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Cartography and Geographic Information Science
ISSN: (Print) (Online) Journal homepage: https://www.tandfonline.com/loi/tcag20
Label-based generalization of bathymetry data for
hydrographic sounding selection
Noel Dyer, Christos Kastrisios & Leila De Floriani
To cite this article: Noel Dyer, Christos Kastrisios & Leila De Floriani (2022): Label-based
generalization of bathymetry data for hydrographic sounding selection, Cartography and
Geographic Information Science, DOI: 10.1080/15230406.2021.2014974
To link to this article: https://doi.org/10.1080/15230406.2021.2014974
© 2022 The Author(s). Published by Informa
UK Limited, trading as Taylor & Francis
Group.
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Label-based generalization of bathymetry data for hydrographic sounding
selection
Noel Dyer
a,b
, Christos Kastrisios
c
and Leila De Floriani
b,d
a
Office of Coast Survey, National Oceanic and Atmospheric Administration, MD, USA;
b
Department of Geographical Sciences, University of
Maryland, MD, USA;
c
Center for Coastal & Ocean Mapping/Joint Hydrographic Center, University of New Hampshire, NH, USA;
d
University of
Maryland Institute for Advanced Computer Studies, University of Maryland, MD, USA
ABSTRACT
Hydrographic sounding selection is the process of generalizing high-resolution bathymetry data to
a more manageable subset capable of supporting nautical chart compilation or bathymetric
modeling, and thus, is a fundamental task in nautical cartography. As technology improves and
bathymetric data are collected at higher resolutions, the need for automated generalization
algorithms that respect nautical cartographic constraints increases, since errors in this phase are
carried over to the nal product. Currently, automated algorithms for hydrographic sounding
selection rely on radius- and grid-based approaches; however, their outputs contain a dense set of
soundings with a signicant number of cartographic constraint violations, thus increasing the
burden and cost of the subsequent, mostly manual, cartographic sounding selection. This work
presents a novel label-based generalization algorithm that utilizes the physical dimensions of the
symbolized depth values on charts to avoid the over-plot of depth labels at scale. Additionally,
validation tests based on cartographic constraints for nautical charting are implemented to
compare the results of the proposed algorithm to radius and grid-based approaches. It is shown
that the label-based generalization approach best adheres to the constraints of functionality
(safety) and legibility.
ARTICLE HISTORY
Received 25 April 2021
Accepted 2 December 2021
KEYWORDS
Bathymetry; generalization;
nautical cartography;
symbology; hydrography;
cartographic constraint
1. Introduction
Electronic Navigational Charts (ENCs) are essential tools
for safe marine navigation. ENCs are mandatory on all
Safety Of Life At Sea (SOLAS) regulated vessels and visua-
lized using onboard Electronic Chart Display and
Information Systems (ECDISs). The main goal of an
ENC is to promote safe navigation through waterways.
Ship groundings are significantly reduced when up-to-
date ENCs are available (Wolfe & Pacheco, 2020).
Consequently, automating digital cartographic processes
has become a priority for increasing the efficiency of ENC
updates. Algorithms that can provide consistent results
while reducing production time and costs are increasingly
valuable to organizations operating in time-sensitive envir-
onments. This is particularly the case in nautical cartogra-
phy, where updates to bathymetry and locations of dangers
to navigation need to be disseminated as quickly as possi-
ble. However, any manual or automated process for updat-
ing nautical charts must adhere to strict cartographic
guidelines and standards to ensure safe maritime naviga-
tion. This makes the development of algorithms for auto-
mated nautical cartography especially difficult.
Vessels traveling the open ocean regularly utilize
nautical charts compiled by different hydrographic
offices around the world. As a result, hydrographic
surveying practices, data formats, compilation guide-
lines, and chart symbology must conform to established
standards in order to maintain consistency across
nations. Regulations and requirements regarding the
specifications of international nautical charts are pub-
lished by the International Hydrographic Organization
(IHO). The IHO publication S-52 Specifications for
Chart Content and Display Aspects of ECDIS
(International Hydrographic Organization, 2017a) is
particularly relevant to this research, as it describes the
symbology of features present in an ENC.
