IEEE Geoscience and Remote Sensing Magazine - June 2017 - 17

Figures 8(b) and 9(b). This is because in remote-sensing
(urban) scenes, different objects lie closely together, and,
because of noise and other effects, different objects are
often connected by a sequence of pixels with similar (or
more extreme) pixel values. Therefore, geodesic reconstruction and AFs consider all those connected objects as
a single object, and objects only disappear when the SE
does not fit the broadest part (for AFs, we take the area
attribute as an example) of the connected object, even
though this part might be far away from the actual object. Partial reconstruction reconstructs only the immediate surrounding area of the surviving part. The edges of
simple objects are reconstructed well, but a full retrieval
of complex elongated shapes might not be obtained. For
simple objects such as rectangles, geodesic reconstruction
and AFs are complete, because, in urban remote-sensing
scenes, most objects are not very complex and the partial
reconstruction of rectangular-shaped objects has been
well suited.
exTension To The AnAlysis of
hyPersPecTrAl imAgery
When dealing with hyperspectral imagery (or other vectorial images), the high dimensionality of hyperspectral data
and the redundancy within the bands make the generation
of MPs/APs based on each spectral band a time-consuming task. To overcome this problem, FE is first used as a
preprocessing step to reduce the dimensionality of these
hyperspectral data and reduce the redundancy within the
bands. Then, morphological/attribute processing is applied on each extracted feature band independently. The
effect of different FE methods on extracting features from

the hyperspectral data to build MPs/APs has been discussed in several studies [54], [62], [63].
An MP/AP consists of the opening profile (OP) and
the closing profile (CP). For the panchromatic image,
the MP/AP is built on the original single-band image directly. The OP or CP with its p scale set at pixel x forms a
p-dimensional vector. By incorporating the OP and the CP,
an MP/AP of pixel x is defined as a (2p + 1)-dimensional
vector. Suppose that r features are extracted from the original hyperspectral data, EMPs/APs (named EMP/EAP) are
defined by concatenating all MPs/APs computed on these r
features [9]. The EMP of pixel x is an r (2p + 1)-dimensional vector, and Figure 10 shows an EMP built on the first two
PCs. Suppose that we want to construct n attributes [e.g.,
area and standard deviation (Std)] in m i ^i ! [1, n]h . For each
attribute with the same scale (e.g., p thresholds), the EAP of
pixel x is an nr (2p + 1)-dimensional vector.
The selected features are rescaled to a defined range
and converted to integer form to be processed by the AFs.
When converting the intensities of the selected features
from double to integer, it is not easy to determine a good
range. For a high range, it increases the computational time.
For a lower range, although reducing the processing time, the
rescaled features are smoothed, which leads to unexpected
effects (e.g., many objects are connected). These connected
objects are often treated as a single object by original-attribute
thinning and thickening, which consequently leads to reduced classification performances. Figures 11 and 12 show
examples of features with different rescaled ranges using
attribute thinning [11], [12]; for the attribute thinning with
partial reconstruction [51], we normalize the resulting
thinning for better visualization.

Morphological Profile from the First PC

Morphological Profile from the Second PC

figure 10. The EMP for a hyperspectral image. PC analysis is used as an example for FE, and the first two PCs are used to build

the EMP.
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Table of Contents for the Digital Edition of IEEE Geoscience and Remote Sensing Magazine - June 2017