## 1 Introduction  
Land-use and land-cover change by modification of the Earth's land surface over time highlights interactions between the human and physical environment [1, 2]. In order to understand the environmental and social impacts of the changes and project future changes and potential impacts, it is essential to quantify the intensity of land-cover changes over time. Remote sensing has become the preferred method for detecting land-cover changes over time due to its advantages of consistent and repeatable procedures [3, 4]. Remotely sensed data provides continuous, quantitative, and spatially explicit observations, which can characterize a variety of land-cover types and transitions between different types [3, 4]. Abrupt land-cover change (shortened to land-cover change hereafter) refers to the conversion of land-cover from one class (e.g., forest) to another class (e.g., grassland). Land-cover change over a period of time, or land-cover trajectory, can be constructed from satellite images acquired at multiple time points [5, 6, 7]. With the recent advances in earth observations, dense time series of satellite images become widely available, such as MODIS (Moderate Resolution Imaging Spectroradiometer) data, which allows researchers to address land-cover trajectories in a continuous time frame. Continuous mapping, moving beyond the annual land-cover \"snapshot\" at a discrete time point, can provide more complete information at each available time point than the traditional annual map. With the improved capacity of multi-temporal satellite data, more and more studies have put effort to analyze long time series to characterize land-cover change trajectories [6, 8, 9]. [PERSON] and [PERSON] [8] proposed a method based on panel econometric techniques to determine the time points of land-cover change in a time series of Landsat Thematic Mapper (TM) images. Changes were identified by comparing a pixel's digital number (DN) values to those of land-cover changes predicted from regressions for each possible date. This method provides an approach different from conventional change detection but it was not designed to detect changes from high-resolution time series. Recently, a regression-based approach was developed to detect trajectories of forest disturbance and recovery using yearly time series images [5, 9]. This approach fits a sequence of straight lines to the observed spectral profiles extracted and eliminates noise. The change detection methods developed at yearly resolution, however, cannot be directly applied to time series data at higher temporal resolution (e.g., monthly) for most vegetated land covers due to the confusion with seasonal variations in vegetation phenology (except for vegetation with little seasonal variation), and thus they are not able to capture accurate change points at scales less than one year. The major challenge for detecting changes in dense satellite time series is to distinguish land-cover change from seasonal phenological variation. Methods have been developed for change point detection in statistics by identifying the points where significant differences between probability distributions are generated over different intervals [10] and in signal processing by data segmentation techniques [11, 12, 13]. These methods were developed for use with signal data and are not well adapted to image time series and land-cover changes which have fewer observations per cycle and smoother transitions at change points compared to common signal data. In fact, methods of detecting dates of land-cover change from image time series have been rarely explored. [PERSON] and [PERSON] [14] employed dense time series of Landsat images to map the event of fire by detecting the negative outliers relative to the median-smoothed time series. [PERSON] _et al._[15] proposed a Breaks for Additive Seasonal and Trend (BFAST) method to analyze the dynamics of time series using the MODIS 16-day NDVI (normalized difference of vegetation index)product from 2000 to 2008.