I. Introduction
The development in hyperspectral sensors is leading to an increased availability of data having both high spectral and spatial resolution. The high spectral resolution (i.e., hundreds of channels acquired in very narrow spectral bands) allows a very accurate identification of surface materials. The high spatial resolution enables precise analysis of small heterogeneous spatial structures present in the surveyed scene. The modeling of the characteristics of spatial objects can be achieved by processing an image with a set of mathematical morphology operators. In this context, region-based filtering tools [1] (called connected operators) have recently received significant attention due to their effectiveness in both extracting spatial information and preserving the geometrical characteristics of the objects in images (i.e., borders of regions are not distorted since only an image is processed by merging its flat zones). Attribute filters (AFs) [2] are a set of connected operators that are able to simplify a grayscale image according to an arbitrary measure (i.e., attribute), such as scale, shape, and contrast. In Dalla Mura et al. [3], the authors proposed to use AFs in a multilevel approach, called attribute profiles (APs), for dealing with the heterogeneity of objects present in remote sensing high-resolution images (both in scale and shape). Dalla Mura et al. [4] showed interesting properties of APs when extended to hyperspectral images [extended APs (EAPs)] and used as spatial features for classification. Dalla Mura et al. [4], [5] applied APs to the first few principal components [i.e., principal component analysis (PCA)] and to the independent components (i.e., independent component analysis), extracted from a hyperspectral image, respectively. Dalla Mura et al. [6] proposed self-dual APs (SDAPs) with an area attribute as a variant of APs for the classification of very high geometrical resolution images. The use of SDAPs proved to be more effective than APs for modeling the spatial information (i.e., bright and dark regions are simultaneously processed) even with a reduced number of features. Subsequently, Cavallaro et al. [7] compared APs with SDAPs obtained by different attributes and filtering strategies and showed that SDAPs could achieve higher classification accuracy. In this letter, we propose extended SDAPs (ESDAPs), a generalization of SDAPs for the extraction of spatial features for the classification of hyperspectral images. A classic approach extracting spectral–spatial classification based on a two-step supervised feature extraction technique [8] is adopted with the nonparametric weighted feature extraction (NWFE) method [9]. We aim to compare the capability of extracting the spatial information of EAPs and ESDAPs components when considering different attributes. This is done by analyzing at the classification accuracies provided by the support vector machines (SVMs) and random forest (RF) classifiers. The remainder of this letter is organized as follows. Section II reviews the features reduction methods by focusing on the supervised NWFE. The concepts of morphological AFs and ESDAPs are introduced in Section III. The experimental analysis (which includes the description of the data sets), the setup and the results are described in Section IV. Section V concludes this letter with some remarks and possible future research directions.