Map Space Modeling Method Reflecting Safety Margin in Coastal Water Based on Electronic Chart for Path Planning

Abstract

Map space composition is the first step in ship route planning. In this study, a map modeling method for path planning is proposed. This method incorporates the safety margin based on the theory of geographic space existing in coastal waters, maneuvering space according to ship characteristics, and the psychological buffer space of a ship navigator. First, the obstacle area was segmented using the binary method—a segmentation method—based on the international standard electronic chart image. Next, the margin space was incorporated through the morphological algorithm for the obstacle area. Finally, to minimize the space lost during the route search, the boundary simplification of the obstacle area was performed through the concave hull method. The experimental results of the proposed method resulted in a map that minimized the area lost due to obstacles. In addition, it was found that the distance and path-finding time were reduced compared to the conventional convex hull method. The study shows that the map modeling method is feasible, and that it can be applied to path planning.

Full text

Citation: Jang, D.-u.; Kim, J.-s. Map
Space Modeling Method Reflecting
Safety Margin in Coastal Water Based
on Electronic Chart for Path Planning.
Sensors 2023,23, 1723. https://
doi.org/10.3390/s23031723
Academic Editors: I-Hsi Kao,
Yi-Horng Lai, Jau-Woei Perng and
Ching-Yao Chan
Received: 13 December 2022
Revised: 21 January 2023
Accepted: 24 January 2023
Published: 3 February 2023
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
sensors
Article
Map Space Modeling Method Reflecting Safety Margin in
Coastal Water Based on Electronic Chart for Path Planning
Da-un Jang 1and Joo-sung Kim 2, *
1Graduate School of Maritime Transportation System, Mokpo National Maritime University, 91,
Haeyangdaehak-ro, Mokpo-si 58628, Jeollanam-do, Republic of Korea
2Division of Navigation Science, Mokpo National Maritime University, 91, Haeyangdaehak-ro,
Mokpo-si 58628, Jeollanam-do, Republic of Korea
*Correspondence: jskim@mmu.ac.kr; Tel.: +82-61-240-7193
Abstract:
Map space composition is the first step in ship route planning. In this study, a map
modeling method for path planning is proposed. This method incorporates the safety margin
based on the theory of geographic space existing in coastal waters, maneuvering space according
to ship characteristics, and the psychological buffer space of a ship navigator. First, the obstacle
area was segmented using the binary method—a segmentation method—based on the international
standard electronic chart image. Next, the margin space was incorporated through the morphological
algorithm for the obstacle area. Finally, to minimize the space lost during the route search, the
boundary simplification of the obstacle area was performed through the concave hull method. The
experimental results of the proposed method resulted in a map that minimized the area lost due to
obstacles. In addition, it was found that the distance and path-finding time were reduced compared
to the conventional convex hull method. The study shows that the map modeling method is feasible,
and that it can be applied to path planning.
Keywords: map space; safety margin; concave hull; morphological; path planning
1. Introduction
Motion-planning and path-planning algorithms are used to find the shortest distance
between two points to avoid collisions of a moving object with impediments within the
configuration space (C-space) [
1
]. C-space is composed of C-space obstacles, where a
moving object collides with physical impediments, or certain designated links collide with
each other [
2
]. Here, C-space refers to a set of locations, where the moving object is able to
move, and a moving object is expressed as a point to resolve the issue of finding routes [
3
].
Therefore, planning a path in C-space, where the moving object is converted to a point,
is simpler than planning the movement of a moving object in real space; furthermore, a
more systematic and algorithm-based approach is ensured through the use of computer
geometry [
4
,
5
]. Thus, through C-space, the geometric relevance between moving objects
and obstacles can be clearly expressed in map space, and the user obtains a solution by
properly mapping the path-planning algorithm to be solved in C-space.
Table 1is a summary of a literature review related to map representation for path
finding. To create a route for a moving object, Ref. [
6
] considered the UKC (Under Keel
Clearance) and generated the region with the risk of standing as grids. Ref. [
7
] proposed
a method that used the A* algorithm to find the shortest route for the environment with
impediments according to the restrictive conditions of the vessel’s rotating radius. In
addition, the generated route was validated through vessel simulation. Ref. [
8
] created
a map space by processing captured images to create a route for rescue activities using a
boat in a submerged environment. Ref. [
9
] proposed a method for generating routes by
combining a quad tree and visibility graph in the coastal waters and setting water depth
and weather information as consideration factors for path generation. Ref. [
10
] created a
Sensors 2023,23, 1723. https://doi.org/10.3390/s23031723 https://www.mdpi.com/journal/sensors

Sensors 2023,23, 1723 2 of 24
map space for route search based on satellite images. Obstacles were identified by image-
processing satellite images, and identified obstacles were incorporated into the map space
through the convex hull algorithm. Ref. [
11
] developed an algorithm for finding a free-space
graph to determine the shortest distance through the boundary of the convex hull of an
object. Ref. [
12
] proposed a method of generating a path that bypasses obstacles through the
convex hull with an arbitrary type of obstacle boundary position and location information
of the starting and arrival points of the moving object in the water space. Ref. [
13
] used the
convex hull concept to propose a method of reducing the number of nodes of a complex
mountainous terrain based on the stratified visibility graph that segments the map into
certain altitudes.
Table 1. A summary of a literature review related to map representation for path finding.
