IEEE Geoscience and Remote Sensing Magazine - June 2017 - 16
that pixel is less than infinite to at least one of the pixels in the marker image f [49], [50]. Generally, a geodesic
distance is the minimum distance between two points
on the Earth's surface. Note that this is not the length of
a straight line (Euclidean distance) but the length of a segment of a circle. Similarly, the geodesic distance between
two pixels is the length of the shortest path between those
pixels. The path is not arbitrary, but it must be a subset of the
foreground pixels of the image.
If we use the Euclidean distance (instead of the geodesic distance), a large object can influence a large part of a
smaller object if both objects lie close to each other, even
if the connection between them is ver y narrow. With
the geodesic distance, only a small area of the smaller
object near the connection is influenced. The study in
[10] proposed a novel partial reconstruction in which a
pixel is reconstructed if the geodesic distance is smaller
than d 1 3. Opening with partial reconstruction [10], cr
is defined as
cr = d df (v ( f )).
(6)
The partial reconstruction is the same as a geodesic dilation of size d [49], [50]. The easiest way to implement this
is by doing successive elementary geodesic dilations, i.e., iterate (2) only d times. This is a dilation with an elementary
SE followed by an intersection with the mask. In gray-scale
morphology, the intersection of two images is the minimum of the two gray-scale values for each pixel. Instead
of using the original image, we can obtain the mask for
partial reconstruction by dilating the opening with a diskshaped SE with radius d followed by the intersection with
the original image.
For rectangular objects and with disk-shaped SEs,
the geodesic distance can be set to d = ^ 2 - 1 h R for
partial reconstruction with R as the radius of the SE, but
the corners of objects are not completely reconstructed
when d 1 ^ 2 - 1 h R. In contrast, partial reconstruction
with d 2 ^ 2 - 1 h R completely reconstructs the corners of
rectangular objects. Many objects of interest in remote
sensed images have a near-rectangular shape. Therefore,
we use a value of d near this value [e.g., d = 2 ^ 2 - 1 h R]
for partial reconstruction. For more details on morphological filters with partial reconstruction, we refer the
reader to [10].
ATTRIBUTE FILTERS WITH PARTIAL
RECONSTRUCTION
To overcome the leakage effects, AFs with partial reconstruction (AFsPR) [51] first separate connected objects
(e.g., roads and parking lots) of a binary image (i.e., at one
gray level) into two disjoint parts by using morphological filters with partial reconstruction [10]. We define two
binary images to include each part of the separated object. Then AFs [11] are applied to these two binary images.
Finally, AFsPR integrate all of the residuals of the filtered
16
images and obtain the final output image by repeating
this for all gray levels. Suppose that fi is the binary in gray
level i and, for opening, fi is referred to the upper-level
set ^ fi = f 2 i h while, for closing, fi is the lower-level set
^ fi = f # i h . A connected object Pk (kth connected component) in fi can be separated into two different adjacent and
nonoverlapping parts Pk1 and Pk2 that satisfy Pk = Pk1 , Pk2
and Pk1 + Pk2 = Q.
A binary image fi can be partitioned in its connected
components (here, we refer to foreground) P1, P2, f, such
that fi is the union of all Pk and each Pk is a connected
component with Pk + Pl = Q if k ! l. Let cr j and zr j denote
morphological opening and closing operators by partial reconstruction using a structuring element of size j. For opening, morphological opening with partial reconstruction is
first applied in the binary image fi (at gray-level i). As the
size of the SE j increases, more and more small, bright objects disappear. Two binary images, f io1 and f io2, are defined
as the filtering outs at scale j. f io1 = cr j ( fi) contains one part
of the connected objects Pk1 in fi, and f io2 = fi - f io1 includes
all disappeared objects of fi (i.e., the other parts of the connected objects Pk2 of fi).
In an opening, for gray-level i, we apply the binary
attribute opening { [58] on both binary images of f io1 and
f io2 and integrate the remaining objects into one filtered
image f io:
f io = { ( f io1) + { ( f io2).
(7)
When repeating (7) at each gray level, the attribute thinning
with partial reconstruction is defined by the maximum
gray level of the results of the filtering for each pixel x as
{r m ( f )(x) = max {i: x ! f io},
(8)
where m = {m 1, m 2, f, m n} is a sequence of ordered criteria,
which is the same as defined in [11]. The attribute thickening with partial reconstruction tr can be straightforwardly
extended from the definition of thinning. We refer the reader to [51] for further details.
Morphological/AP with partial reconstruction (APPR)
can be obtained similarly as in (4) and (5) by replacing the
connected filters by the filters with partial reconstruction.
