Linear and kernel methods for multivariate change detection

doi:10.1016/j.cageo.2011.05.012

Computers & Geosciences

Volume 38, Issue 1, January 2012, Pages 107-114

https://doi.org/10.1016/j.cageo.2011.05.012 Get rights and content

Abstract

The iteratively reweighted multivariate alteration detection (IR-MAD) algorithm may be used both for unsupervised change detection in multi- and hyperspectral remote sensing imagery and for automatic radiometric normalization of multitemporal image sequences. Principal components analysis (PCA), as well as maximum autocorrelation factor (MAF) and minimum noise fraction (MNF) analyses of IR-MAD images, both linear and kernel-based (nonlinear), may further enhance change signals relative to no-change background. IDL (Interactive Data Language) implementations of IR-MAD, automatic radiometric normalization, and kernel PCA/MAF/MNF transformations are presented that function as transparent and fully integrated extensions of the ENVI remote sensing image analysis environment. The train/test approach to kernel PCA is evaluated against a Hebbian learning procedure. Matlab code is also available that allows fast data exploration and experimentation with smaller datasets. New, multiresolution versions of IR-MAD that accelerate convergence and that further reduce no-change background noise are introduced. Computationally expensive matrix diagonalization and kernel image projections are programmed to run on massively parallel CUDA-enabled graphics processors, when available, giving an order of magnitude enhancement in computational speed. The software is available from the authors' Web sites.

Highlights

► Easy-to-use IDL software implementations of change detection and kernel-based postprocessing algorithms are documented. ► Computationally expensive elements are programmed to run optionally on massively parallel CUDA-enabled graphics processors. ► New multiresolution versions of the iteratively re-weighted multivariate alteration detection transformation are presented. ► The train/test approach to kernel principal components analysis is evaluated against a Hebbian learning procedure.

Introduction

In a standard change detection situation involving optical remote sensing imagery, two multi- or hyperspectral images of the same scene are acquired at two different points in time and then compared. Between acquisitions, ground reflectance changes will have occurred at some locations, but in general not everywhere. In order to observe the changes, the images are accurately registered to one another and—optionally—corrected for atmospheric and illumination effects. The necessary preprocessing steps having been performed, it is common to examine functions of the spectral bands (differences, ratios, or other linear or nonlinear band combinations) that bring change information contained within them to the fore. Singh (1989) gives a good, but now somewhat outdated, survey of change detection algorithms for remotely sensed data. For more recent reviews in a more general context, see Radke et al. (2005) or Coppin et al. (2004) and in the context of very-high-resolution imagery, Marchesi et al. (2010). Alternatively, the objective may not be to observe change, but rather to eliminate relative differences between the images arising from effects due to the atmosphere, sensor gain, or differing solar illumination conditions. This can sometimes be achieved by linear radiometric normalization using invariant pixels identified within the images, that is, on the basis of no-change rather than change observations (Schott et al., 1988, Hall et al., 1991, Moran et al., 1992, Yang and Lo, 2000, Furby and Campbell, 2001, Du et al., 2002).

In a series of publications (Nielsen et al., 1998, Canty et al., 2004, Canty and Nielsen, 2006, Canty and Nielsen, 2008, Nielsen, 2007), the multivariate alteration detection (MAD) transformation and a modification involving iterative reweighting (IR-MAD or iMAD) were proposed, both for unsupervised change detection and for automatic radiometric normalization. More recently, Nielsen (2011) discussed, among other applications, the successful use of kernel versions of maximum autocorrelation factor (MAF) and minimum noise fraction (MNF) transformations for the postprocessing of difference images for change detection.

In this contribution, we present efficient and easy-to-use software implementations for IR-MAD and radiometric normalization, as well as for kernelized versions of principal components analysis (PCA), and the MAF and MNF transformations. The paper is organized as follows. In Section 2 we briefly outline the IR-MAD transformation, pointing out its advantages both for change detection and for radiometric normalization, and introduce new, multiresolution variants of IR-MAD. In Section 3 the kernel methods are summarized. In Section 4 we outline some specific choices made in the software implementations and describe IDL and Matlab programs for IR-MAD, radiometric normalization, kernel PCA, MAF, and MNF. The IDL routines, which function as fully integrated extensions of the ENVI remote sensing image analysis environment, can run on conventional CPU architectures as well as take advantage of the massively parallel capabilities of graphics processors. In Section 5, examples illustrating IR-MAD applied to multispectral imagery and the postprocessing of change images with kernel transformations are presented and the adopted train/test approach to kernel transformations is examined. Conclusions are drawn in Section 6.