Author
(Year) Achievement Map Representation Method Approach
Classification Considering Factor
Lee et al. [6]
(2019)
Shortest route on
coastal Cell decomposition
Sensors 2023, 23, x FOR PEER REVIEW 3 of 26
Based on the safe water-depth information, a hydrograph that incorporates the water ar-
eas inhibited for navigating was created. The hydrograph was transformed into a binary
image that was treated with binarization in the form of a virtual grid. Here, the threshold
image-segmentation technique was used to transform the electronic hydrograph image
into the binary image. The boundary-extraction technique—an image-processing
method—was used to express the boundary of the water inhibited for navigation from the
impediments on the binary image. Additionally, the concave hull method was used to
minimize the loss of the navigable area instead of the convex hull method. The convex
hull method was frequently used in previous studies, among geometrical algorithms, for
simplifying the boundary of the impediment [15]. Finally, to incorporate the safe distance
for avoiding collision with impediments, the image-expansion method was used to create
the C-space obstacles that enlarged the size of the impediments. Subsequently, the binary
occupancy grid map was generated, and route generation through the PRM (Probabilistic
Road Map) algorithm was chosen. The remainder of this paper is organized as follows: In
Section 2, the background theory of this study is discussed. In Section 3, we will describe
the methodology of C-space. In Section 4, we describe the simulation performed on the
coast of South Korea and the simulation results. In Section 5, we draw conclusions and
discuss recommendations for future studies.
Table 1. A summary of a literature review related to map representation for path finding.
Author
(Year) Achievement Map Representation Method Approach
Classification Considering Factor
Lee et al. [6]
(2019)
Shortest route on
coastal Cell decomposition  Water depth
 Fuel consumption  A*
Ari et al. [7]
(2013)
Shortest route on
coastal Cell decomposition  Ship’s Turning radius  A
Ozkan et al. [8]
(2019)
Composition of
obstacle Roadmap  Aerial image
 Obstacles
 A*, GA, PRM
 Image processing
Lee et al. [9]
(2017)
Shortest route on
coastal
Cell decomposition
Roadmap
 Coastline
 Weather data
 A*
 Quadtree
 Visibility graph
Shi et al. [10]
(2018)
Composition of
obstacle Roadmap  Satellite image
 Obstacle boundaries
 Dijkstra
 Image processing
 Convex hull
Masaudi [11]
(2017)
Reduction of
calculation time Roadmap  Obstacles boundary
 Points
 A*, Dijkstra
 Convex hull
Kim and Park [12]
(2010)
Composition of
obstacle Roadmap  Obstacles boundary
Points  Convex hull
Lim et al. [13]
(2019)
Reduction of
calculation time Roadmap  3D Obstacles
 Contour line
 Visibility graph
 Convex hull
2. Background Theory
2.1. Obstacles Area in Coastal Waters
The No-Go Area (NGA) indicates information on water areas that are not navigable
according to the obstacle and water safety depth safe for the vessel as shown in Figure 1.
In this study, the NGA set according to the safety depth of obstacles and vessels was des-
ignated as the obstacles area of C-space. In this study, the standard for safe water depth
for designating obstacles area was based on the water depth design standard presented
by PIANC.
Water depth
Sensors 2023, 23, x FOR PEER REVIEW 3 of 26
Based on the safe water-depth information, a hydrograph that incorporates the water ar-
eas inhibited for navigating was created. The hydrograph was transformed into a binary
image that was treated with binarization in the form of a virtual grid. Here, the threshold
image-segmentation technique was used to transform the electronic hydrograph image
into the binary image. The boundary-extraction technique—an image-processing
method—was used to express the boundary of the water inhibited for navigation from the
impediments on the binary image. Additionally, the concave hull method was used to
minimize the loss of the navigable area instead of the convex hull method. The convex
hull method was frequently used in previous studies, among geometrical algorithms, for
simplifying the boundary of the impediment [15]. Finally, to incorporate the safe distance
for avoiding collision with impediments, the image-expansion method was used to create
the C-space obstacles that enlarged the size of the impediments. Subsequently, the binary
occupancy grid map was generated, and route generation through the PRM (Probabilistic
Road Map) algorithm was chosen. The remainder of this paper is organized as follows: In
Section 2, the background theory of this study is discussed. In Section 3, we will describe
the methodology of C-space. In Section 4, we describe the simulation performed on the
coast of South Korea and the simulation results. In Section 5, we draw conclusions and
discuss recommendations for future studies.
Table 1. A summary of a literature review related to map representation for path finding.
Author
(Year) Achievement Map Representation Method Approach
Classification Considering Factor
Lee et al. [6]
(2019)
Shortest route on
coastal Cell decomposition  Water depth
 Fuel consumption  A*
Ari et al. [7]
(2013)
Shortest route on
coastal Cell decomposition  Ship’s Turning radius  A
Ozkan et al. [8]
(2019)
Composition of
obstacle Roadmap  Aerial image
 Obstacles
 A*, GA, PRM
 Image processing
Lee et al. [9]
(2017)
Shortest route on
coastal
Cell decomposition
Roadmap
 Coastline
 Weather data
 A*
 Quadtree
 Visibility graph
Shi et al. [10]
(2018)
Composition of
obstacle Roadmap  Satellite image
 Obstacle boundaries
 Dijkstra
 Image processing
 Convex hull
Masaudi [11]
(2017)
Reduction of
calculation time Roadmap  Obstacles boundary
 Points
 A*, Dijkstra
 Convex hull
Kim and Park [12]
(2010)
Composition of
obstacle Roadmap  Obstacles boundary
Points  Convex hull
Lim et al. [13]
(2019)
Reduction of
calculation time Roadmap  3D Obstacles
 Contour line
 Visibility graph
 Convex hull
2. Background Theory
2.1. Obstacles Area in Coastal Waters
The No-Go Area (NGA) indicates information on water areas that are not navigable
according to the obstacle and water safety depth safe for the vessel as shown in Figure 1.