Thus, the partial reconstruction [10] solved the problem
of over-reconstruction while preserving the shape of objects as much as possible and made a great improvement
in the classification of remote sensing imagery [2], [20],
[51], [53], [54]. As shown in Figures 5(c), 6(c), and 7(c),
the shapes of objects are better preserved with partial
reconstruction compared to the MP without reconstruction. However, some of the more complex shapes are not
as well preser ved as with connected filters. Yet many
small objects that remain present in the profile generated by geodesic reconstruction and AFs now disappear
when using the filters with partial reconstruction. We
can see objects disappear per their real attribute values in
ieee Geoscience and remote sensing magazine
june 2017
Table of Contents for the Digital Edition of IEEE Geoscience and Remote Sensing Magazine - June 2017
IEEE Geoscience and Remote Sensing Magazine - June 2017 - Cover1
IEEE Geoscience and Remote Sensing Magazine - June 2017 - Cover2
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 1
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 2
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 3
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 4
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 5
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 6
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 7
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 8
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 9
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 10
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 11
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 12
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 13
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 14
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 15
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 16
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 17
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 18
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 19
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 20
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 21
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 22
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 23
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 24
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 25
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 26
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 27
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 28
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 29
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 30
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 31
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 32
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 33
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 34
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 35
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 36
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 37
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 38
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 39
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 40
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 41
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 42
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 43
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 44
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 45
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 46
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 47
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 48
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 49
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 50
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 51
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 52
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 53
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 54
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 55
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 56
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 57
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 58
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 59
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 60
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 61
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 62
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 63
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 64
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 65
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 66
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 67
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 68
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 69
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 70
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 71
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 72
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 73
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 74
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 75
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 76
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 77
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 78
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 79
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 80
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 81
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 82
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 83
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 84
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 85
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 86
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 87
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 88
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 89
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 90
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 91
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 92
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 93
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 94
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 95
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 96
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 97
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 98
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 99
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 100
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 101
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 102
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 103
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 104
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 105
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 106
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 107
IEEE Geoscience and Remote Sensing Magazine - June 2017 - 108
IEEE Geoscience and Remote Sensing Magazine - June 2017 - Cover3
IEEE Geoscience and Remote Sensing Magazine - June 2017 - Cover4
https://www.nxtbook.com/nxtbooks/ieee/geoscience_december2023
https://www.nxtbook.com/nxtbooks/ieee/geoscience_september2023
https://www.nxtbook.com/nxtbooks/ieee/geoscience_june2023
https://www.nxtbook.com/nxtbooks/ieee/geoscience_march2023
https://www.nxtbook.com/nxtbooks/ieee/geoscience_december2022
https://www.nxtbook.com/nxtbooks/ieee/geoscience_september2022
https://www.nxtbook.com/nxtbooks/ieee/geoscience_june2022
https://www.nxtbook.com/nxtbooks/ieee/geoscience_march2022
https://www.nxtbook.com/nxtbooks/ieee/geoscience_december2021
https://www.nxtbook.com/nxtbooks/ieee/geoscience_september2021
https://www.nxtbook.com/nxtbooks/ieee/geoscience_june2021
https://www.nxtbook.com/nxtbooks/ieee/geoscience_march2021
https://www.nxtbook.com/nxtbooks/ieee/geoscience_december2020
https://www.nxtbook.com/nxtbooks/ieee/geoscience_september2020
https://www.nxtbook.com/nxtbooks/ieee/geoscience_june2020
https://www.nxtbook.com/nxtbooks/ieee/geoscience_march2020
https://www.nxtbook.com/nxtbooks/ieee/geoscience_december2019
https://www.nxtbook.com/nxtbooks/ieee/geoscience_september2019
https://www.nxtbook.com/nxtbooks/ieee/geoscience_june2019
https://www.nxtbook.com/nxtbooks/ieee/geoscience_march2019
https://www.nxtbook.com/nxtbooks/ieee/geoscience_december2018
https://www.nxtbook.com/nxtbooks/ieee/geoscience_september2018
https://www.nxtbook.com/nxtbooks/ieee/geoscience_june2018
https://www.nxtbook.com/nxtbooks/ieee/geoscience_march2018
https://www.nxtbook.com/nxtbooks/ieee/geoscience_december2017
https://www.nxtbook.com/nxtbooks/ieee/geoscience_september2017
https://www.nxtbook.com/nxtbooks/ieee/geoscience_june2017
https://www.nxtbook.com/nxtbooks/ieee/geoscience_march2017
https://www.nxtbook.com/nxtbooks/ieee/geoscience_december2016
https://www.nxtbook.com/nxtbooks/ieee/geoscience_september2016
https://www.nxtbook.com/nxtbooks/ieee/geoscience_june2016
https://www.nxtbook.com/nxtbooks/ieee/geoscience_march2016
https://www.nxtbook.com/nxtbooks/ieee/geoscience_december2015
https://www.nxtbook.com/nxtbooks/ieee/geoscience_september2015
https://www.nxtbook.com/nxtbooks/ieee/geoscience_june2015
https://www.nxtbook.com/nxtbooks/ieee/geoscience_march2015
https://www.nxtbook.com/nxtbooks/ieee/geoscience_december2014
https://www.nxtbook.com/nxtbooks/ieee/geoscience_september2014
https://www.nxtbook.com/nxtbooks/ieee/geoscience_june2014
https://www.nxtbook.com/nxtbooks/ieee/geoscience_march2014
https://www.nxtbook.com/nxtbooks/ieee/geoscience_december2013
https://www.nxtbook.com/nxtbooks/ieee/geoscience_september2013
https://www.nxtbook.com/nxtbooks/ieee/geoscience_june2013
https://www.nxtbook.com/nxtbooks/ieee/geoscience_march2013
https://www.nxtbookmedia.com