MONITORING URBAN SPRAWL FROM SATELLITE ...

MONITORING URBAN SPRAWL FROM SATELLITE IMAGE TIME SERIES François Petitjean† , Anne Puissant‡ , and Pierre Gançarski† †

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LSIIT/University of Strasbourg, UMR 7005 – 67412 Illkirch Cedex – France ‡ LIVE/University of Strasbourg, ERL7230 – 67000 Strasbourg – France

ABSTRACT Satellite Image Time Series are becoming increasingly available and will continue to do so in the coming years thanks to the launch of space missions which aim at providing a coverage of the Earth every few days with high spatial resolution. In the case of optical imagery, it will be possible to produce land use and cover change maps with detailed nomenclatures. It has been shown that the Dynamic Time Warping (DTW) similarity measure makes it possible to compare radiometric time series with different lengths and sampling. This work aims at showing that DTW is also able to capture distorted phenomena sensed over a long satellite image time series. This article details the analysis of a satellite image time series sensed over 20 years; we show that DTW makes it possible to extract static phenomena, as well as distorted ones such as urbanized areas. Index Terms— Remote Sensing, Urban areas, Time series analysis, Image classification, Image sequences. I. INTRODUCTION HE management of cities is at the heart of the major contemporary concerns. Monitoring urban sprawl and its consequences remains a major challenge for urban planning and management. Satellite Image Time Series (SITS, for short) are a precious resource for urban planning. In the coming years, both high temporal and high spatial resolution SITS are going to be widely available thanks to the ESA’s S ENTINEL program. In order to efficiently use the huge amounts of data that will be produced by, for instance, S ENTINEL -2 (global cover every five days with 10 m to 60 m resolution and 13 spectral bands), new methods for SITS analysis have to be developed. Our research group focuses on the comparison of radiometric time series. The similarity measure is the key tool of many classification algorithms. In this way, having a similarity measure between radiometric time series makes it possible to easily provide a temporal analysis of the sensed scene. We have recently introduced the Dynamic Time

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∗ The authors would like to thank the Foster project for partially supporting this work as well as the French Space Agency (CNES) and Thales Alenia Space for supporting F. Petitjean’s work under research contract n°1520011594.

Warping (DTW) similarity measure to the remote sensing community [1]–[3]. We have shown that this measure makes it possible to consistently and robustly analyze agronomical radiometric behaviors over a cultural year. However, these evolution behaviors are almost synchronous, with a jitter of a few days from one field to another of the crop class. Conversely, different areas of the same sensed area can become urbanized at different times. Moreover, the urbanization process can takes from, say several weeks to several months. This evolution behavior results in distortions of canonical temporal profiles of, say NDVI or other physical variables. In our previous work, we have shown that the mining of frequent sub-sequences allowed us to extract urbanized areas [4]. However, this family of methods produces a significant amount of patterns (more than a thousand), which makes if difficult for the urban planner to analyze the sensed scene in a global way. In this work, we thus focus on the classification of the entire sensed scene, where each area (x, y) is described by a radiometric time series from the SITS. To this end, similarity measures that have some kind of invariance to temporal stretching, shift, or dilatation are of major interest for the classification, since the comparison operator concentrates the similarity between objects. This paper aims at showing the DTW similarity measure to compare (possibly distorted) temporal profiles in order to classify a scene sensed by a satellite image time series. II. STATE OF THE ART SITS analysis allows the analysis, through observations of land phenomena with a broad range of applications such as the study of land-cover or even the mapping of damage following a natural disaster. These changes may be of different types, origins and durations. For a detailed survey of these methods, the reader should refer to [5]. In the literature, we find three main families of methods. Bi-temporal analysis can locate and study abrupt changes occurring between two observations. Bi-temporal methods include image differencing [6], image ratioing [7] or change vector analysis (CVA) [8]. A second family of mixed methods, mainly statistical methods, applies to two or more images. They include linear data transformation (PCA and MAF) [9] and frequency analysis (e.g., Fourier, wavelet)

to gather locally time-distorted sequences (e.g., time shifts, local time distortions).

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Fig. 1. Example of the matrix computed by DTW. (a) The matrix and the warping path computed by DTW. (b) The resulting alignment of the two sequences.