In this study, the NGA set according to the safety depth of obstacles and vessels was des-
ignated as the obstacles area of C-space. In this study, the standard for safe water depth
for designating obstacles area was based on the water depth design standard presented
by PIANC.
Fuel consumption
Sensors 2023, 23, x FOR PEER REVIEW 3 of 26
Based on the safe water-depth information, a hydrograph that incorporates the water ar-
eas inhibited for navigating was created. The hydrograph was transformed into a binary
image that was treated with binarization in the form of a virtual grid. Here, the threshold
image-segmentation technique was used to transform the electronic hydrograph image
into the binary image. The boundary-extraction technique—an image-processing
method—was used to express the boundary of the water inhibited for navigation from the
impediments on the binary image. Additionally, the concave hull method was used to
minimize the loss of the navigable area instead of the convex hull method. The convex
hull method was frequently used in previous studies, among geometrical algorithms, for
simplifying the boundary of the impediment [15]. Finally, to incorporate the safe distance
for avoiding collision with impediments, the image-expansion method was used to create
the C-space obstacles that enlarged the size of the impediments. Subsequently, the binary
occupancy grid map was generated, and route generation through the PRM (Probabilistic
Road Map) algorithm was chosen. The remainder of this paper is organized as follows: In
Section 2, the background theory of this study is discussed. In Section 3, we will describe
the methodology of C-space. In Section 4, we describe the simulation performed on the
coast of South Korea and the simulation results. In Section 5, we draw conclusions and
discuss recommendations for future studies.
Table 1. A summary of a literature review related to map representation for path finding.
Author
(Year) Achievement Map Representation Method Approach
Classification Considering Factor
Lee et al. [6]
(2019)
Shortest route on
coastal Cell decomposition  Water depth
 Fuel consumption  A*
Ari et al. [7]
(2013)
Shortest route on
coastal Cell decomposition  Ship’s Turning radius  A
Ozkan et al. [8]
(2019)
Composition of
obstacle Roadmap  Aerial image
 Obstacles
 A*, GA, PRM
 Image processing
Lee et al. [9]
(2017)
Shortest route on
coastal
Cell decomposition
Roadmap
 Coastline
 Weather data
 A*
 Quadtree
 Visibility graph
Shi et al. [10]
(2018)
Composition of
obstacle Roadmap  Satellite image
 Obstacle boundaries
 Dijkstra
 Image processing
 Convex hull
Masaudi [11]
(2017)
Reduction of
calculation time Roadmap  Obstacles boundary
 Points
 A*, Dijkstra
 Convex hull
Kim and Park [12]
(2010)
Composition of
obstacle Roadmap  Obstacles boundary
Points  Convex hull
Lim et al. [13]
(2019)
Reduction of
calculation time Roadmap  3D Obstacles
 Contour line
 Visibility graph
 Convex hull
2. Background Theory
2.1. Obstacles Area in Coastal Waters
The No-Go Area (NGA) indicates information on water areas that are not navigable
according to the obstacle and water safety depth safe for the vessel as shown in Figure 1.
In this study, the NGA set according to the safety depth of obstacles and vessels was des-
ignated as the obstacles area of C-space. In this study, the standard for safe water depth
for designating obstacles area was based on the water depth design standard presented
by PIANC.
A*
Ari et al. [7]
(2013)
Shortest route on
coastal Cell decomposition
Sensors 2023, 23, x FOR PEER REVIEW 3 of 26
Based on the safe water-depth information, a hydrograph that incorporates the water ar-
eas inhibited for navigating was created. The hydrograph was transformed into a binary
image that was treated with binarization in the form of a virtual grid. Here, the threshold
image-segmentation technique was used to transform the electronic hydrograph image
into the binary image. The boundary-extraction technique—an image-processing
method—was used to express the boundary of the water inhibited for navigation from the
impediments on the binary image. Additionally, the concave hull method was used to
minimize the loss of the navigable area instead of the convex hull method. The convex
hull method was frequently used in previous studies, among geometrical algorithms, for
simplifying the boundary of the impediment [15]. Finally, to incorporate the safe distance
for avoiding collision with impediments, the image-expansion method was used to create
the C-space obstacles that enlarged the size of the impediments. Subsequently, the binary
occupancy grid map was generated, and route generation through the PRM (Probabilistic
Road Map) algorithm was chosen. The remainder of this paper is organized as follows: In
Section 2, the background theory of this study is discussed. In Section 3, we will describe
the methodology of C-space. In Section 4, we describe the simulation performed on the
coast of South Korea and the simulation results. In Section 5, we draw conclusions and
discuss recommendations for future studies.
Table 1. A summary of a literature review related to map representation for path finding.
Author
(Year) Achievement Map Representation Method Approach
Classification Considering Factor
Lee et al. [6]
(2019)
Shortest route on
coastal Cell decomposition  Water depth
 Fuel consumption  A*
Ari et al. [7]
(2013)
Shortest route on
coastal Cell decomposition  Ship’s Turning radius  A
Ozkan et al. [8]
(2019)
Composition of
obstacle Roadmap  Aerial image
 Obstacles
 A*, GA, PRM
 Image processing
Lee et al. [9]
(2017)
Shortest route on
coastal
Cell decomposition
Roadmap
 Coastline
 Weather data
 A*
 Quadtree
 Visibility graph
Shi et al. [10]
(2018)
Composition of
obstacle Roadmap  Satellite image
 Obstacle boundaries
 Dijkstra
 Image processing
 Convex hull
Masaudi [11]
(2017)
Reduction of
calculation time Roadmap  Obstacles boundary
 Points
 A*, Dijkstra
 Convex hull
Kim and Park [12]
(2010)
Composition of
obstacle Roadmap  Obstacles boundary
Points  Convex hull
Lim et al. [13]
(2019)
Reduction of
calculation time Roadmap  3D Obstacles
 Contour line
 Visibility graph
 Convex hull
2. Background Theory
2.1. Obstacles Area in Coastal Waters
The No-Go Area (NGA) indicates information on water areas that are not navigable
according to the obstacle and water safety depth safe for the vessel as shown in Figure 1.
