Sub-pixel Land Cover Mapping Based on Markov Random Field Models Teerasit Kasetkasem
Manoj K. Arora, and Pramod K. Varshney
Electrical Engineering Department Kasetsart University Chatuchak, Bangkok 10900 Thailand Email:
[email protected]
Department of Electrical Engineering and Computer Science Syracuse University Syracuse, NY 13244 USA Email:
[email protected] and
[email protected]
Abstract— Occurrence of mixed pixels in remote sensing images is a common phenomenon particularly in coarse spatial resolution images. In these cases, sub-pixel or soft classification may be preferred over conventional hard classification. However, sub-pixel classification fails to account for the spatial distribution of class proportions within the pixel. A better approach may be to generate a land cover map at a finer resolution from the coarse resolution images based on image models that accurately characterize the spatial distribution of the classes. The resulting fine resolution map may be called a sub-pixel or super resolution map. In this paper, an approach based on Markov random fields is introduced to generate sub-pixel land cover maps from remote sensing images dominated by mixed pixels.
between pixels. Markov random field (MRF) models describe the spatial dependence quite accurately and are employed in this paper for sub-pixel mapping. MRF models have been applied in various image processing tasks such as image classification and change detection (e.g., [5-6]). In this paper, we develop an approach based on the MRF model and implement it to generate land cover classification from 4 m IKONOS imagery in the form of a subpixel map at 1 m resolution. The approach is based on an iterative optimization algorithm that considers the spatial structure of land cover classes from the neighboring pixels.
I. I NTRODUCTION
II. MRF BASED S UB - PIXEL M APPING
Land cover classification is one of the most important applications of remote sensing data. Either crisp (per pixel) or fuzzy (sub-pixel) classification may be performed to obtain a land cover map. However, in general and particularly in coarse spatial resolution images such as AVHRR (resolution 1.1 km), majority of pixels may be mixed. Even where the spatial resolution is fine (e.g., 4 m multi-spectral IKONOS), the high spatial frequency of some classes such as urban and built-up areas may result in a large number of mixed pixels [1]. The presence of mixed pixels happens to be a recurring problem in extracting accurate land cover information from remote sensing images. Therefore, sub-pixel classification may be more appropriate than crisp classification. The output of subpixel classification is a set of fraction images each describing the proportion of a particular land cover class within a pixel. While, under most circumstances, sub-pixel classification is meaningful and informative, it fails to account for the spatial distribution of class proportions within the pixel [2]. An alternative could be to produce a fine resolution land cover map from a coarse resolution image based on an accurate characterization of the spatial distribution of classes within the mixed pixels. This process is called sub-pixel mapping [2] or super-resolution mapping [3]. A limited amount of work on this subject has been reported in the literature [2-4], and Tatem et al. [3] provide an excellent review. A range of algorithms based upon knowledge-based analysis procedures, Hopfield neural networks, and linear optimization methods have been proposed for sub-pixel mapping. The major assumption in all these algorithms is related to the spatial dependence within and
Let Y be the observed coarse spatial resolution image having M × N pixels and X be the fine resolution sub-pixel map (SPM) having aM × aN pixels where a is a scale factor. This means that a particular pixel in the observed coarse image contains a2 pixels of the SPM. Assume that pixels of the fine resolution map are pure and mixed pixels can only occur in the observed image. Thus, more than one land cover class can occupy a pixel in a coarse resolution image. In general, a can be any positive real number, but, for simplicity, here it is assumed to be a positive integer. Also, let S and T denote the sets of all the sites (i.e., pixels) belonging to the observed image and the SPM, respectively. Thus, the number of sites in T will the number of sites in the set S. Let n be a2 times o j T = tj1 , . . . , tja2 represent the set of all pixels in the set T that correspond to the same area as the pixel sj in the set S. The observed multi-spectral image is usually represented in a vector form such as, y(sj )∈
