Morphological Hyperspectral Image Classification: A Parallel Processing Perspective

Abstract

Mathematical morphology (MM) is a theory for spatial structure analysis that was established by introducing fundamental operators applied to two sets [1]. A set is processed by another one having a carefully selected shape and size, known as the structuring element (SE). In the context of image processing, the SE acts as a probe for extracting or suppressing specific structures of the image objects, checking that each position of the SE fits within those objects. Based on these ideas, two fundamental operators are defined in MM, namely erosion and dilation. The application of the erosion operator to an image yields an output image, which shows where the SE fits the objects in the image. On the other hand, the application of the dilation operator to an image produces an output image, which shows where the SE hits the objects in the image. All other MM operations can be expressed in terms of erosion and dilation [2]. For instance, the notion behind the opening operator is to dilate an eroded image in order to recover as much as possible of the eroded image. In contrast, the closing operator erodes a dilated image so as to recover the initial shape of image structures that have been dilated. The filtering properties of the opening and closing are based on the fact that, depending on the size and shape of the considered SE, not all structures from the original image will be recovered when these operators are applied. Because of the nonlinear properties of MM filters, their application generally results in an irreversible, though controlled, loss of information.Although MM operators were originally defined for binary images, they were soon extended to gray-tone (mono-channel) images by viewing these data as an imaginary topographic relief in which the brighter the gray tone, the higher the corresponding elevation [3]. Here, morphological operations can be graphically 353interpreted as the result of sliding a flat SE over the topographical relief, so that the SE defines the new (dilated or eroded) scene based on its spatial properties such as height or width (see Figure 13.1). However, extension of MM operators to multichannel data such as hyperspectral imagery with hundreds of spectral channels is not straightforward. A simple approach consists in applying grayscale MM techniques to each channel separately, an approach that has been called marginal MM in the literature [4]. However, the marginal approach is often unacceptable in remote sensing applications because, when MM techniques are applied independently to each image channel, analysis techniques are subject to the well-known problem of ''false colors''; that is, it is very likely that new spectral constituents not present in the original image may be created as a result of processing the channels separately [5]. An alternative way to approach the problem of multichannel MM is to treat the data at each pixel as a vector. Unfortunately, there is no unambiguous means of defining the minimum and maximum values between two vectors of more than one dimension, and th...