Data generalization is one of the most time-
consuming tasks in digital cartography and a target for
automation (e.g. McMaster & Shea, 1992; Stoter et al.,
2014; Wang & Müller, 1998; Rocca et al., 2017; Yan &
Weibel, 2008; Yan et al., 2017; Yu, 2018; Lu et al., 2019;
Arundel & Sinha, 2020). Within the subdomain of nau-
tical cartography, the generalization of bathymetry is
particularly challenging. This is primarily due to the
CONTACT Noel Dyer ndyer214@gmail.com
Supplemental data for this article can be accessed here.
CARTOGRAPHY AND GEOGRAPHIC INFORMATION SCIENCE
https://doi.org/10.1080/15230406.2021.2014974
© 2022 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use,
distribution, and reproduction in any medium, provided the original work is properly cited.
disparity between resolutions at which ENCs are pro-
duced and bathymetry data are collected. ENCs are
produced at specific scales that are intended for different
usage from overview (≥1:2,500,000) to berthing
(≤1:10,000; Weintrit, 2018). Contemporary bathymetric
data collection techniques are capable of collecting sub-
meter resolution data to ensure full seafloor-bottom
coverage for safe navigation as well as to support other
various scientific uses of the data (see, Lecours et al.,
2016 for survey). These high-resolution data must be
generalized for compatibility with nautical charting
practices.
All data composing the ENC are generalized to the
required scale by a trained cartographer. The ENC data
are attributed to IHO S-57 standards (International
Hydrographic Organization, 2014), which are referenced
by the ECDIS to symbolize features strictly to IHO S-52
standards (International Hydrographic Organization,
2017a). These symbolized features are rendered on the
ECDIS screen and used by the mariner to navigate. The
ENC is a Digital Landscape Model (DLM) of a specific
area, which is converted to a Digital Cartographic Model
(DCM) when rendered on the ECDIS. The system is not
performing any on-the fly cartographic generalization of
the ENC and strictly displays its content. This ensures the
cartographer is making the final cartographic judgment of
how the ENC will be portrayed as a DCM, rather than
questionable algorithms.
There are specific cartographic constraints that govern
the generalization of bathymetry for ENCs, which are
based on supporting safe maritime navigation. Adapted
from Ruas and Plazanet (1997) and Zhang and Guilbert
(2011), the cartographic constraints for bathymetric gen-
eralization in the context of nautical cartography are
defined as follows, in descending order of importance:
(1) Functional: emphasize features relevant to the
purpose of the chart. This is often referred to as
the safety constraint, or shoal-bias, where depth
information on the chart must not appear deeper
than the source data at any location.
(2) Legibility: the perceptibility threshold of map
features on chart. In order to detect legibility
issues, it is necessary to assess the symbolization
of features and separation and visibility limits
(Rytz et al., 1980). Sounding labels on nautical
charts, for example, must avoid over-plot in
order to maintain chart readability.
(3) Displacement: the maximum allowed displace-
ment of an object according to its nature. The
point of origin for a sounding label (sounding
coordinates) must not be displaced from the
source data.
(4) Shape: although the level of detail is reduced dur-
ing generalization, characteristics and the general
shape of the seafloor should be preserved.
Morphological details should be maintained as
much as possible.
Compromises in satisfying these constraints must be
made during the generalization process. The function-
ality constraint is the most important to safe marine
navigation. The legibility and displacement constraints
are equally as important; in the case of soundings, depth
labels must be readable and the exact locations of depths
must be preserved. Generalization methods in cartogra-
phy for preserving morphological features have been
presented in the literature (Yu et al., 2021); however,
the morphology constraint is the least important of all.
When in direct conflict, functionality, legibility, and
displacement constraints should be favored over mor-
phological details. For example, indiscernible overlap-
ping sounding labels in an area of high seafloor
complexity does not provide any added value.
Sounding selection, the process of generalizing source
bathymetry data to the scale of a target chart while adher-
ing to nautical cartographic constraints, is notoriously
time-consuming. Sounding selection can be separated
into two categories: hydrographic and cartographic.