Section snippets

Change detection

The observations (pixel vectors) in a bitemporal, p-band, multispectral image may be represented by random vectors $X = (X_{1} \dots X_{p})^{T}$ and $Y = (Y_{1} \dots Y_{p})^{T}$ for the first and second acquisitions, respectively. The components X_i and Y_i correspond to the original spectral bands and are conventionally ordered by wavelength. The MAD algorithm determines transformation matrices $A = (a_{1}, a_{2} \dots a_{p}), B = (b_{1}, b_{2} \dots b_{p})$ such that the components of the transformed random vectors $U = A^{T} X, V = B^{T} Y$ are ordered by similarity, where similarity

Kernel transformations for postprocessing

As opposed to linear spectral transformations (PCA, MAF/MNF), nonlinear transformations, especially kernel MAF/MNF analysis of difference images, have been found to give conspicuously better suppression of both noise and signal in the no-change background (Nielsen, 2011). The kernel versions of PCA and MAF/MNF handle nonlinearities by implicitly transforming data by nonlinear mapping functions $ϕ$ into higher, even infinite, dimensional feature space and then performing a linear analysis in that

Software

High-level program scripts were written in IDL and Matlab to code the methods outlined in the two preceding sections and are described below in 4.1 ENVI/IDL, 4.2 Matlab, respectively. We present first some general design decisions made in the implementations.

Sign ambiguity: To avoid ambiguity in the signs of the canonical transformations and hence of the IR-MAD variates, it was required that the correlations of the canonical variates, like those of the original bitemporal image bands, be

Examples

In previous publications, several studies of the application of IR-MAD and its associated automatic radiometric normalization to multi- and hypervariate imagery have been given (Canty et al., 2004, Canty and Nielsen, 2006, Canty and Nielsen, 2008, Nielsen, 2007). Therefore, in this section, we restrict ourselves to examples involving the new multiresolution algorithms (Section 2.3) and kernel postprocessing (Section 3).

Conclusion

We have presented and illustrated efficient and easy-to-use IDL and Matlab software for multivariate change detection and radiometric normalization as well as for kernelized versions of principal components, maximum autocorrelation factors, and maximum noise fraction transformations. Comparison with the kernel Hebbian algorithm indicates that the use of 1% subsampling for kernel methods will give satisfactorily reproducible results for the first five or six eigenvectors. We have also introduced

Acknowledgment

Thanks to Dr. Luis Gomez-Chova, University of Valencia, Spain, for suggesting the centering of the test data with the training data mean.

References (25)

M.J. Canty et al.
Automatic radiometric normalization of multitemporal satellite imagery with the iteratively re-weighted MAD transformation
Remote Sensing of Environment
(2008)
M.J. Canty et al.
Automatic radiometric normalization of multitemporal satellite imagery
Remote Sensing of Environment
(2004)
Y. Du et al.
Radiometric normalization of multitemporal high-resolution images with quality control for land cover change detection
Remote Sensing of Environment
(2002)
S.L. Furby et al.
Calibrating images from different dates to like-value counts
Remote Sensing of Environment
(2001)
F.G. Hall et al.
Radiometric rectification: Toward a common radiometric response among multidate, multisensor images
Remote Sensing of Environment
(1991)
A.A. Nielsen et al.
Multivariate alteration detection (MAD) and MAF post-processing in multispectral, bitemporal image data: New approaches to change detection studies
Remote Sensing of Environment
(1998)
J.R. Schott et al.
Radiometric scene normalization using pseudo-invariant features
Remote Sensing of Environment
(1988)
M.J. Canty et al.
Visualization and unsupervised classification of changes in multispectral satellite imagery
International Journal of Remote Sensing
(2006)
P. Coppin et al.
Digital change detection methods in ecosystem monitoring: a review
International Journal of Remote Sensing
(2004)
I. Daubechies
Orthonormal bases of compactly supported wavelets
Communications on Pure and Applied Mathematics
(1988)

S. Günter et al.

Fast iterative kernel principal component analysis

Journal of Machine Learning Research

(2007)

Halfhill, T.R., 2008. Parallel processing with CUDA. In: Microprocessor Report, Reed Electronics, Scottsdale, Az, pp....

Cited by (34)

