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11: Teerasit Kasetkasem, Manoj K. Arora, Pramod K. Varshney
that considers this spatial distribution within and between pixels in order to
produce maps at sub-pixel scale. This process is called super-resolution mapping (Tatem et al. 2002) or sub-pixel mapping (Verhoeye and Wulf 2002) to
distinguish it from sub-pixel classification. Thus, a sub-pixel map is a map
that is derived at an improved spatial resolution finer than the size of the pixel
of the coarse resolution image being classified. Tatem et al. (2002) provide an
excellent review on this subject. A range of algorithms based on knowledgebased procedures (Schneider, 1993), Hopfield neural networks (Tatem et al.
2002) and linear optimization methods (Verhoeye and Wulf 2002) have been
proposed for sub-pixel mapping. Knowledge based procedures depend on the
accurate identification of boundary features that divide the mixed pixels into
pure components at improved resolution. The drawbacks of this technique
are:
1. The information on accurate boundary features may not be readilyavailable and
2. It does not consider the spatial dependence within and between pixels.
Similarly, for Hopfield neural network and linear optimization based methods, the availability of an accurate sub-pixel classification derived from some
other techniques is a pre-requisite. Thus, the accuracy of the resulting sub-pixel
map is limited by the accuracy of the sub-pixel classification technique used.
Moreover, in these algorithms, the spatial dependence within and between
pixels is incorporated only after the fraction images from a sub-pixel classification technique are obtained. In contrast, the Markov random field (MRF)
model based algorithm, proposed here, neither relies on the availability of accurate boundary features nor on sub-pixel classification produced from other
techniques. Under an MRF model, the intensity values of pixels in a particular
spatial structure (i. e. neighborhood) are allowed to have higher probability
(i. e. weight) than others. For instance, in a remotely sensed land cover classification, the spatial structure is usually in the form of homogenous regions of
land cover classes. As a result, an MRF model assigns higher weights to these
regions than to the isolated pixels thereby accounting for spatial dependence
in the dataset.
The aim of this chapter is to introduce an MRF model based approach for
obtaining a sub-pixel map from hyperspectral images. The approach is based
on an optimization algorithm whereby raw coarse resolution images are first
used to generate an initial sub-pixel classification, which is then iteratively
refined to accurately characterize the spatial dependence between the class
proportions of the neighboring pixels. Thus, spatial relations within and between pixels are considered throughout the process of generating the sub-pixel
map. Therefore, the proposed approach may be more suitable for sub-pixel
mapping as the MRF models can describe the spatial dependence in a more
accurate manner than algorithms proposed in Verhoeye and Wulf (2002) and
Tatem et al. (2002).
This chapter is organized as follows. In Sect. 11.2, the theoretical concept of
MRF models for sub-pixel mapping is presented. The details of an MRF based
11: Teerasit Kasetkasem, Manoj K. Arora, Pramod K. Varshney
that considers this spatial distribution within and between pixels in order to
produce maps at sub-pixel scale. This process is called super-resolution mapping (Tatem et al. 2002) or sub-pixel mapping (Verhoeye and Wulf 2002) to
distinguish it from sub-pixel classification. Thus, a sub-pixel map is a map
that is derived at an improved spatial resolution finer than the size of the pixel
of the coarse resolution image being classified. Tatem et al. (2002) provide an
excellent review on this subject. A range of algorithms based on knowledgebased procedures (Schneider, 1993), Hopfield neural networks (Tatem et al.
2002) and linear optimization methods (Verhoeye and Wulf 2002) have been
proposed for sub-pixel mapping. Knowledge based procedures depend on the
accurate identification of boundary features that divide the mixed pixels into
pure components at improved resolution. The drawbacks of this technique
are:
1. The information on accurate boundary features may not be readilyavailable and
2. It does not consider the spatial dependence within and between pixels.
Similarly, for Hopfield neural network and linear optimization based methods, the availability of an accurate sub-pixel classification derived from some
other techniques is a pre-requisite. Thus, the accuracy of the resulting sub-pixel
map is limited by the accuracy of the sub-pixel classification technique used.
Moreover, in these algorithms, the spatial dependence within and between
pixels is incorporated only after the fraction images from a sub-pixel classification technique are obtained. In contrast, the Markov random field (MRF)
model based algorithm, proposed here, neither relies on the availability of accurate boundary features nor on sub-pixel classification produced from other
techniques. Under an MRF model, the intensity values of pixels in a particular
spatial structure (i. e. neighborhood) are allowed to have higher probability
(i. e. weight) than others. For instance, in a remotely sensed land cover classification, the spatial structure is usually in the form of homogenous regions of
land cover classes. As a result, an MRF model assigns higher weights to these
regions than to the isolated pixels thereby accounting for spatial dependence
in the dataset.
The aim of this chapter is to introduce an MRF model based approach for
obtaining a sub-pixel map from hyperspectral images. The approach is based
on an optimization algorithm whereby raw coarse resolution images are first
used to generate an initial sub-pixel classification, which is then iteratively
refined to accurately characterize the spatial dependence between the class
proportions of the neighboring pixels. Thus, spatial relations within and between pixels are considered throughout the process of generating the sub-pixel
map. Therefore, the proposed approach may be more suitable for sub-pixel
mapping as the MRF models can describe the spatial dependence in a more
accurate manner than algorithms proposed in Verhoeye and Wulf (2002) and
Tatem et al. (2002).
This chapter is organized as follows. In Sect. 11.2, the theoretical concept of
MRF models for sub-pixel mapping is presented. The details of an MRF based