Hydrographic sounding selection involves generalizing
bathymetric datasets to produce a shoal-biased and
dense, yet manageable, subset of soundings without
label over-plot that can support nautical chart compila-
tion or bathymetric modeling (MacDonald, 1984; Oraas,
1975; Zoraster & Bayer, 1992). The hydrographic sound-
ing selection reduces data redundancy while enforcing
nautical cartographic constraints as much as possible.
However, the soundings for chart display must be limited
to the least amount necessary to illustrate the seafloor, in
order to maintain legibility when other features are pre-
sent. Therefore, a cartographic sounding selection, the
identification of soundings from the hydrographic selec-
tion for chart display, must be produced. This is
a separate process that further aids navigation by illus-
trating seafloor characteristics as well as highlighting
hazards and transportation routes.
The primary difference between the hydrographic
and cartographic selections is that the hydrographic
selection only considers the source bathymetry,
whereas the cartographic selection must incorporate
navigational features present on the ENC that also
affect sounding distribution, e.g. rocks, wrecks,
obstructions, dredged areas, shoreline, and depth con-
tours. Thus, the hydrographic sounding selection is
a preliminary generalization step focusing on sound-
ing distribution, where the reduced density subset
2N. DYER ET AL.
should be shoal-biased and retain the maximum num-
ber of soundings possible without degrading legibility.
This is only achieved by incorporated the nautical
cartographic constraints into the generalization.
There are also research efforts that attempt to derive
a cartographic sounding selection from the source
bathymetry (e.g. Haigang et al., 1999; Lovrinčević,
2019; Yu, 2018). However, due to the complexity of
the procedure and recognized deficiencies with existing
approaches (see, Cavanagh, 2019), cartographic sound-
ing selection remains a semi-manual process (Kastrisios
& Calder, 2018). The lack of a fully automated solution
results in the continued practice of identifying sound-
ings for chart display from the hydrographic sounding
selection. Thus, the focus of this work is to produce an
optimal hydrographic sounding selection, from which
cartographers can select chart-ready soundings or uti-
lize as input into another algorithm. Consequently, the
generalization process must adhere to the aforemen-
tioned cartographic constraints as much as possible to
avoid carrying errors into the cartographic sounding
selection and, ultimately, the final cartographic product.
This workflow is summarized in Figure 1.
Traditionally, the hydrographic sounding selection
was in the form of a sheet of paper, known as a smooth-
sheet. The smooth-sheet was a manual shoal-bias selec-
tion from the source data, where the physical dimen-
sions of the paper and label sizes limited the quantity of
soundings that could be included. Figure 2 shows an
example of a smooth-sheet (Putnam, 2013).
Today with digital cartographic production systems,
hydrographic sounding selections are stored in a digital
format, namely point clouds. Existing algorithms in the
literature to derive such point clouds are intrinsically
limited in that they do not consider the final DCM of
the data during generalization and rely on simple dis-
tance metrics. Moreover, these approaches require user-
defined input parameters, which can significantly affect
the results depending on the selected values. This results
in hydrographic selections with an enormously large
number of soundings that are still difficult to work with
for the semi-manual cartographic sounding selection.
In this work we introduce a novel sounding label-
based generalization algorithm to provide a shoal-
biased hydrographic sounding selection that is pro-
duct-driven and independent of user-defined para-
meters. The hydrographic sounding selection
produced by the label-based generalization is com-
pared with selections produced by existing radius-
and grid-based methods. Furthermore, for the first
time in the literature, the hydrographic selections
produced by each approach are validated using the
four aforementioned cartographic constraints. The
incorporated validation aims to serve as a basis for
standardizing a performance evaluation method for
future automation efforts. It is demonstrated with
the support of four test datasets that the proposed
label-based generalization algorithm performs the
best in regard to the fundamental constraints of nau-
tical cartography: functionality and legibility.
The remainder of this paper is organized in the follow-
ing manner. Section 2 discusses related work. Section 3
with the accompanying Appendix A (in Supplementary
Materials) proposes the new methodology. Section 4 pre-
sents experimental results and a comparison to existing
algorithms. Finally, Section 5 draws concluding remarks.
2. Related work
A common approach to hydrographic sounding selec-
tion involves using a fixed or variable sized radius (also
referred to as a radius of inuence) to reduce sounding
density (Haigang et al., 2005, 1999; Oraas, 1975).
