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Interpolation methods for gap filling in satellite images

Karavolia Angeliki

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Summary

Nowadays, satellite images are crucial for a variety of applications such as detecting changes on Earth following human interventions and natural disasters. Satellite images often contain gaps thus creating problems in further processing, especially if the processing steps are automatized. The objectives of this thesis are to investigate methodologies for gap filling in satellite images; more specifically, the comparison of deterministic methodologies with the stochastic INNC method based on the Ising model. The existence of gaps is due to optically thick aerosol layers, satellite trajectories and sensor malfunction. The data used to test the gap-filling methodologies are divided into two categories: synthetic and satellite data. The synthetic data were generated using the Ackley function. The satellite data involve two datasets, one real and one simulated. The real data comprises daytime surface temperatures of the Earth measured by the Terra instrument of the MODIS satellite for the year 2016. The simulated data set was implemented by fitting a Gaussian spatial model to a random sample of 2.500 observations from the aforementioned MODIS data. We first performed an exploratory statistical analysis of spatial continuity in the data using the autocorrelation function and the variogram in the two orthogonal directions of the grid. The deterministic methodologies that were used for interpolation are: the nearest neighbor method, the minimum curvature interpolation method, the natural neighbor interpolation method, the cubic interpolation method and the linear interpolation method. These methodologies were implemented via the griddata command and some of them via the scatteredInterpolant command in the Matlab programming environment. Both commands perform interpolation of the surface at the points of investigation based on known measurements at the sample points. The deterministic interpolation methodologies were implemented with both functions because the implementation of the algorithms differs between the two functions. In addition, we have applied a stochastic methodology with nearest neighbor interactions, which is based on the Ising model (INNC). The INNC method approximates continuous variables according to a number of discrete classes we have defined. It also takes into account local values of the sample in order to estimate the prediction. Applying an approach based on Monte Carlo methodology, it predicts the class of the target variable at points where no measurements are provided. The statistical method of cross validation was used to select the optimal spatial interpolation methodology. A comparative analysis of the methodologies included a visual overview of the reconstructed images, scatterplots of the estimated and measured values (confirmation values), as well as statistical measures of cross validation. In addition, different spatial configurations and locations of missing points/areas were examined in the analysis of the synthetic data. Specifically, we used the following configurations with gaps for testing: 1) the random distribution of 40 missing pixels, 2) the continuous region of 303 missing pixels, and 3) the random distribution of 303 missing pixels.The minimum curvature interpolation method (implemented by griddata, option v4) is the best method for the synthetic data with a random distribution of 40 missing pixels. The INNC method with eight classes and a 5 × 5 stencil is optimal, compared to the nearest neighbor method (implemented by griddata and scatteredInterpolant, option nearest neighbor). The natural neighbor interpolation method (implemented by griddata and scatteredInterpolant, option natural neighbour) is computationally faster compared to the previous methodologies. The linear interpolation method (implemented by scatteredInterpolant, option linear) is the best method for the continuous region of 303 missing pixels in the case where the missing pixels are located in the right part of the image. Also, the natural neighbour interpolation method (implemented by scatteredInterpolant, option natural neighbour) is preferable in terms of computational time. The INNC method did not have satisfying results, compared to the previous methodologies. Then the continuous region of 303 missing pixels was explored, with the gaps being located in the center. The linear interpolation method (implemented by scatteredInterpolant, option linear) is the best method as we concluded in the case when the gaps are located in the right part of the image. The nearest neighbor method (implemented by scatteredInterpolant, option nearest neighbor) is more efficient method in terms of computational time. The INNC method with eight classes and a 30 × 30 stencil is a better method compared to the nearest neighbor method (implemented by griddata, option nearest neighbor) and the least curvature interpolation method (implemented by griddata, option v4). Furthermore, the random distribution of 303 missing pixels was examined using the same methodologies. The minimum curvature interpolation method (implemented by griddata, option v4) is considered to be the best method, like in the case of the random distribution of 40 missing pixels. The INNC method with 16 classes and a 5 × 5 stencil is more efficient method in terms of computational time, compared to the deterministic methodologies.The natural neighbor interpolation method (implemented by scatteredInterpolant, option natural neighbor) is the best method for satellite data. According to the results, the linear interpolation method (implemented by scatteredInterpolant, option linear) is better in terms of computational time for the real satellite data. In contrast, for simulated data, the method of natural neighbour interpolation (implemented by scatteredInterpolant, option natural neighbour) is more efficient in terms of computational time. Finally, the INNC method needed significantly more time for implementation on the satellite data.

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