A general and extensible framework for assessing change detection techniques
2023, Computers and Geosciences
Change detection techniques play an essential role in Remote Sensing applications, such as environmental monitoring, governmental planning, and studies of areas affected by natural disasters. This fact makes the development of more accurate change detection techniques a constant challenge. However, the lack of public benchmarks available to analyze and compare the performance of change detection techniques hampers quantitative comparisons. In light of this reality, this study proposes and formalizes a novel framework for imagery dataset simulation. In contrast with other image simulation methods, images synthesized by the proposed method are explicitly designed to assess and compare change detection methods. The framework is extensible and general allowing, in particular, the use of both supervised and unsupervised change detection methods. As an application, we compare the performance of well-known algorithms to data sets that mimic what the Landsat 5 TM sensor observed over a forest area subjected to deforestation for agricultural purposes. The results support discussing the performance of methods and show the usefulness of the proposed framework. We provide the source codes in a public repository.
Semi-supervised label propagation for multi-source remote sensing image change detection
2023, Computers and Geosciences
Citation Excerpt :
Many works have emerged for change detection in recent years. They can be broadly divided into supervised (Volpi et al., 2013; Camps-Valls et al., 2008; Qin et al., 2006) and unsupervised change detection (Celik, 2009; Canty and Nielsen, 2012; Ouma et al., 2008) according to whether the prior knowledge exists or not (Lu et al., 2004). Supervised change detection is mainly based on the classification framework (Camps-Valls et al., 2008), but it needs a large number of labeled training data, which brings large consumptions of time and labor.
Remote sensing image change detection remains a challenging task. Most existing approaches are based on fully supervised learning, but labeled data are so scarce for change detection. It is difficult to exhibit high detection performance with a limited amount of labeled data. In this paper, we propose a semi-supervised Label Propagation (SSLP) approach for multi-source remote sensing image change detection. First, a clustering label propagation (CLP) method is designed to cluster pre and post images, respectively, and assign pseudo labels to unlabeled pixel pairs that have similar mapping relationships to labeled pixel pairs. Second, a pixel density metric is investigated to filter out the data with low density and retain the data with high density, which can ensure the reliability of the propagated data. Third, a secondary expansion method based on pixel neighborhood is used to generate enough training data for training a classifier. Finally, the effectiveness of SSLP is validated on three real datasets by comparing to other related methods.
Modelling the spatial impact of regional planning and climate change prevention strategies on land consumption in the Rhine-Ruhr Metropolitan Area 2017–2030
2022, Landscape and Urban Planning
Citation Excerpt :
Following the generation of accurate output for the baseline year, the iteratively reweighted multivariate alteration detection (IR-MAD) was used (Nielsen, 2007; Canty & Nielsen, 2008), in order to derive the areas with no change, which are the base for the extraction of reference samples for the classification of the preceding time steps. The IR-MAD transformation identifies suitable invariant pixels for radiometric normalization with an multivariate change detection algorithm (Pal, 2005) that iteratively increases the weight of non-change observations and thereby enhances the discrimination of substantial spectral changes between images from different time periods (Yang & Sun, 2017; Canty & Nielsen, 2012). A stepwise classification framework to former years by selecting new training samples through the integration of spectral information from unchanged pixels was applied (Ghazaryan et al., 2021).
Urban sprawl is a ubiquitous with a complex network of driving forces and human and natural impacts on various scales of the coupled human-environment urban system. In Germany, a land consumption of 30 ha per day is envisaged. In that regard, the effect of growing metropolitan areas on the climate of local neighborhoods becomes more and more a topic in regional planning. Accordingly, the objectives of the study are a) to contribute to the climate change related land cover simulation efforts in Germany in a spatially explicit manner with a resolution of 30 m, b) to investigate future land consumption rates and population growth rates having a view on goal 11 of UN’s SDG, and c) analyze the spatial impact of planning policies in regard to land use planning and official climate change prevention strategies using Rhine-Ruhr Metropolitan Area (RRMA) in Western Germany as a study area. The study makes use of land use and land cover classification of multispectral satellite data and the derivation of land surface temperature based on Landsat satellite in order to calibrate and validate the urban growth model SUSM (scenario-based urban growth simulation model). Two scenarios for future land consumption 2030 are implemented and the future impacts of urban growth with the projection of land consumption rate (LCR), population growth rate (PGR), and LCRPGR index on municipality level, as well as the impact on regions vulnerable to climate change evaluated. The comparison of simulated urban growth to observed urban growth from 2005 to 2017 shows that the PA of SUSM for historic scenario is 68.06% with an overall accuracy of 97.15%, a Matthews correlation coefficient of 0.66, a figure of merit of 0.51 and area under curve of 0.84. The total quantity of new urban areas of our SUSM simulation 2030 were approximately 283 km². While the difference in the simulated total quantity is nearly zero, the simulated allocation of new urban areas across the districts can differ by up to 25 km² in the two scenarios. The number of municipalities with efficient urban land development rates increases in the SUSM scenario where no regional land development plan has been incorporated. This holds true for the number of municipalities with inefficient land use where even an increase from no plan to plan can be observed. LCRPGR is negative in most municipalities reflecting opposing trends of population and land consumption development. Most of new urban areas are distributed in open spaces important for the regional climate change prevention strategy. 32.98 % of new urban areas in our region of interest can be found in these zones in the planning scenario and 25.76 % in the scenario without planning information in SUSM model. It can be concluded that regional planning in RRMA region has no positive effect on the interregional development of future land consumption in terms of quantity, allocation, and impact on climate change prevention.