Soundings are sorted from shallow to deep and begin-
ning with the shallowest sounding, the target sounding,
Figure 1. Workflow from source bathymetry to ENC.
Figure 2. Example smooth-sheet (Putnam, 2013).
CARTOGRAPHY AND GEOGRAPHIC INFORMATION SCIENCE 3
a buffer is applied using the input radius value. All of the
soundings inside this buffer that are deeper than the
target sounding are then removed from the list. The
process is repeated for the remaining soundings in the
list until all soundings have been examined. Figure 3
illustrates the radius- and grid-based (described later in
this section) generalization algorithms, where for the
radius-based approach (Figure 3A) the deep soundings
are removed in favor of the target sounding.
The main advantage of radius-based approaches is
that the output is evenly distributed. Soundings can
have equal spacing, in the case of a fixed radius, or
exhibit increased spacing with depth, as with a variable
length radius that increases with depth. However, these
approaches violate both legibility and functionality con-
straints by under- and over-generalizing in different
regions of the bathymetry.
A fixed-length radius approach seems suitable for
generalizing a dataset that covers a mostly flat seafloor
topography where the bathymetry does not exhibit
a wide depth range. If all depths had the same number
of digits composing their labels, for example, the user
could set the length of the radius to correspond to the
width of sounding label. However, the width of the
sounding label is not equal to the height, which means
that this approach would still result in legibility and
safety constraint violations. Furthermore, this limited
depth range and equal sounding label width is not
common in most hydrographic surveys, or in the full
extent of a nautical chart, and does not accurately gen-
eralize bathymetry with broader ranges of depth. This is
due to the difference in the number of the glyphs (repre-
sentation of a digit) and their vertical position that make
up the sounding label (see Appendix A for details).
It could be assumed that the use of a variable length
radius that increases with depth could help reduce the
under- and/or over-generalization that can occur with
the fixed length radius, where the user could select
a starting radius equal to the label size of the shallowest
sounding and the ending radius equal to the deepest
sounding label. The shallower depths would be generalized
with the smaller radius and the deeper depths would be
generalized with the larger radius. However, as shown in
Section 4, it is clear that this is not the case for the datasets
examined. On the contrary, it is demonstrated that this
approach still results in functionality and legibility con-
straint violations similar to that of the fixed-radius. The
problem partially arises from depths within the same depth
range that have very different label widths and heights.
Depths of 9.9, 10, and 10.1 meters (m), for example, would
have very similar radius lengths for generalization; how-
ever, their respective depth labels have different heights
and widths due to the number of digits and presence of
decimal values (see, Figure 4). Hence, depths with only
a two decimeter difference can have very different label
footprints (see, Section 3.1 and Appendix A).
Furthermore, using a circular shape for generalizing
bathymetry is not ideal for hydrographic sounding
selection, as the sounding label footprint is rectangular
(depths without a decimal) or polygonal (depths with
a decimal) and the circular shape can over- and/or
under-generalize depending on the depth value. Over-
Figure 3. Common generalization approaches: a) radius-based and b) grid-based.
4N. DYER ET AL.
generalization occurs when the circle is larger than the
label footprint and soundings are removed that could be
retained without overlap. Under-generalization occurs
when the circle does not cover the entire depth label and
soundings are retained that will overlap. Figure 4 shows
how over- and under-generalization can occur with the
radius-based approaches for labels composing of one,
two, or three glyphs (digits), with or without decimals.
Figure 4 also illustrates the increased complexity of
label placement in ECDIS portrayal, where the pivot
point is not always in the center of the label and can
vary depending on the number of digits and the pre-
sence of decimals. The pivot point for three-digit labels
with no decimal value (far-right labels in Figure 4), for
example, is located in the center of the tens column. The
pivot point for the two-digit label with a decimal value
(second from right labels in Figure 4) is located between
the tens and ones columns and also vertically offset.
Another generalization approach involves superim-
posing a triangular or rectangular grid over the data,
and identifying the shallowest sounding for each grid
cell (Skopeliti et al., 2020; Tsoulos & Stefanakis, 1997).
This concept is illustrated in Figure 3b, where a single
sounding has been identified for each grid cell.
