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Motivation & Aim Traditional Change Analysis Techniques Pseudo-code for Change Analysis in SITS Experiments Conclusions

A L2-Norm Regularized Pseudo-Code for Change Analysis 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 2014 First International Workshop on Learning over Multiple Contexts @ ECML

• A. Radoi, M. Datcu

A L2-Norm Regularized Pseudo-Code for Change Analysis

Motivation & Aim Traditional Change Analysis Techniques Pseudo-code for Change Analysis in SITS Experiments Conclusions

1

Motivation & Aim

2

Traditional Change Analysis Techniques

3

Pseudo-code for Change Analysis in SITS

4

Experiments

5

Conclusions

• A. Radoi, M. Datcu

A L2-Norm Regularized Pseudo-Code for Change Analysis

Motivation & Aim Traditional Change Analysis Techniques Pseudo-code for Change Analysis in SITS Experiments Conclusions

Motivation

Big Data - the actual technological developments bring large quantities of information that have to be understood and classified fast & precise Earth Observation - increasing interest in satellite image time series (SITS)

• A. Radoi, M. Datcu

A L2-Norm Regularized Pseudo-Code for Change Analysis

Motivation & Aim Traditional Change Analysis Techniques Pseudo-code for Change Analysis in SITS Experiments Conclusions

Motivation

Big Data - the actual technological developments bring large quantities of information that have to be understood and classified fast & precise Earth Observation - increasing interest in satellite image time series (SITS) ⇒ Discover patterns of change in the temporal data

• A. Radoi, M. Datcu

A L2-Norm Regularized Pseudo-Code for Change Analysis

Motivation & Aim Traditional Change Analysis Techniques Pseudo-code for Change Analysis in SITS Experiments Conclusions

Motivation

Big Data - the actual technological developments bring large quantities of information that have to be understood and classified fast & precise Earth Observation - increasing interest in satellite image time series (SITS) ⇒ Discover patterns of change in the temporal data ⇒ Data mining in change analysis

• A. Radoi, M. Datcu

A L2-Norm Regularized Pseudo-Code for Change Analysis

Is there any difference?

Is there any difference?

June 2001 October 2001 LANDSAT 7 : April 15, 1999 - still operational 16 days revisit time Our change analysis aims to:

1 reveal more than what we can learn by simply screening the

images (preferably, in an unsupervised way);

2 describe the dynamic evolution of the Earth’s surface 3 keep the main properties (e.g., user-defined class) even in a

time-evolving context of change.

Motivation & Aim Traditional Change Analysis Techniques Pseudo-code for Change Analysis in SITS Experiments Conclusions

Traditional Change Analysis Techniques

algebra-based techniques: image differencing and image rationing I(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 used pros: simple to implement, low complexity cons: 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.

• A. Radoi, M. Datcu

A L2-Norm Regularized Pseudo-Code for Change Analysis

Motivation & Aim Traditional Change Analysis Techniques Pseudo-code for Change Analysis in SITS Experiments Conclusions

Proposed Approach

Encode change by minimizing a convex 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

2

2 + λ · di ⊙ C(t) λ,i2 2

• (3)

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

i }N i=1 descriptors

C(t)

λ =

• C(t)

λ,1, C(t) λ,2, . . . , C(t) λ,N

• ∈ Rd×N set of learned codes
• A. Radoi, M. Datcu

A L2-Norm Regularized Pseudo-Code for Change Analysis

Motivation & Aim Traditional Change Analysis Techniques Pseudo-code for Change Analysis in SITS Experiments Conclusions

Datasets & Features

Dataset: Landsat 7 SITS

Multispectral: visible (R,G,B), near-IR (NIR), shortwave IR (SWIR 1,2) Period: 2001 – 2003 Spatial resolution: 30 meters Location: 59 × 51 km2 around Bucharest, Romania

Features

Pixel-level: intensity of each pixel Patch-level: sparse representation of each patch

• A. Radoi, M. Datcu

A L2-Norm Regularized Pseudo-Code for Change Analysis

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 · ti2

2 + µ · ti1

• ,

(4) where B = [Bj]j=1,...,d – learned dictionary ti – d - dimensional vectors that represent the projection of vector Yi onto the learned dictionary B ·2 and ·1 – L2 - norm and L1 - norm µ 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}4

j=1

K clusters determined with K-Means → {Ck}K

k=1

nk,j = |Ck ∩ Sj|, nk =

j nk,j, nj = k nk,j

Complete agreement or independent partitions?

Purity = 1 N

K

• k=1

max

j=1,...,|S| |Ck ∩ Sj|

(5) ARI(C, S) =

• k,j

nk,j 2

• −
• k

nk 2

j

nj 2

• N

2

• k

nk 2

• +

j

nj 2

• 2

−

• k

nk 2

j

nj 2

• N

2

• (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 20 60 65 70 75 80 85 90 95 100 Number of clusters Purity [%] Pixels difference Pixels ratio Pixels, λ = 0.5 Pixels, λ = 1 Pixels, λ = 5 Patches difference Patches Ratio Patches, λ = 0.5 Patches, λ = 1 Patches, λ = 5

(a) Purity

4 6 8 10 12 14 16 18 20 0.1 0.2 0.3 0.4 0.5 0.6 Number of clusters ARI Pixels difference Pixels ratio Pixels, λ = 0.5 Pixels, λ = 1 Pixels, λ = 5 Patches difference Patches ratio Patches, λ = 0.5 Patches, λ = 1 Patches, λ = 5

(b) ARI

Figure : Performance measures

Motivation & Aim Traditional Change Analysis Techniques Pseudo-code for Change Analysis in SITS Experiments Conclusions

Conclusions

1 Purity increases with the number of clusters

ARI decreases with the number of clusters ⇒ compromise determine the optimal number of clusters

2 The proposed pseudo-encoder leads to a better separation of

K-Means clusters (types of changes)

3 The method keeps the intrinsic properties as perceived by a

user even if the context changes over time

4 O(C) ≈ O(DIFF) ≈ O(R)

• A. Radoi, M. Datcu

A L2-Norm Regularized Pseudo-Code for Change Analysis