In this study, the NGA set according to the safety depth of obstacles and vessels was des-
ignated as the obstacles area of C-space. In this study, the standard for safe water depth
for designating obstacles area was based on the water depth design standard presented
by PIANC.
Ship’s Turning
radius
Sensors 2023, 23, x FOR PEER REVIEW 3 of 26
Based on the safe water-depth information, a hydrograph that incorporates the water ar-
eas inhibited for navigating was created. The hydrograph was transformed into a binary
image that was treated with binarization in the form of a virtual grid. Here, the threshold
image-segmentation technique was used to transform the electronic hydrograph image
into the binary image. The boundary-extraction technique—an image-processing
method—was used to express the boundary of the water inhibited for navigation from the
impediments on the binary image. Additionally, the concave hull method was used to
minimize the loss of the navigable area instead of the convex hull method. The convex
hull method was frequently used in previous studies, among geometrical algorithms, for
simplifying the boundary of the impediment [15]. Finally, to incorporate the safe distance
for avoiding collision with impediments, the image-expansion method was used to create
the C-space obstacles that enlarged the size of the impediments. Subsequently, the binary
occupancy grid map was generated, and route generation through the PRM (Probabilistic
Road Map) algorithm was chosen. The remainder of this paper is organized as follows: In
Section 2, the background theory of this study is discussed. In Section 3, we will describe
the methodology of C-space. In Section 4, we describe the simulation performed on the
coast of South Korea and the simulation results. In Section 5, we draw conclusions and
discuss recommendations for future studies.
Table 1. A summary of a literature review related to map representation for path finding.
Author
(Year) Achievement Map Representation Method Approach
Classification Considering Factor
Lee et al. [6]
(2019)
Shortest route on
coastal Cell decomposition  Water depth
 Fuel consumption  A*
Ari et al. [7]
(2013)
Shortest route on
coastal Cell decomposition  Ship’s Turning radius  A
Ozkan et al. [8]
(2019)
Composition of
obstacle Roadmap  Aerial image
 Obstacles
 A*, GA, PRM
 Image processing
Lee et al. [9]
(2017)
Shortest route on
coastal
Cell decomposition
Roadmap
 Coastline
 Weather data
 A*
 Quadtree
 Visibility graph
Shi et al. [10]
(2018)
Composition of
obstacle Roadmap  Satellite image
 Obstacle boundaries
 Dijkstra
 Image processing
 Convex hull
Masaudi [11]
(2017)
Reduction of
calculation time Roadmap  Obstacles boundary
 Points
 A*, Dijkstra
 Convex hull
Kim and Park [12]
(2010)
Composition of
obstacle Roadmap  Obstacles boundary
Points  Convex hull
Lim et al. [13]
(2019)
Reduction of
calculation time Roadmap  3D Obstacles
 Contour line
 Visibility graph
 Convex hull
2. Background Theory
2.1. Obstacles Area in Coastal Waters
The No-Go Area (NGA) indicates information on water areas that are not navigable
according to the obstacle and water safety depth safe for the vessel as shown in Figure 1.
In this study, the NGA set according to the safety depth of obstacles and vessels was des-
ignated as the obstacles area of C-space. In this study, the standard for safe water depth
for designating obstacles area was based on the water depth design standard presented
by PIANC.
A
Ozkan et al. [8]
(2019)
Composition of
obstacle Roadmap
Sensors 2023, 23, x FOR PEER REVIEW 3 of 26
Based on the safe water-depth information, a hydrograph that incorporates the water ar-
eas inhibited for navigating was created. The hydrograph was transformed into a binary
image that was treated with binarization in the form of a virtual grid. Here, the threshold
image-segmentation technique was used to transform the electronic hydrograph image
into the binary image. The boundary-extraction technique—an image-processing
method—was used to express the boundary of the water inhibited for navigation from the
impediments on the binary image. Additionally, the concave hull method was used to
minimize the loss of the navigable area instead of the convex hull method. The convex
hull method was frequently used in previous studies, among geometrical algorithms, for
simplifying the boundary of the impediment [15]. Finally, to incorporate the safe distance
for avoiding collision with impediments, the image-expansion method was used to create
the C-space obstacles that enlarged the size of the impediments. Subsequently, the binary
occupancy grid map was generated, and route generation through the PRM (Probabilistic
Road Map) algorithm was chosen. The remainder of this paper is organized as follows: In
Section 2, the background theory of this study is discussed. In Section 3, we will describe
the methodology of C-space. In Section 4, we describe the simulation performed on the
coast of South Korea and the simulation results. In Section 5, we draw conclusions and
discuss recommendations for future studies.
Table 1. A summary of a literature review related to map representation for path finding.