A grid-based approach can violate the legibility
constraint in many of the same ways as the fixed
radius-based approach. The grid cell size is fixed and
will under- and over-generalize for bathymetry with
broad depth ranges. Furthermore, depending on the
grid point of origin as well as grid cell size and
shape, soundings can be located in different grid
cells, thus resulting in inconsistent outputs based
on the implementation. Moreover, as shown in the
far-left column of the grid in Figure 3b, soundings
can be within close proximity of one another regard-
less of cell size, which can further add legibility
constraint violations. A minimum distance between
soundings can be maintained (e.g. Skopeliti et al.,
2020), yet, the outcome of both radius- and grid-
based approaches remains highly dependent on user-
defined input parameters and, as such, they generally
result in datasets with considerable functionality and
legibility constraint violations. Figure 5 illustrates
this further by portraying the vertical profile of
a seabed and the resulting sounding selections
derived from grid-based (Figure 5a and 5b) and
radius-based (Figure 5c and 5d) approaches. The
use of different points of origin for the grid-based
Figure 4. Over- and under- generalization as a result of the radius-based generalization approaches, where the radius length, R, is
based on the width or height of the sounding label and D represents a given glyph.
CARTOGRAPHY AND GEOGRAPHIC INFORMATION SCIENCE 5
approach (Figure 5a and 5b), as well as different
thinning distances (Figure 5c and 5d) results in dif-
ferent selections. The solid lines for the radius size in
Figure 5c and Figure 5d are used to indicate the
areas where neighbor soundings have not yet been
evaluated, and the dashed lines indicate areas that
have been previously evaluated and a shallow sound-
ing was selected.
Figure 5a and 5d show soundings that could be
potentially selected from either the grid- (A1) or radius-
based (D1-D4) approaches. Sounding A1 in Figure 5a is
the shallowest depth for the grid cell, but not the shal-
lowest depth within the x-dimension of the A1 depth
label (shown by green bar). A peak is present in the grid
cell to the right, which would be contained by the depth
label of sounding A1. If sounding A1 became a charted
depth through the subsequent cartographic sounding
selection process, a deeper depth would be displayed
in favor of a shallow depth, resulting in a violation of
the functionality constraint and danger to navigation.
Similarly, for soundings D1-D4 in Figure 5d, the carto-
grapher would have to manually select one of these
soundings for chart display in order to avoid label over-
lap and crowding the chart. Selecting the incorrect
sounding would be a violation of the safety constraint.
However, our proposed label-based approach would
automatically select the correct shallow sounding, D1,
and eliminate soundings D2-D4, which are deeper and
within the D1 depth label.
In summary, existing algorithms for hydrographic
sounding selection are inconsistent and highly depen-
dent on input parameters. Thus, in the following section
we propose a label-based generalization algorithm that
is product-driven in relation to S-52 and independent of
user-defined parameters.
3. Proposed methodology
Our label-based generalization process involves the
removal of soundings from the source bathymetry
data using label footprints at scale and shoal-bias in
order to enforce the aforementioned cartographic con-
straints to the maximum extent possible. The basis of
our approach consists of rounding the depth values to
S-52 standards for ENCs, calculating the sounding
label footprint, and generalizing the bathymetry using
the label footprint while preserving shallow depths.
Our approach utilizes bathymetry data represented as
a set of points, where the generalization algorithm is
agnostic of the data collection method or data
distribution.
Figure 5. Vertical profile of seabed and the selection with grid- (a, b) and radius-based (c, d) generalization approaches using different
grid point of origin (a – b) and radius size (c – d).
6N. DYER ET AL.
Section 3.1 with the accompanying Appendix
A describes the methods for rounding depth values
according to S-52 standards and sounding label dimen-
sions. Section 3.2 describes the algorithm for general-
izing the bathymetry using the sounding label
footprint.
3.1 Sounding label footprint
Calculating the sounding label footprint requires first
rounding the survey depth value and then using sound-
ing label portrayal information and relevant visual per-
ception limits to determine the label footprint at chart
scale (see Appendix A). The IHO S-52 publication pro-
vides standards for safely rounding depths from surveys
to ENCs, where depths ranging from 0 to 31 m are
rounded down to the nearest decimeter and depths
over 31 m are rounded down to the nearest meter.
