Research Center for Spatial Information (CEOSpaceTech)Dept. of Applied Electronics, University Politehnica of Bucharest

2German Aerospace Center (DLR)

LMCE 2014First International Workshop on Learning over Multiple

Contexts @ ECML

A. Radoi, M. Datcu A L2-Norm Regularized Pseudo-Code for Change Analysis

@



1 Motivation & Aim

2 Traditional Change Analysis Techniques

3 Pseudo-code for Change Analysis in SITS

4 Experiments

5 Conclusions




Motivation

Big Data - the actual technological developments bring largequantities of information that have to be understood andclassified fast & precise

Earth Observation - increasing interest in satellite image timeseries (SITS)

⇒ Discover patterns of change in the temporal data⇒ Data mining in change analysis




Motivation



⇒ Discover patterns of change in the temporal data

⇒ Data mining in change analysis




Motivation



⇒ Discover patterns of change in the temporal data⇒ Data mining in change analysis


Is there any difference?

June 2001 October 2001LANDSAT 7 :

April 15, 1999 - still operational16 days revisit time

Our change analysis aims to:

1 reveal more than what we can learn by simply screening theimages (preferably, in an unsupervised way);

2 describe the dynamic evolution of the Earth’s surface3 keep the main properties (e.g., user-defined class) even in a

time-evolving context of change.



Traditional Change Analysis Techniques

algebra-based techniques: image differencing and image rationingI(t−1) and I(t) two temporal images

DIFF(t) = I(t) − I(t−1) (1)

R(t) =I(t)

I(t−1)(2)

most frequently usedpros: simple to implement, low complexitycons: not good at revealing the types of the changes

linear transformations (e.g., PCA, Tasseled Cap Transform)

classification-based methods (e.g., NN, ANN)

combinations of the above methods.




Proposed Approach

Encode change by minimizing aconvex cost function:

I(t−1) I(t)

Descriptor D(t−1) Descriptor D(t)

Change matrix C(t)λ = Cλ(D(t−1),D(t))

K-Means clustering

Change Maps

J(C(t)λ ) =

N∑i=1

(‖D(t)

i − C(t)λ,i �D

(t−1)i ‖22 + λ · ‖di � C

(t)λ,i‖

22

)(3)

Images divided into N non-overlapping p × p patches ⇒ {D(t)i }

Ni=1 descriptors

C(t)λ =

[C(t)λ,1,C(t)

λ,2, . . . ,C(t)λ,N

]∈ Rd×N set of learned codes




Datasets & Features

Dataset: Landsat 7 SITSMultispectral: visible (R,G,B), near-IR (NIR), shortwave IR (SWIR 1,2)Period: 2001 – 2003Spatial resolution: 30 meters

Location: 59 × 51 km2 around Bucharest, Romania

Features

Pixel-level: intensity of each pixel

Patch-level: sparse representation of each patch


Learning sparse image representations

Given:

Image divided into N non-overlapping p × p patches

Each patch Xi ∈ Rp×p → column-wise version Yi ∈ Rp2×1

Solve: the minimization problem

J ′ (B, {ti}i=1,...,N) =n∑

i=1

(‖Yi − B · ti‖22 + µ · ‖ti‖1

), (4)

whereB = [Bj ]j=1,...,d – learned dictionaryti – d - dimensional vectors that represent the projection of vectorYi onto the learned dictionary B‖·‖2 and ‖·‖1 – L2 - norm and L1 - normµ models the degree of sparsity for the representation.Solution: stochastic gradient descent

Learning sparse image representations

(a) Blue filterbank (b) Green filterbank (c) Red filterbank

(d) NIR filterbank (e) SWIR1 filterbank (f) SWIR2 filterbank

Figure : Learned filterbanks from SITS

Clustering performance measures

Descriptor D(t−1) Descriptor D(t)

Change matrix C(t)λ = Cλ(D(t−1),D(t))

K-Means clustering

Given: N feature points divided in:

4 ground-truth classes (Water, Urban,Forest, Agriculture) → {Sj}4j=1

K clusters determined with K-Means→ {Ck}Kk=1

nk,j = |Ck ∩ Sj |, nk =∑

j nk,j , nj =∑

k nk,j

Complete agreement or independent partitions?

Purity =1

N

K∑k=1

maxj=1,...,|S|

|Ck ∩ Sj | (5)

ARI(C,S) =

∑k,j

(nk,j2

)−

∑k

(nk2

)∑j

(nj2

)(N2

)∑

k

(nk2

)+∑

j

(nj2

)2

−∑

k

(nk2

)∑j

(nj2

)(N2

)(6)

Results

(a) Image from SITS

void water forest agriculture urban

(b) Ground truth 2001 - 2002

void C1 C2 C3 C4 C5 C6 C7 C8 C9 C10

(c) Clustering map pixel-level

void C1 C2 C3 C4 C5 C6 C7 C8 C9 C10

(d) Clustering map patch-level

Results

4 6 8 10 12 14 16 18 2060

65

70

75

80

85

90

95

100

Number of clusters

Pu

rity

[%

]

Pixels differencePixels ratioPixels, λ = 0.5Pixels, λ = 1Pixels, λ = 5Patches differencePatches RatioPatches, λ = 0.5Patches, λ = 1Patches, λ = 5

(a) Purity

4 6 8 10 12 14 16 18 20

0

0.1

0.2

0.3

0.4

0.5

0.6

Number of clusters

AR

I

Pixels differencePixels ratioPixels, λ = 0.5Pixels, λ = 1Pixels, λ = 5Patches differencePatches ratioPatches, λ = 0.5Patches, λ = 1Patches, λ = 5

(b) ARI

Figure : Performance measures



Conclusions

1 Purity increases with the number of clustersARI decreases with the number of clusters⇒ compromise determine the optimal number of clusters

2 The proposed pseudo-encoder leads to a better separation ofK-Means clusters (types of changes)

3 The method keeps the intrinsic properties as perceived by auser even if the context changes over time

4 O(C ) ≈ O(DIFF ) ≈ O(R)


a l2-norm regularized pseudo-code for change analysis...

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