Author
(Year) Achievement Map Representation Method Approach
Classification Considering Factor
Lee et al. [6]
(2019)
Shortest route on
coastal Cell decomposition  Water depth
 Fuel consumption  A*
Ari et al. [7]
(2013)
Shortest route on
coastal Cell decomposition  Ship’s Turning radius  A
Ozkan et al. [8]
(2019)
Composition of
obstacle Roadmap  Aerial image
 Obstacles
 A*, GA, PRM
 Image processing
Lee et al. [9]
(2017)
Shortest route on
coastal
Cell decomposition
Roadmap
 Coastline
 Weather data
 A*
 Quadtree
 Visibility graph
Shi et al. [10]
(2018)
Composition of
obstacle Roadmap  Satellite image
 Obstacle boundaries
 Dijkstra
 Image processing
 Convex hull
Masaudi [11]
(2017)
Reduction of
calculation time Roadmap  Obstacles boundary
 Points
 A*, Dijkstra
 Convex hull
Kim and Park [12]
(2010)
Composition of
obstacle Roadmap  Obstacles boundary
Points  Convex hull
Lim et al. [13]
(2019)
Reduction of
calculation time Roadmap  3D Obstacles
 Contour line
 Visibility graph
 Convex hull
2. Background Theory
2.1. Obstacles Area in Coastal Waters
The No-Go Area (NGA) indicates information on water areas that are not navigable
according to the obstacle and water safety depth safe for the vessel as shown in Figure 1.
In this study, the NGA set according to the safety depth of obstacles and vessels was des-
ignated as the obstacles area of C-space. In this study, the standard for safe water depth
for designating obstacles area was based on the water depth design standard presented
by PIANC.
Aerial image
Sensors 2023, 23, x FOR PEER REVIEW 3 of 26
Based on the safe water-depth information, a hydrograph that incorporates the water ar-
eas inhibited for navigating was created. The hydrograph was transformed into a binary
image that was treated with binarization in the form of a virtual grid. Here, the threshold
image-segmentation technique was used to transform the electronic hydrograph image
into the binary image. The boundary-extraction technique—an image-processing
method—was used to express the boundary of the water inhibited for navigation from the
impediments on the binary image. Additionally, the concave hull method was used to
minimize the loss of the navigable area instead of the convex hull method. The convex
hull method was frequently used in previous studies, among geometrical algorithms, for
simplifying the boundary of the impediment [15]. Finally, to incorporate the safe distance
for avoiding collision with impediments, the image-expansion method was used to create
the C-space obstacles that enlarged the size of the impediments. Subsequently, the binary
occupancy grid map was generated, and route generation through the PRM (Probabilistic
Road Map) algorithm was chosen. The remainder of this paper is organized as follows: In
Section 2, the background theory of this study is discussed. In Section 3, we will describe
the methodology of C-space. In Section 4, we describe the simulation performed on the
coast of South Korea and the simulation results. In Section 5, we draw conclusions and
discuss recommendations for future studies.
Table 1. A summary of a literature review related to map representation for path finding.
Author
(Year) Achievement Map Representation Method Approach
Classification Considering Factor
Lee et al. [6]
(2019)
Shortest route on
coastal Cell decomposition  Water depth
 Fuel consumption  A*
Ari et al. [7]
(2013)
Shortest route on
coastal Cell decomposition  Ship’s Turning radius  A
Ozkan et al. [8]
(2019)
Composition of
obstacle Roadmap  Aerial image
 Obstacles
 A*, GA, PRM
 Image processing
Lee et al. [9]
(2017)
Shortest route on
coastal
Cell decomposition
Roadmap
 Coastline
 Weather data
 A*
 Quadtree
 Visibility graph
Shi et al. [10]
(2018)
Composition of
obstacle Roadmap  Satellite image
 Obstacle boundaries
 Dijkstra
 Image processing
 Convex hull
Masaudi [11]
(2017)
Reduction of
calculation time Roadmap  Obstacles boundary
 Points
 A*, Dijkstra
 Convex hull
Kim and Park [12]
(2010)
Composition of
obstacle Roadmap  Obstacles boundary
Points  Convex hull
Lim et al. [13]
(2019)
Reduction of
calculation time Roadmap  3D Obstacles
 Contour line
 Visibility graph
 Convex hull
2. Background Theory
2.1. Obstacles Area in Coastal Waters
The No-Go Area (NGA) indicates information on water areas that are not navigable
according to the obstacle and water safety depth safe for the vessel as shown in Figure 1.
In this study, the NGA set according to the safety depth of obstacles and vessels was des-
ignated as the obstacles area of C-space. In this study, the standard for safe water depth
for designating obstacles area was based on the water depth design standard presented
by PIANC.
Obstacles
Sensors 2023, 23, x FOR PEER REVIEW 3 of 26
Based on the safe water-depth information, a hydrograph that incorporates the water ar-
eas inhibited for navigating was created. The hydrograph was transformed into a binary
image that was treated with binarization in the form of a virtual grid. Here, the threshold
image-segmentation technique was used to transform the electronic hydrograph image
into the binary image. The boundary-extraction technique—an image-processing
method—was used to express the boundary of the water inhibited for navigation from the
impediments on the binary image. Additionally, the concave hull method was used to
minimize the loss of the navigable area instead of the convex hull method. The convex
hull method was frequently used in previous studies, among geometrical algorithms, for
simplifying the boundary of the impediment [15]. Finally, to incorporate the safe distance
for avoiding collision with impediments, the image-expansion method was used to create
the C-space obstacles that enlarged the size of the impediments. Subsequently, the binary
occupancy grid map was generated, and route generation through the PRM (Probabilistic
Road Map) algorithm was chosen. The remainder of this paper is organized as follows: In
Section 2, the background theory of this study is discussed. In Section 3, we will describe
the methodology of C-space. In Section 4, we describe the simulation performed on the
coast of South Korea and the simulation results. In Section 5, we draw conclusions and
discuss recommendations for future studies.