Signal-to-noise ratio in reproducing kernel Hilbert spaces
2018, Pattern Recognition Letters
Citation Excerpt :
Gómez-Chova et al. [7] extended the standard formulation by studying both signal and noise directly in the feature space (explicit kMNF). In this way, kSNR can effectively express nonlinear relations between signal and noise and, at the same time, reduces the number of parameters needed [4,5]. Later, we introduced in [6] the main ideas for exploiting the presented kSNR in machine learning applications beyond feature extraction.
This paper introduces the kernel signal-to-noise ratio (kSNR) for different machine learning and signal processing applications. The kSNR seeks to maximize the signal variance while minimizing the estimated noise variance explicitly in a reproducing kernel Hilbert space (rkHs). The kSNR gives rise to considering complex signal-to-noise relations beyond additive noise models, and can be seen as a useful regularizer for feature extraction and dimensionality reduction. We show that the kSNR generalizes kernel PCA (and other spectral dimensionality reduction methods), least squares SVM, and kernel ridge regression to deal with cases where signal and noise cannot be assumed independent. We give computationally efficient alternatives based on reduced-rank Nyström and projection on random Fourier features approximations, and analyze the bounds of performance and its stability. We illustrate the method through different examples, including nonlinear regression, nonlinear classification in channel equalization, nonlinear feature extraction from high-dimensional spectral satellite images, and bivariate causal inference. Experimental results show that the proposed kSNR yields more accurate solutions and extracts more noise-free features when compared to standard approaches.
Finding a needle by removing the haystack: A spatio-temporal normalization method for geophysical data
2016, Computers and Geosciences
Citation Excerpt :
Spatial information is commonly used in satellite image processing. Such image processing techniques have been applied, among others, for feature extraction (e.g. van der Werff et al., 2006; Soto-Pinto et al., 2013), change detection (e.g. Coppin et al., 2004; Canty and Nielsen, 2012), normalization of specific influences in the satellite signal (e.g. Yang and Lo, 2000; Canty and Nielsen, 2008; Ulusoy et al., 2012), active fire monitoring (e.g. Giglio et al., 1999, 2003; Ichoku et al., 2003; Stolle et al., 2004; Kuenzer et al., 2007, 2008; Calle et al., 2008; Xu et al., 2010; Wooster et al., 2012), and studies of volcanic and geothermal activity (e.g. Coolbaugh et al., 2007; Ganci et al., 2011; Koeppen et al., 2011; Murphy et al., 2011; Steffke and Harris, 2011; Gutierrez et al., 2012; Vaughan et al., 2012; Blackett, 2014, 2015; van der Meer et al., 2014). A main aim is often the selection of an optimum background: this is used to contrast with an expected change or to describe a representative average state of a given neighbourhood.
We introduce a normalization algorithm which highlights short-term, localized, non-periodic fluctuations in hyper-temporal satellite data by dividing each pixel by the mean value of its spatial neighbourhood set. In this way we suppress signal patterns that are common in the central and surrounding pixels, utilizing both spatial and temporal information at different scales. We test the method on two subsets of a hyper-temporal thermal infra-red (TIR) dataset. Both subsets are acquired from the SEVIRI instrument onboard the Meteosat-9 geostationary satellite; they cover areas with different spatiotemporal TIR variability. We impose artificial fluctuations on the original data and apply a window-based technique to retrieve them from the normalized time series. We show that localized short-term fluctuations as low as 2 K, which were obscured by large-scale variable patterns, can be retrieved in the normalized time series. Sensitivity of retrieval is determined by the intrinsic variability of the normalized TIR signal and by the amount of missing values in the dataset. Finally, we compare our approach with widely used techniques of statistical and spectral analysis and we discuss the improvements introduced by our method.
Change Detection Analysis using Bitemporal PRISMA Hyperspectral Data: Case Study of Magelang and Boyolali Districts, Central Java Province, Indonesia
2022, Journal of the Indian Society of Remote Sensing

View all citing articles on Scopus

^☆: Code available from: http://mcanty.homepage.t-online.de/software.html, http://www2.imm.dtu.dk/∼aa/software.html.

View full text

Linear and kernel methods for multivariate change detection☆

Abstract

Highlights

Introduction

Section snippets

Change detection

Kernel transformations for postprocessing

Software

Examples

Conclusion

Acknowledgment

Remote Sensing of Environment

Remote Sensing of Environment

Remote Sensing of Environment

Remote Sensing of Environment

Remote Sensing of Environment

Remote Sensing of Environment

Remote Sensing of Environment

Visualization and unsupervised classification of changes in multispectral satellite imagery

International Journal of Remote Sensing

Digital change detection methods in ecosystem monitoring: a review

International Journal of Remote Sensing

Orthonormal bases of compactly supported wavelets

Communications on Pure and Applied Mathematics

Fast iterative kernel principal component analysis

Journal of Machine Learning Research