IEEE Geoscience and Remote Sensing Magazine - June 2017 - 12
(a)
(b)
figure 3. The University of Pavia hyperspectral image: (a) LiDAR data
and (b) ground truth.
(a)
(b)
figure 4. The University of Houston image: (a) LiDAR data and (b)
ground truth.
its ground truth are shown in Figure 4. For more information, see [2] and [55].
The training and test sets for each data set (shown in
Tables 1 and 2) are pixels selected from the data provided
by experts who are knowledgeable about the corresponding
predefined species/classes. Note that the color in the cell
denotes different classes in the classification maps. Pixels
from the training set were excluded from the test set in each
case and vice versa.
morPhologicAl feATures generATed
by connecTed filTers
Mathematical morphology [7], [49], [50] is a popular tool
in image and video processing and has been widely used
in diverse tasks such as FE, segmentation, and restoration.
Successful applications of mathematical morphology in
remote sensing image processing have been reported in
[12], [24]-[26], [31]-[34], [36], and [37]. Morphological
operators [7] and AFs [11] are two of the most widely used
12
operators of mathematical morphology in remote sensing
image processing.
Morphological operators act on the values of the pixels according to transformations that consider the pixels'
neighborhood (with a given size and shape). The basic
operators are dilation and erosion [7]. These operators are
applied to an image with a set of known shapes referred
to as the SEs. In the case of erosion, a pixel takes the minimum value of all the pixels in its neighborhood defined
by the SE. By contrast, dilation takes the maximum value
of all the pixels in its neighborhood. Dilation and erosion
are usually employed in tandem, either with the dilation
of an image followed by erosion of the dilated result or
with erosion of an image followed by the dilation of the
eroded result. These combinations are known as morphological opening and closing.
AFs, such as attribute openings and closings [11], are
connected operators, defined in the mathematical morphology framework, that process an image by merging its
connected components at different gray levels. Connected
components are the flat zones where the image-constant
intensity is continuous. An opening acts on bright objects
(for LiDAR data, the bright regions are areas with high elevation such as the top of a roof ) compared with their
surroundings; closings, on the other hand, act on dark
(low height in the LiDAR data) objects [2]. For example,
an opening merges bright objects that are smaller than the
threshold into their background, while the dark objects
are left unchanged. The opposite operation of the opening is the closing, which removes small, dark objects
while leaving bright objects unchanged. Morphological
features are typically generated by applying a sequence of
morphological operators or AFs on an image, where MPs
contain low-level features (size and shape information)
and APs can model middle-level features (e.g., homogeneity and textures).
MORPHOLOGICAL OPERATORS BY RECONSTRUCTION
By increasing the size of the SE, more and more objects are removed, as shown in Figures 5-7. However, aside from deleting
objects smaller than the SE, classical morphological openings and closings degrade borders and deform the shapes
of the objects, as shown in Figures 5(a), 6(a), and 7(a), and
round the corners of rectangular objects. To preserve the
shapes of objects, morphological openings and closings by
reconstruction (i.e., geodesic reconstruction [49], [50]) are
generally the tools of choice [56], [57]. With geodesic reconstruction, the whole object is reconstructed if at least
one pixel of the object survives the opening or closing. Two
pixels are considered to belong to the same object if they are
connected in the original image (or mask). The image on
which the reconstruction is performed is called the marker.
The geodesic dilation (of size 1) of the gray-scale marker
image f and the mask image g is defined as
d 1g ( f ) = d 1 ( f ) / g,
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