Table 1. A summary of a literature review related to map representation for path finding.
Author
(Year) Achievement Map Representation Method Approach
Classification Considering Factor
Lee et al. [6]
(2019)
Shortest route on
coastal Cell decomposition  Water depth
 Fuel consumption  A*
Ari et al. [7]
(2013)
Shortest route on
coastal Cell decomposition  Ship’s Turning radius  A
Ozkan et al. [8]
(2019)
Composition of
obstacle Roadmap  Aerial image
 Obstacles
 A*, GA, PRM
 Image processing
Lee et al. [9]
(2017)
Shortest route on
coastal
Cell decomposition
Roadmap
 Coastline
 Weather data
 A*
 Quadtree
 Visibility graph
Shi et al. [10]
(2018)
Composition of
obstacle Roadmap  Satellite image
 Obstacle boundaries
 Dijkstra
 Image processing
 Convex hull
Masaudi [11]
(2017)
Reduction of
calculation time Roadmap  Obstacles boundary
 Points
 A*, Dijkstra
 Convex hull
Kim and Park [12]
(2010)
Composition of
obstacle Roadmap  Obstacles boundary
Points  Convex hull
Lim et al. [13]
(2019)
Reduction of
calculation time Roadmap  3D Obstacles
 Contour line
 Visibility graph
 Convex hull
2. Background Theory
2.1. Obstacles Area in Coastal Waters
The No-Go Area (NGA) indicates information on water areas that are not navigable
according to the obstacle and water safety depth safe for the vessel as shown in Figure 1.
In this study, the NGA set according to the safety depth of obstacles and vessels was des-
ignated as the obstacles area of C-space. In this study, the standard for safe water depth
for designating obstacles area was based on the water depth design standard presented
by PIANC.
A*, GA, PRM
Sensors 2023, 23, x FOR PEER REVIEW 3 of 26
Based on the safe water-depth information, a hydrograph that incorporates the water ar-
eas inhibited for navigating was created. The hydrograph was transformed into a binary
image that was treated with binarization in the form of a virtual grid. Here, the threshold
image-segmentation technique was used to transform the electronic hydrograph image
into the binary image. The boundary-extraction technique—an image-processing
method—was used to express the boundary of the water inhibited for navigation from the
impediments on the binary image. Additionally, the concave hull method was used to
minimize the loss of the navigable area instead of the convex hull method. The convex
hull method was frequently used in previous studies, among geometrical algorithms, for
simplifying the boundary of the impediment [15]. Finally, to incorporate the safe distance
for avoiding collision with impediments, the image-expansion method was used to create
the C-space obstacles that enlarged the size of the impediments. Subsequently, the binary
occupancy grid map was generated, and route generation through the PRM (Probabilistic
Road Map) algorithm was chosen. The remainder of this paper is organized as follows: In
Section 2, the background theory of this study is discussed. In Section 3, we will describe
the methodology of C-space. In Section 4, we describe the simulation performed on the
coast of South Korea and the simulation results. In Section 5, we draw conclusions and
discuss recommendations for future studies.
Table 1. A summary of a literature review related to map representation for path finding.
Author
(Year) Achievement Map Representation Method Approach
Classification Considering Factor
Lee et al. [6]
(2019)
Shortest route on
coastal Cell decomposition  Water depth
 Fuel consumption  A*
Ari et al. [7]
(2013)
Shortest route on
coastal Cell decomposition  Ship’s Turning radius  A
Ozkan et al. [8]
(2019)
Composition of
obstacle Roadmap  Aerial image
 Obstacles
 A*, GA, PRM
 Image processing
Lee et al. [9]
(2017)
Shortest route on
coastal
Cell decomposition
Roadmap
 Coastline
 Weather data
 A*
 Quadtree
 Visibility graph
Shi et al. [10]
(2018)
Composition of
obstacle Roadmap  Satellite image
 Obstacle boundaries
 Dijkstra
 Image processing
 Convex hull
Masaudi [11]
(2017)
Reduction of
calculation time Roadmap  Obstacles boundary
 Points
 A*, Dijkstra
 Convex hull
Kim and Park [12]
(2010)
Composition of
obstacle Roadmap  Obstacles boundary
Points  Convex hull
Lim et al. [13]
(2019)
Reduction of
calculation time Roadmap  3D Obstacles
 Contour line
 Visibility graph
 Convex hull
2. Background Theory
2.1. Obstacles Area in Coastal Waters
The No-Go Area (NGA) indicates information on water areas that are not navigable
according to the obstacle and water safety depth safe for the vessel as shown in Figure 1.
In this study, the NGA set according to the safety depth of obstacles and vessels was des-
ignated as the obstacles area of C-space. In this study, the standard for safe water depth
for designating obstacles area was based on the water depth design standard presented
by PIANC.
Image processing
Lee et al. [9]
(2017)
Shortest route on
coastal
Cell decomposition
Roadmap
Sensors 2023, 23, x FOR PEER REVIEW 3 of 26
Based on the safe water-depth information, a hydrograph that incorporates the water ar-
eas inhibited for navigating was created. The hydrograph was transformed into a binary
image that was treated with binarization in the form of a virtual grid. Here, the threshold
image-segmentation technique was used to transform the electronic hydrograph image
into the binary image. The boundary-extraction technique—an image-processing
method—was used to express the boundary of the water inhibited for navigation from the
impediments on the binary image. Additionally, the concave hull method was used to
minimize the loss of the navigable area instead of the convex hull method. The convex
hull method was frequently used in previous studies, among geometrical algorithms, for
simplifying the boundary of the impediment [15]. Finally, to incorporate the safe distance
for avoiding collision with impediments, the image-expansion method was used to create
the C-space obstacles that enlarged the size of the impediments. Subsequently, the binary
occupancy grid map was generated, and route generation through the PRM (Probabilistic
Road Map) algorithm was chosen. The remainder of this paper is organized as follows: In
Section 2, the background theory of this study is discussed. In Section 3, we will describe
the methodology of C-space. In Section 4, we describe the simulation performed on the
coast of South Korea and the simulation results. In Section 5, we draw conclusions and
discuss recommendations for future studies.