This rounded depth value is the value displayed on the
ENC and is used to calculate the footprint of the sound-
ing label.
The calculation of the label footprint requires the glyph
(D in Figure 6) height (D
H
), glyph width (D
W
), stroke
width (S
W
), spacing between glyphs (D
S
), and label spacing
(L
S
). A minimum label spacing must be maintained to
ensure legibility and avoid confusion between two neigh-
boring labels that can be interpreted as a single label, e.g.
a 23 m label from individual labels of 2 m and 3 m. The
above values depend on the mapping application, the dis-
play medium, expected viewing distance, and human per-
ception limits (e.g. Rytz et al., 1980; HFES, 2007; Ware,
2013; Lakshminarayanan, 2015). The reader is referred to
Appendix A for a more detailed analysis of the label
footprint. Figure 6 shows a diagram illustrating the vari-
ables used to calculate the polygonal footprint, where
values are given at millimeters (mm) at scale.
Referring to Figure 6, the difference in height is
a result of the vertical offset for the decimal value
(required by S-52 standards), as described in Appendix
A. This example illustrates the complexity of the pro-
blem, which cannot be approximated with a single value
parameter for use with the radius or grid-based
approaches and exemplifies the need for the proposed
label-based generalization approach.
3.2 Label-based generalization
Our label-based generalization approach has two com-
ponents. The first component consists of removing deep
soundings directly inside the sounding label footprint to
enforce shoal-bias, while the second component
removes soundings whose labels overlap with shallower
sounding labels.
The label-based generalization was initially developed
as a single process; however, it was found that the pro-
posed sequential approach resulted in fewer functionality
constraint violations. The algorithm for both components
is the same, the difference is that the second component
uses a larger footprint to generalize the data in order to
remove overlapping labels. This is illustrated in Figure 7,
where the black rectangle represents the footprint used in
the first component and the red rectangle, referred to as
the legibility rectangle, is used in the second component of
the label-based generalization. In this example, the 22.2 m
soundings are within the legibility rectangle and will be
eliminated because, when rendered at scale, they overlap
with the 20 m target label. Conversely, the 22.5 m sound-
ings are marginally outside the legibility rectangle, and, as
such, are retained in the generalized dataset. The example
of Figure 7 is one of the many legibility rectangles that
have been developed and implemented to account for the
various cases of the target and neighboring soundings.
The input to the first component of the algorithm
consists of a set of source soundings and the scale at
which the bathymetry data are to be processed. Each
input sounding consists of three real values that repre-
sent longitude, latitude, and depth, respectively. Such
information are maintained in a list, that we call the
source soundings list, and the data structures used when
processing the input data encode just the indices of the
soundings in such list.
The soundings are inserted into a bucketed point-
region (PR) quadtree (Samet, 1984), where sounding
indices inside the source sounding list are stored in its
leaf nodes. A bucketed PR-quadtree recursively decom-
poses a square domain in the plane containing the
Figure 6. The general case of the polygon label footprint with
the label spacing.
CARTOGRAPHY AND GEOGRAPHIC INFORMATION SCIENCE 7
soundings by subdividing it into nested square regions,
called blocks. Each block has a maximum capacity, speci-
fied as input, and it is recursively split into four quadrants
when the number of soundings in the block exceeds the
capacity. The primary factors influencing the efficiency of
the data structure and associated capacity value are
related to the data distribution, i.e. uniformity, regularity,
and density. Experiments were conducted using the four
datasets in this study to test the efficiency of different
capacity values and it was found that a capacity value of
0.04% of the number of points achieved suitably efficient
results.
An auxiliary list is also created, sorted source
soundings, containing the indices of the source sound-
ings sorted from shallow to deep. Beginning with the
first element in sorted source soundings, called the
target sounding, the label polygon of target sounding
is calculated based on the input scale, as discussed in
Section 3.1 and Appendix A. This label footprint is
then used to traverse the quadtree, where the indices
of those soundings that fall inside the label footprint
and are deeper than the target sounding are removed
from the quadtree. The sounding indices removed
during this process are also removed from sorted
source soundings, as they no longer require considera-
tion. This process is repeated iteratively on sorted
source soundings, until each element of such list has
been assessed. The output of this process is the quad-
tree containing the generalized sounding indices for
the first component of the label-based generalization
and the generalized soundings in sorted source sound-
ings. Algorithm 1 describes the generalization algo-
rithm in a pseudo-code format.
