Spatially adaptive smoothing parameter selection for Markov random field based sub-pixel mapping of remotely sensed images

Sub-pixel mapping is a process to provide the spatial distributions of land cover classes with finer spatial resolution than the size of a remotely sensed image pixel. Traditional Markov random field-based sub-pixel mapping (MRF_SPM) adopts a fixed smoothing parameter estimated based on the entire image to balance the spatial and spectral energies. However, the spectra of the remotely sensed pixels are always spatially variable. Adopting a fixed smoothing parameter disregards the local properties provided by each pixel spectrum, and may probably lead to insufficient smoothing in the homogeneous region and over-smoothing between class boundaries simultaneously. This article proposes a spatially adaptive parameter selection method for the MRF_SPM model to overcome the limitation of the fixed parameter. As pixel class proportions are indicators of the type and proportion of land cover classes within each coarse pixel, in the proposed method, fraction images providing pixel class proportions as local properties of each pixel spectrum are employed to constrain the smoothing parameter. Consequently, the smoothing parameter is spatially adaptive to each pixel spectrum of the remotely sensed image. Synthetic images and IKONOS multi-spectral images were employed. Results showed that compared with the hard classification method and the non-spatially adaptive MRF_SPM adopting a fixed smoothing parameter, the spatially adaptive MRF_SPM with the smoothing parameter constrained to each pixel spectrum yielded sub-pixel maps not only with higher accuracy but also with shapes and boundaries visually reconstructed more closely to the reference map.