Table 1. A summary of a literature review related to map representation for path finding.
Author
(Year) Achievement Map Representation Method Approach
Classification Considering Factor
Lee et al. [6]
(2019)
Shortest route on
coastal Cell decomposition  Water depth
 Fuel consumption  A*
Ari et al. [7]
(2013)
Shortest route on
coastal Cell decomposition  Ship’s Turning radius  A
Ozkan et al. [8]
(2019)
Composition of
obstacle Roadmap  Aerial image
 Obstacles
 A*, GA, PRM
 Image processing
Lee et al. [9]
(2017)
Shortest route on
coastal
Cell decomposition
Roadmap
 Coastline
 Weather data
 A*
 Quadtree
 Visibility graph
Shi et al. [10]
(2018)
Composition of
obstacle Roadmap  Satellite image
 Obstacle boundaries
 Dijkstra
 Image processing
 Convex hull
Masaudi [11]
(2017)
Reduction of
calculation time Roadmap  Obstacles boundary
 Points
 A*, Dijkstra
 Convex hull
Kim and Park [12]
(2010)
Composition of
obstacle Roadmap  Obstacles boundary
Points  Convex hull
Lim et al. [13]
(2019)
Reduction of
calculation time Roadmap  3D Obstacles
 Contour line
 Visibility graph
 Convex hull
2. Background Theory
2.1. Obstacles Area in Coastal Waters
The No-Go Area (NGA) indicates information on water areas that are not navigable
according to the obstacle and water safety depth safe for the vessel as shown in Figure 1.
In this study, the NGA set according to the safety depth of obstacles and vessels was des-
ignated as the obstacles area of C-space. In this study, the standard for safe water depth
for designating obstacles area was based on the water depth design standard presented
by PIANC.
Coastline
Sensors 2023, 23, x FOR PEER REVIEW 3 of 26
Based on the safe water-depth information, a hydrograph that incorporates the water ar-
eas inhibited for navigating was created. The hydrograph was transformed into a binary
image that was treated with binarization in the form of a virtual grid. Here, the threshold
image-segmentation technique was used to transform the electronic hydrograph image
into the binary image. The boundary-extraction technique—an image-processing
method—was used to express the boundary of the water inhibited for navigation from the
impediments on the binary image. Additionally, the concave hull method was used to
minimize the loss of the navigable area instead of the convex hull method. The convex
hull method was frequently used in previous studies, among geometrical algorithms, for
simplifying the boundary of the impediment [15]. Finally, to incorporate the safe distance
for avoiding collision with impediments, the image-expansion method was used to create
the C-space obstacles that enlarged the size of the impediments. Subsequently, the binary
occupancy grid map was generated, and route generation through the PRM (Probabilistic
Road Map) algorithm was chosen. The remainder of this paper is organized as follows: In
Section 2, the background theory of this study is discussed. In Section 3, we will describe
the methodology of C-space. In Section 4, we describe the simulation performed on the
coast of South Korea and the simulation results. In Section 5, we draw conclusions and
discuss recommendations for future studies.
Table 1. A summary of a literature review related to map representation for path finding.
Author
(Year) Achievement Map Representation Method Approach
Classification Considering Factor
Lee et al. [6]
(2019)
Shortest route on
coastal Cell decomposition  Water depth
 Fuel consumption  A*
Ari et al. [7]
(2013)
Shortest route on
coastal Cell decomposition  Ship’s Turning radius  A
Ozkan et al. [8]
(2019)
Composition of
obstacle Roadmap  Aerial image
 Obstacles
 A*, GA, PRM
 Image processing
Lee et al. [9]
(2017)
Shortest route on
coastal
Cell decomposition
Roadmap
 Coastline
 Weather data
 A*
 Quadtree
 Visibility graph
Shi et al. [10]
(2018)
Composition of
obstacle Roadmap  Satellite image
 Obstacle boundaries
 Dijkstra
 Image processing
 Convex hull
Masaudi [11]
(2017)
Reduction of
calculation time Roadmap  Obstacles boundary
 Points
 A*, Dijkstra
 Convex hull
Kim and Park [12]
(2010)
Composition of
obstacle Roadmap  Obstacles boundary
Points  Convex hull
Lim et al. [13]
(2019)
Reduction of
calculation time Roadmap  3D Obstacles
 Contour line
 Visibility graph
 Convex hull
2. Background Theory
2.1. Obstacles Area in Coastal Waters
The No-Go Area (NGA) indicates information on water areas that are not navigable
according to the obstacle and water safety depth safe for the vessel as shown in Figure 1.
In this study, the NGA set according to the safety depth of obstacles and vessels was des-
ignated as the obstacles area of C-space. In this study, the standard for safe water depth
for designating obstacles area was based on the water depth design standard presented
by PIANC.
