Towards a polyalgorithm for land use change detection
Introduction
Land use change is described as changes in how humans use the surface of the Earth (e.g., for agriculture, plantations, pastures, managed woods, conservation, settlements, or leaving it alone as natural ecosystem). Changes in land use lead to changes in albedo, thereby directly affecting the temperatures of the surrounding area. Significant and lasting changes in land use and land cover (LULC) have more profound effects. The past century has seen an exponential growth in human activities such as deforestation and urbanization causing significant changes in land cover in several parts of the world (Hansen et al., 2013). Simultaneously, significant changes in the global climate have also been observed, driven in part by LULC change (LULCC) (e.g., Fall et al., 2010). LULCC also has impacts on a wide variety of other ecosystem services. Monitoring LULCC across the globe, therefore, has become the need du jour. Land use change detection comprises any methodology used for determining the occurrence and nature of change in LULC.
Earth observation satellites (EOS) such as Landsat capture images of the Earth’s surface at regular intervals using multiple spectral frequencies. These images hold valuable information that, if harnessed well, can be immensely helpful in understanding, monitoring, and managing our natural resources, as well as studying LULCC. One way of analyzing these satellite images for LULCC studies is time series analysis (or, temporal trajectory analysis). For time series analysis, several images of the scene under consideration, taken over a period of time, are stacked together chronologically and subsequently analyzed. Commonly, the time series for each pixel is treated individually; the full image stack is thus a collection of many time series. The choice of spectral band(s) varies from application to application. The objective is to discover a ‘trend’ in how different relevant variables (indicators) evolve over time. In change detection analysis, when the trajectory of one or more of the variables departs from the normal, a change is detected. Time series analysis for LULCC studies has been receiving increasing attention in the last decade, specifically, after the Landsat data became freely accessible in 2008 (Woodcock et al., 2008). Several time series analysis algorithms have been proposed by different groups in the remote sensing community.
Despite a plethora of time series analysis algorithms available in remote sensing, design and selection of algorithms for LULCC detection in remote sensing appears to be almost always context specific. Most of the methods proposed to date seem to perform well on the type of data that they are designed for. Their performance on randomly picked datasets from across the globe has not been studied. The onus of choosing an appropriate algorithm that will perform well on their particular dataset falls on the user. Unfortunately, no single algorithm designed so far seems to work for all datasets (Cohen et al., 2017). For example, the Western Antarctica as well as the Greenland Ice Sheets are beginning to collapse due to global warming, the melting leading to continually receding snow covers at the respective locations. For these regions, using LULC algorithms based on periodicity assumptions is expected to lead to incorrect predictions and/or false alarms, although the nature and extent of this has not been studied yet. Even if there were no global warming, mild shifts in the ‘phase’ and ‘amplitude’ of seasons are known to take place (Petitjean et al., 2011). Time warping techniques (Petitjean et al., 2011) to deal with these issues may be helpful in some contexts, but their accuracy and scalability has not yet been satisfactorily investigated. Approaches based on periodicity and a moving window are possible, with additional computational costs.
A polyalgorithm is an effective strategy to unite the strengths and circumvent the weaknesses of multiple algorithms that are also individually designed to solve the same problem. The concept of polyalgorithm was introduced by Rice and Rosen (1966). A polyalgorithm uses a combination of several basic methods in a framework. Each of these basic methods is applicable to the same problem, with only their performance and/or success being different for different datasets (inputs). The construction of this framework involves experimenting with an increasingly heterogeneous set of situations to evolve a robust algorithm that is capable of choosing a correct subset of algorithms suitable for a given input, and has performance metrics to integrate their outputs. The details of algorithm selection and processing stay hidden from the user. Polyalgorithms have been designed in the past for solving various problems, for example, nonlinear systems of equations (Rice and Rosen, 1966, Rice, 1969, Rice, 2014, Rice, 1967), matrix computations on parallel architectures (Li, 1996, Häfner et al., 1999), and certain chemical models (Gomeni and Gomeni, 1979).
This work lays the foundation for a polyalgorithm for LULCC detection. Three currently existing, fundamentally different from each other, change detection algorithms are utilized. A similar work in this direction is Zhan et al. (2002), wherein a framework is developed to evaluate five different algorithms on the input dataset, compare them based on certain scores, and then return the best results. Similar approaches are also gaining ground recently in the field of classification algorithms (Dietterich et al., 2001, Kittler et al., 1998, Wozniak et al., 2014). Most recently, in Healey et al. (2017), multiple change detection algorithms are utilized to build a decision trees based ensemble algorithm for LULCC.
