Land-Cover Separability Analysis of MODIS Time-Series Data Using a Combined Simple Harmonic Oscillator and a Mean Reverting Stochastic Process

Abstract

Abstract-It is proposed that the time series extracted from Moderate Resolution Imaging Spectroradiometer satellite data be modeled as a simple harmonic oscillator with additive colored noise. The colored noise is modeled with an Ornstein-Uhlenbeck process. The Fourier transform and maximum likelihood parameter estimation are used to estimate the harmonic and noise parameters of the Colored Simple Harmonic Oscillator. Two case studies in South Africa show that reliable class differentiation can be obtained between natural vegetation and settlement land cover types, when using the parameters of the Colored Simple Harmonic Oscillator as input features to a classifier. The two case studies were conducted in the Gauteng and Limpopo provinces of South Africa. In the case of the Gauteng case study we obtained an average κ = 0.86 for single band classification, while standard harmonic features only achieved an average κ = 0.61. In conclusion the results obtained from the Colored Simple Harmonic Oscillator approach outperformed standard harmonic features and the minimum distance classifier.

Using Page's Cumulative Sum Test on MODIS Time Series to Detect Land-Cover Changes

“…The NDVI time series was computed using the first two spectral land bands. The Gauteng and Limpopo datasets are respectively divided into the three classes: natural vegetation (592 Gauteng pixels and 1497 Limpopo pixels), settlements (333 Gauteng pixels and 1735 Limpopo pixels) and real land cover change from vegetation to settlement (181 Gauteng pixels and 117 Limpopo pixels) [12].…”

“…The classes (data sets) under consideration are almost cyclostationary and as such an assumption of zero inter-annual variation is acceptable [12]. The CSHO also minimizes the error incurred due to inter-annual variation as it generates the average behavior of a class in an average year [12].…”

“…The CSHO also minimizes the error incurred due to inter-annual variation as it generates the average behavior of a class in an average year [12].…”

“…As the densities appear Gaussian for our case study a good simplification (alternative) would be to use 2 × 45 parametric Gaussian densities instead. As the means in our case study appear to be sinusoidal [12], a further simplification would be to parameterize the mean and variance using harmonic models to avoid using 45 different values for the mean and variance respectively. The log-likelihood deviation measure was used as an effective compact aggregate way of detecting mean (level) changes, while incorporating seasonal variation.…”

“…The densities at each time-step thus circumvents intra-annual variation. The densities are constructed by using the Colored Simple Harmonic Oscillator (CSHO) which can replicate average pixel behavior which implies that the effect of inter-annual variation is also minimized [12].…”