# Retrieval of Similar Evolution Patterns from Satellite Image Time Series +
## 1 Introduction  
Over the years, the remote sensing domain has been characterized by numerous technological improvements (e.g., increased spatial resolution, shorter revisit time, increased number of spectral bands). These improvements were made possible through several Earth Observation missions, e.g., the Landsat program sustained by NASA and the United Stated Geological Survey (USGS), the Sentinel program financed by European Space Agency, Envisat's ASAR mission. In addition, many of the recent missions have functioned under an open data access policy for research purposes. This fact has a direct impact on the interest manifested in using this type of data in many realms, such as agriculture, land cover and land use planning, resource management, urbanization, and sustainable development. One possible method for the analysis of satellite image time series (SITS) is to compare two satellite images captured at two successive moments of time, over the same area of interest [1; 2; 3; 4]. These methods are generally called change detection methods. However, although they can successfully detect abrupt changes (e.g., deforestation, natural disasters, building construction), these methods are not able to identify complex spatio-temporal structures that evolve in a defined time-frame (e.g., measuring theeffects of floods, urban expansion, land cover and land use modifications). In the later cases, SITS analysis methods that involve information extraction from multi-temporal data are usually preferred. The main difficulties when dealing with SITS are the irregular time sampling, the missing samples (e.g., due to cloud cluttering and haze that affect images captured by optical sensors, technical artifacts) and, also, the high spatial and temporal data dimensionality. In general, multi-temporal approaches require the processing of large amounts of data characterized by a high degree of variability in terms of temporal, spatial and multi-spectral information. The spatio-temporal evolution patterns may span different periods of time and may affect small to large regions. For example, urban transformations affect small regions and have multiple construction phases spanning several years. In contrast, flood events may affect larger areas then in the previous case, but, depending on their intensity, the consequences may be observed over shorter or longer periods of time (e.g., land slides are irreversible). In this context, the characterization of temporal evolutions is strictly related to the fact that the processes that occur in dynamic scenes have different time scales and affect small to large areas. Therefore, the requirements that SITS analysis methods must fulfill are: (1) the ability to capture complex spatio-temporal changes and (2) the potential to emphasize both short-term and long-term modifications. Developing an algorithm that can deal with the spatial, temporal and spectral diversity of Earth Observation data is a challenging task to accomplish and more so when the amount of knowledge that a human expert transfers to the system is limited. Many multi-temporal analysis techniques use a SITS classification that incorporates various dissimilarity measures to compare two temporal sequences. In SITS, by similar evolution, we understand a group of scene points that share the same behavior for the entire period of time or for most of it. Each point in a SITS is characterized by a spectro-temporal signature. An example of a spectro-temporal signature is provided in Figure 1 for a SITS acquired by the Landsat sensor with six spectral bands. Some of the methods used to assess the degree of similarity between temporal sequences have emerged directly from text classification, speech recognition, or genomic data classification [5, 6]. Dynamic Time Warping (DTW) has proved to be an essential tool not only for spoken-word recognition, but also for understanding similarities between evolution profiles in SITS [7, 8].