[10]. Eventually, we find methods designed towards image time series and based on radiometric trajectory analysis [1], [11]. This work focuses on the classification of SITS as radiometric evolutions of atomic sensed areas (i.e., pixels) through time. This data structure enables the mining of structured information and the analysis of evolution behaviors from the image series. III. DYNAMIC TIME WARPING When studying radiometric evolutions of sensed areas over time, the core of the process generally consists of comparing data in order to estimate (dis)similarity, whatever the method is. The distance tool provides an estimation of this similarity. It is a critical tool, on which results of analysis methods heavily rely. When the data is temporal, the choice of the distance is crucial since it completely defines the way of tackling the temporality of the data. This work focuses on the Dynamic Time Warping similarity measure introduced in [12]. This similarity measure can exploit the temporal distortions and compare shifted or distorted evolution profiles and whose time sampling is irregular, thanks to the optimal alignment of radiometric profiles. DTW is able to find optimal global alignment between sequences and is probably the most commonly used measure to quantify the dissimilarity between sequences. It also provides an overall real number that quantifies the similarity between the two sequences. An example of DTW-alignment of two sequences is presented in Figure 1. DTW makes it possible to find the best global alignment between two numerical sequences. Providing the cost of this alignment, DTW is generally used as a dissimilarity measure between two sequences. This measure enables to bring closer two sequences with time shifts and, more generally, time distortions. In this way, Dynamic Time Warping is a time-designed similarity measure, with the desired property of being able

IV. MATERIALS AND METHODS This article presents a standard unsupervised classification example by using the K- MEANS algorithm. The area of study for this work is located near the Arcachon’s bay in the West of France. There are 33 S POT 1-2-4 images sensed from 1986 to 2006. The temporal distribution of the images is given in Figures 2(a) and 2(b); the first and last images of the SITS are given in Figures 2(c) and 2(d). From these images, we use the standard Normalized Difference Vegetation Index (NDVI), built from the multi-spectral product, at a spatial resolution of 20 m. Actually, this physical variable makes the values quite comparable to each other through the series, and is a quite consistent index for the description of the sensed scene. Nevertheless, the proposed approach is generic and could be used on other physical variables as well as on the multi-spectral product. Before being used in this work, the S POT products have been orthorectified (guaranteeing that a pixel (x, y) covers the same geographic area throughout the image series). V. EXPERIMENTS In this experiment, the NDVI time series are clustered using the K- MEANS algorithm. In this way, the geographic areas (identified by their coordinates (x, y)) that have had a similar evolution (in terms of DTW) are clustered together. Results obtained are depicted in Figure 3. Globally, these results confirm the relevance of the use of DTW for the comparison of long-term evolutions. The main classes of evolutions and non-evolution are well distinguished. Note that a static class is also a class of evolution. In addition, even if areas such as static urban areas appears to be non-evolving, they are composed of sub-pixel vegetation areas that are evolving with time. In particular, the artificialisation process is well identified (pink) allowing to estimate spot of urbanization, even though the beginning, end and duration of the process were different from an area to another. We can also note that a specific class of changes is appeared in dark blue. This class of evolution is surprising because it corresponds in the north to swamps and in the south west to the management of golf course (herbaceous surfaces well irrigated). The visual identification of these changes is difficult because of the similarity of the radiometric classes along a long time series. However, the proposed method allowed distinguishing modification of texture in vegetation. A more detailed analysis for this class could be done to understand this type of change. VI. CONCLUSION This paper showed that DTW makes it possible to consistently extract the main evolution behaviors and is a useful tool for the mapping and monitoring of urban sprawl.

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day of year J

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(c) July, 16th 1986

(d) June, 3rd 2006

Fig. 2. (a) Annual distribution over the 20 years. (b) Monthly distribution for all years. (c) (resp. (d)) First (resp.last) image of the studied satellite image time series.

Vegetation — Vegetation Mineral — Mineral Water —- Water

Dry vegetation  Highly wet vegetation Vegetation −→ Mineral

Fig. 3. Obtained clustering result with the proposed approach. For understanding purpose, the clustering result has been manually recolorized, according the the interpretation of the expert.

We believe this work opens up a number of research directions. For instance, exploiting the mean evolution profile of each class would help the expert to better understand the changes that happened over the sensed period. Another direction could be to use recent object-based temporal methods [13], which enables to consider the spatial context of the pixels for SITS analysis.

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