IEEE Geoscience and Remote Sensing Magazine - September 2021 - 45

the grayscale image :, ,
A toy example of AFs is presented in Figure 2. Given
" 6
◗ the adaptation of APs to various modalities besides sinXE
01 2@ of Figure 2(a), we first
obtain the max-tree T of X using four-connectivity. Then,
we compute the area (number of pixels) of the nodes of T.
Subsequently, we prune the nodes of T with an area less
than a given parameter k. In our case, k is equal to eight,
and the nodes composed of fewer than eight pixels are
pruned from the tree. Finally, we reconstruct the image
from the pruned tree, resulting in
area thinning of X for k 8= .
gle-band images and, in particular, multiband data (the
" Input Data " section)
◗ the construction of APs using various hierarchical image
representations (the " Tree Construction " section)
◗ the determination of attributes and thresholds (the " Attribute
and Threshold Selection " section)
X .l Hence, Xl is the
RECENT ADVANCES FROM APs
Each of the four AP construction stages has received various
forms of extensions and contributions from the scientific
community. Moreover, AP-based image analysis pipelines
often include some form of preprocessing, usually to adapt
multiband input [since (1) expects single-band data] as well
as postprocessing steps to increase description capability.
We now revisit the recently proposed developments
that have provided significant contributions to the AP
framework for remote sensing image classification. Here,
our study focuses on the following key concepts:
◗ tree-filtering rules used in the construction of APs (the
" Tree Filtering " section)
◗ postprocessing techniques intended for feature enhancement
(the " Postprocessing of Output Profiles " section).
For other AP-related notions, including profiles computed
with different morphological filters and imagereconstruction
techniques, we refer readers to the related
references for additional details (the " Extensions and Generalization
of APs " section).
INPUT DATA
Since APs were originally proposed to deal with only singleband
images [7], their adaptation to other kinds of remote
sensing data became necessary early on. In particular,
their adaptation to multichannel images (multispectral and
Image X
Tree From X
Tree With Attribute A
100
39
p∈CCi
Pixel p
Tree Construction
1
(a)
(b)
With Respect to
Node ni
Attribute Computation
2
(c)
3
(d)
19 20 9
8
52
44
Pruned Tree
φk
A ≥ 10
p∈CCi-1
With Respect to
Node ni-1
Attribute Filtering on Tree Image Reconstruction
4
(e)
FIGURE 1. The AP generation framework, which involves four main stages: (1) tree construction, (2) attribute computation, (3) tree-based
attribute filtering (pruning), and (4) image reconstruction from the filtered (pruned) tree. The (a) image, (b) max-tree, (c) area attribute,
(d) area filtering, and (e) reconstruction are shown. (Source: [18]; used with permission.)
25
L0
2210 2
2210 2
1110 1
0001 1
2001 2
(a)
(b)
FIGURE 2. (a) The original grayscale image :, ,.
XE 01 2 " 6
9
L1
L2
41 21
(c)
(d)
(e)
pixels) of the nodes of T . (d) The area filtering of T with regard to the threshold k 8= (e) The image Xl reconstructed from the pruned tree.
SEPTEMBER 2021 IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE
@ (b) The max-tree T of X computed using four-connectivity. (c) The area (number of
.
45
7
1110 0
1110 0
1110 0
0000 0
0000 0
Filtered Image
X′ = φk (X)
IEEE Geoscience and Remote Sensing Magazine - September 2021

Table of Contents for the Digital Edition of IEEE Geoscience and Remote Sensing Magazine - September 2021