The rest of this paper is organized as follows: Section 2 presents background on state-of-the-art change detection algorithms available in remote sensing, puts them in the context of the general time series literature, and explains the choice of algorithms used in this work. Section 3 defines the notation. Sections 4 Exponentially weighted moving average change detection (EWMACD), 5 LandTrendR, 6 Breaks for additive and seasonal trend (BFAST) describe three different trend and change detection algorithms — EWMACD, BFAST, and LandTrendR; experimental results demonstrating the successes, failures, and sensitivity to parameters for each algorithm are presented. Prospects for a viable polyalgorithm are discussed in Sections 7 Prospects for a viable polyalgorithm, 8 Conclusions and future work concludes with an assessment and future work.
Section snippets
Background
Most of the LULC algorithms proposed in the remote sensing literature can be divided into two categories: bitemporal analysis and temporal trajectory analysis. Bitemporal analysis was more popular before 2008 (when the availability of satellite data to the public was very limited) and forms the classical way of analyzing images — these algorithms analyze changes occurring between two images (dates). The more preferred bitemporal algorithms rely on image differencing (Banner and Lynham, 1981,
Preliminaries
Notation and definitions. For an matrix A, an n-vector , let denote the submatrix of A formed from the rows indexed by I and the columns indexed by J, and denote the subvector of x indexed by J. () are the rows (columns) of A indexed by I (J), respectively. An image is an matrix D, where each (pixel) is an matrix, whose element is the signal value at time index s and frequency band index b. is the number of missing data values
Exponentially weighted moving average change detection (EWMACD)
EWMACD, proposed in Brooks et al. (2014), is a kernel regression approach modeling the time series as a linear combination of trigonometric polynomials. The model is trained over data collected in the initial two (or more) years. When the observations in the subsequent years deviate from the values forecast by the model for a ‘substantial’ length of time (persistence), a change is declared (recovery or disturbance). The training period as well as the persistence are parameters of the algorithm.
LandTrendR
LandTrendR was proposed in (Kennedy et al., 2010). Starting with a linear regression fit to the entire time series, LandTrendR partitions the time series step by step, adding breakpoints (called vertices here) at each step. A set of potential vertices is thus generated in a straight top-down approach. Once these vertices have been generated, they are refined in multiple passes: (i) first the least influential vertices (corresponding to most obtuse angles) are discarded; (ii) then, of the now
Breaks for additive and seasonal trend (BFAST)
BFAST (Verbesselt et al., 2010a) decomposes the given time series iteratively into three components: trend, seasonal, and noise. BFAST computes and evaluates least squares fits in windows of increasing size. Qualitatively, (i) first the possibility of there being any structural change in the given time series is determined by computing the partial sums of residuals of least squares fits in windows (OLS-MOSUM). The limiting process of these partial sums is the increments of a Brownian bridge
Prospects for a viable polyalgorithm
Once the algorithms have been implemented, the next step is to develop a procedure to choose the most appropriate outcome for the input. One possibility is to draw a consensus between algorithm outcomes: if more than half the algorithms being used predict breakpoint sets that are in proximity of each other, one of those algorithms gets chosen as the most appropriate algorithm. To this end, a method to measure the distance between the breakpoint sets is needed. Hausdorff distance from topology
Conclusions and future work
At present, the polyalgorithm offers some improvement over EWMACD or LandTrendR alone, but not over BFAST. Since BFAST is the most rigourous/exhaustive component algorithm, and the polyalgorithm is not as good as BFAST yet, there is surely room for improvement of the polyalgorithm. The experiments carried out in this work are just the beginning of further work towards a viable polyalgorithm. Several directions of research/development must be pursued in this regard.
First, the number of
Author contributions
RS wrote the codes and conducted the experiments; RS, LTW, and RHW wrote the paper; EBB, VAT, YZ, and REK assisted in data collection and validation.
Acknowledgements
This work was supported in part by USDA Forest Service Grant 13-JV-11330145-046, NSF Grant CNS-1565314, U.S. Geological Survey Contract G12PC00073, NASA Grants NNX17AI07G and NNX17AI09G, and the Virginia Agricultural Experiment Station and the McIntire-Stennis Program of NIFA, USDA (Project Number 1007054, “Detecting and Forecasting the Consequences of Subtle and Gross Disturbance on Forest Carbon Cycling”). The authors thank the anonymous reviewers for their insightful feedback on the original
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