Remote Sensing Image Change Detection Based on Low-Rank Representation - Advances in Image and Graphics Technologies - page 337

analysis (PCA) [7] and vegetation index differencing [8].Therefore, in this paper, we
focus on the problem of unsupervised change detection.
As mentioned in [5], the procedure of unsupervised change detection algorithms
has three major steps generally: (1) image preprocessing, (2) obtaining the difference
image, and (3) analyzing the difference image and post-processing. Among them, the
construction of difference map can greatly affect the result of change detection. Al-
though we can use some conventional methods ( e . g ., subtraction or logarithm ratio
operator), they cannot make full use of multi-temporal remote sensing images. There-
fore, how to obtain more accurate difference image is still an open problem.
On the other hand, low-rank representation (LRR) [9] has attracted wide concern in
computer vision and machine learning field. Compared with sparse representation
(SR) [10, 11] which computes the sparse representation of each data vector indivi-
dually, LRR makes use of matrix decomposition to obtain the low-rank and sparse
parts of data vectors jointly which can reveal the common and specific characteristics
of data. Considering the problem of change detection, if we use LRR to decompose
the matrix consisting of multi-temporal images, the low-rank part will correspond to
the unchanged areas and the sparse part will correspond to the changed areas. In other
words, the difference image can be generated by the sparse part. Therefore, LRR can
effectively detect the change information from a global perspective.
Motivated by the above discussion, in this paper, we propose an unsupervised me-
thod for change detection, which applies subtraction operator, logarithm ratio operator
and LRR to construct the difference image. Specifically, we firstly use the subtraction
and logarithm ratio operators to generate two difference images. At the same time, we
apply LRR to decompose the data matrix which is composed of the image before
change and the image after change. Based on these three difference images, LRR is
used again to extract the low-rank part from three difference images, which can re-
flect the common characteristics of them and thus can be viewed as the final differ-
ence result. Finally k -means is applied to cluster the final difference image into two
clusters. Experiments on real remote sensing images demonstrate the feasibility and
effectiveness of the proposed method.
The contribution of this paper includes two aspects. On one hand, we propose a
novel method of generating the difference image through LRR. Since LRR can de-
scribe the common and specific characteristics of data, it can detect the change infor-
mation of multi-temporal images. On the other hand, we use the LRR-based fusion
scheme to combine multiple difference images constructed by various change detec-
tion methods, which can effectively improve the stability of change detection.
The remainder of this paper is organized as follows: Section 2 describes low-rank
representation (LRR) in detail. Section 3 introduces the proposed method. Section 4
presents the experimental results and the conclusion is given in Section 5.

2 Low-Rank Representation

2.1

Algorithm Description

[ ]

As proposed in [9], for a set of data vectors

Xxx x =

1 ,,, n

 (each column is a sam-

ple) in

D

, the decomposition model that approximates matrix X can be characterized:

R