Weather data
Sensors 2023, 23, x FOR PEER REVIEW 3 of 26
Based on the safe water-depth information, a hydrograph that incorporates the water ar-
eas inhibited for navigating was created. The hydrograph was transformed into a binary
image that was treated with binarization in the form of a virtual grid. Here, the threshold
image-segmentation technique was used to transform the electronic hydrograph image
into the binary image. The boundary-extraction technique—an image-processing
method—was used to express the boundary of the water inhibited for navigation from the
impediments on the binary image. Additionally, the concave hull method was used to
minimize the loss of the navigable area instead of the convex hull method. The convex
hull method was frequently used in previous studies, among geometrical algorithms, for
simplifying the boundary of the impediment [15]. Finally, to incorporate the safe distance
for avoiding collision with impediments, the image-expansion method was used to create
the C-space obstacles that enlarged the size of the impediments. Subsequently, the binary
occupancy grid map was generated, and route generation through the PRM (Probabilistic
Road Map) algorithm was chosen. The remainder of this paper is organized as follows: In
Section 2, the background theory of this study is discussed. In Section 3, we will describe
the methodology of C-space. In Section 4, we describe the simulation performed on the
coast of South Korea and the simulation results. In Section 5, we draw conclusions and
discuss recommendations for future studies.
Table 1. A summary of a literature review related to map representation for path finding.
Author
(Year) Achievement Map Representation Method Approach
Classification Considering Factor
Lee et al. [6]
(2019)
Shortest route on
coastal Cell decomposition  Water depth
 Fuel consumption  A*
Ari et al. [7]
(2013)
Shortest route on
coastal Cell decomposition  Ship’s Turning radius  A
Ozkan et al. [8]
(2019)
Composition of
obstacle Roadmap  Aerial image
 Obstacles
 A*, GA, PRM
 Image processing
Lee et al. [9]
(2017)
Shortest route on
coastal
Cell decomposition
Roadmap
 Coastline
 Weather data
 A*
 Quadtree
 Visibility graph
Shi et al. [10]
(2018)
Composition of
obstacle Roadmap  Satellite image
 Obstacle boundaries
 Dijkstra
 Image processing
 Convex hull
Masaudi [11]
(2017)
Reduction of
calculation time Roadmap  Obstacles boundary
 Points
 A*, Dijkstra
 Convex hull
Kim and Park [12]
(2010)
Composition of
obstacle Roadmap  Obstacles boundary
Points  Convex hull
Lim et al. [13]
(2019)
Reduction of
calculation time Roadmap  3D Obstacles
 Contour line
 Visibility graph
 Convex hull
2. Background Theory
2.1. Obstacles Area in Coastal Waters
The No-Go Area (NGA) indicates information on water areas that are not navigable
according to the obstacle and water safety depth safe for the vessel as shown in Figure 1.
In this study, the NGA set according to the safety depth of obstacles and vessels was des-
ignated as the obstacles area of C-space. In this study, the standard for safe water depth
for designating obstacles area was based on the water depth design standard presented
by PIANC.
A*
Sensors 2023, 23, x FOR PEER REVIEW 3 of 26
Based on the safe water-depth information, a hydrograph that incorporates the water ar-
eas inhibited for navigating was created. The hydrograph was transformed into a binary
image that was treated with binarization in the form of a virtual grid. Here, the threshold
image-segmentation technique was used to transform the electronic hydrograph image
into the binary image. The boundary-extraction technique—an image-processing
method—was used to express the boundary of the water inhibited for navigation from the
impediments on the binary image. Additionally, the concave hull method was used to
minimize the loss of the navigable area instead of the convex hull method. The convex
hull method was frequently used in previous studies, among geometrical algorithms, for
simplifying the boundary of the impediment [15]. Finally, to incorporate the safe distance
for avoiding collision with impediments, the image-expansion method was used to create
the C-space obstacles that enlarged the size of the impediments. Subsequently, the binary
occupancy grid map was generated, and route generation through the PRM (Probabilistic
Road Map) algorithm was chosen. The remainder of this paper is organized as follows: In
Section 2, the background theory of this study is discussed. In Section 3, we will describe
the methodology of C-space. In Section 4, we describe the simulation performed on the
coast of South Korea and the simulation results. In Section 5, we draw conclusions and
discuss recommendations for future studies.
Table 1. A summary of a literature review related to map representation for path finding.
Author
(Year) Achievement Map Representation Method Approach
Classification Considering Factor
Lee et al. [6]
(2019)
Shortest route on
coastal Cell decomposition  Water depth
 Fuel consumption  A*
Ari et al. [7]
(2013)
Shortest route on
coastal Cell decomposition  Ship’s Turning radius  A
Ozkan et al. [8]
(2019)
Composition of
obstacle Roadmap  Aerial image
 Obstacles
 A*, GA, PRM
 Image processing
Lee et al. [9]
(2017)
Shortest route on
coastal
Cell decomposition
Roadmap
 Coastline
 Weather data
 A*
 Quadtree
 Visibility graph
Shi et al. [10]
(2018)
Composition of
obstacle Roadmap  Satellite image
 Obstacle boundaries
 Dijkstra
 Image processing
 Convex hull
Masaudi [11]
(2017)
Reduction of
calculation time Roadmap  Obstacles boundary
 Points
 A*, Dijkstra
 Convex hull
Kim and Park [12]
(2010)
Composition of
obstacle Roadmap  Obstacles boundary
Points  Convex hull
Lim et al. [13]
(2019)
Reduction of
calculation time Roadmap  3D Obstacles
 Contour line
 Visibility graph
 Convex hull
2. Background Theory
2.1. Obstacles Area in Coastal Waters
The No-Go Area (NGA) indicates information on water areas that are not navigable
according to the obstacle and water safety depth safe for the vessel as shown in Figure 1.
In this study, the NGA set according to the safet