Algorithm 1: Label-based generalization
Input: S, sorted list of source sounding indices
Input: L, list of source soundings
Input: R, scale of chart
Input: Qt, bucketed PR-quadtree of source sounding indices
Output: Qt, the bucketed PR-quadtree containing generalized sounding
indices
1: for index in S:
2: # Retrieve sounding
3: target_sounding = L[index]
4: # Call function to calculate sounding label footprint
5: label_footprint = get_sounding_label(target_sounding.get_z(), R)
6: # Traverse PR-quadtree and identify indices of soundings inside the
label footprint
7: overlap_indices = Qt.traverse(label_footprint)
8: # Remove deep sounding indices from PR-quadtree and source
sounding list
9: for overlap_index in overlap_indices:
10: if L[overlap_index].get_z() > target_sounding.get_z():
11: Qt.remove(overlap_index)
12: S.remove(overlap_index)
The second component of the label-based general-
ization removes deep soundings whose labels overlap
with shallow sounding labels. This is achieved by using
Algorithm 1 and a larger legibility footprint calculated
based on the label of the target sounding, labels of
potential neighbors, and a label separation value
(0.75 mm) to maintain legibility among soundings, as
described in Section 3.1 and Appendix A.
As previously described, the capacity value for the
quadtree is based on a percentage of the total quantity
of input soundings. The first component of the label-
based generalization process removes a large quantity of
soundings, which in turn, significantly reduces the capa-
city value for the second generalization component. It
was found through the testing of the datasets used in this
work, that the first generalization component removes
approximately 96.7% to 99.2% of the original number of
soundings. Thus, the capacity value for the first general-
ization component would be far too large for the second
generalization component and not provide an adequate
decomposition of the domain. Therefore, the quadtree is
updated using recursive node merging to reflect the
change in capacity value.
Overlapping labels are removed by utilizing the
updated quadtree and the remaining soundings in sorted
source soundings. Beginning with the first element in
sorted source soundings, called generalized sounding, the
larger footprint of generalized sounding, called the legibil-
ity rectangle, is calculated based on the input scale. The
legibility rectangle is then used to traverse the PR-
quadtree, where the label footprint for each sounding
inside legibility rectangle is calculated. Indices of deep
soundings whose label overlaps with the label of general-
ized sounding are removed from the quadtree and sorted
source soundings, as they no longer require consideration.
Figure 7. Example generalization footprints for the first (black)
and second (red) components of the label-based generalization
process.
8N. DYER ET AL.
This is then repeated for the next element in sorted source
soundings, until each element has been assessed. This
results in a final set of soundings where sounding labels
do not overlap at the selected scale.
4. Experimental results
In this section, we compare the output of the proposed
algorithm to the output of the fixed-radius, variable-radius,
and grid-based approaches, described in Section 2. Our
label-based algorithm has been implemented in Python,
and we also developed Python implementations for the
other three approaches, because of the lack of availability of
existing public-domain implementations.
The hydrographic survey data used in our experiments
were identified using the National Centers for
Environmental Information (NCEI) bathymetric data
viewer portal (National Centers for Environmental
Information (NCEI), 2021). The data were selected to be
representative of a variety of geographic regions of the
U.S., depth ranges of the surveys, and scale of largest
ENC in the area. Each of the datasets are horizontally
referenced to their respective North American Datum of
1983 Universal Transverse Mercator zone and vertically
referenced to mean lower low water. Figure 8 shows the
bathymetry for each survey. Table 1 summarizes metadata
information for each survey, where the depths are rounded
for chart display, as discussed in the previous section.
Each dataset was generalized using the proposed label-
based algorithm as well as the radius and grid-based
approaches. The label polygons for the label-based
algorithm were calculated based on those discussed in
Section 3.1 and Appendix A. All approaches were pro-
cessed for largest scale ENC in the region, shown in Table 1.
BBH¼CHþ0:5ND
ð Þ½ þ SW
BBW¼CWNCþCSNC1ð Þ þ SW
Where (in parenthesis are the values used for ENCs):
BB
H
is the bounding box height,
BB
W
is the bounding box width,
C
H
is the glyph height (2.5 mm),
C
W
is the glyph width (1.25 mm),
S
W
is the stroke width (0.32 mm),
C
S
is the spacing between two glyphs with the stroke
width included (1 mm),
N
c
is the total number of glyphs of the depth
value, and
N
D
is the number of decimal glyphs in the depth
value ({0, 1}).
Equation 1. Formula for calculating height and width
of a symbolized sounding bounding box.
In practice, we are aware of hydrographic offices using
a universal value of 0.4 mm at scale (or even as low as
0.1 mm) as the input parameter for radius- and grid-
based approaches. However, this value results in an
extremely dense set of soundings that is far from being
comparable with the label-based approach. Table 2 shows
the total soundings from the fixed-radius with a radius
length of 0.4 mm, a variable-radius with a minimum
length of 0.4 mm and maximum length of 0.8 mm, and
grid cell height and width of 0.4 mm to the scale.
Figure 8. Bathymetry for surveys in a) Charleston Harbor, b) Narragansett Bay, c) Tampa Bay, and d) Strait of Juan de Fuca.
CARTOGRAPHY AND GEOGRAPHIC INFORMATION SCIENCE 9
Due to this, we used input parameters for the radius-
and grid-based approaches based on statistics of the
depth values for each survey and their corresponding
depth label dimensions, shown in Table 1. Using the
depth value information in Table 1, we calculate the
width and height of the corresponding depth label
bounding box for the radius and grid cell dimensions
that are given by Equation 1 in mm at scale. These
values, described in the following paragraph and sum-
marized in Table 3, further reduce the number of
selected soundings and demonstrate our effort to opti-
mize the parameters for the radius- and grid-based
approaches. However, as can be seen in Table 4, they
still result in denser datasets than the label-based
approach. We considered increasing the radii lengths
and grid cell sizes to further reduce the number of
soundings in the resulting hydrographic selections,
however, this would only increase the over-
generalization problem described in Section 2 and
would not have any solid foundation for comparison
with the label-based approach. This further demon-
strates the utility of the product-driven label-based
approach, which does not require such parameters.
Fixed radius and grid-based approaches have a single
input parameter determining the size of the area for
generalization. Thus, the width of the sounding label
bounding box at scale for the average depth of each
survey was calculated using Equation 1 and halved for
the fixed radius approach. Similarly, the variable radius
lengths were determined by using the minimum depth as
the starting radius length and the maximum depth as the
ending radius length. The height and width of the average
depth sounding label bounding box were also used for the
grid cell size, where the southwest corner of the data set is
the point of origin. The only parameter for the proposed
label-based algorithm was the target scale, at which each
individual sounding label footprint is calculated. Table 3
summarizes the input parameters of the existing
approaches for each survey in mm at chart scale
and m. This illustrates how sounding labels on a smaller
scale chart (Tampa Bay) occupy a larger real-world area
compared to larger scales (Narragansett Bay).
The increases between the minimum and maximum
radii length in each of the datasets are due to the differ-
ences in label widths between the minimum and max-
imum depths. All of the datasets have a minimum depth
label consisting of two digits and a maximum depth
label consisting of three digits, where the maximum
and average depth label of the Strait of Juan de Fuca
data set were the only labels without decimal values.
Ideally, the average value used to calculate the fixed
radius length should be between the minimum and
maximum radii length. This is not the case for any of
the datasets, which is due to the fact that despite the
larger value of the average depth, both the average and
minimum depths have the same number of digits (two)
composing the label. This is important to note, as label
widths can change when decimal values are involved
and not from just shallow to deep. This further exem-
plifies the difficulty associated with identifying optimal
parameters with respect to the legibility constraint for
the radius and grid – based approaches.
Table 1. Metadata of the hydrographic surveys used in this work.
Dataset
Survey
Number
Minimum Depth
(m)
Maximum Depth
(m)
Average Depth
(m)
Largest Scale ENC in the
Area
Charleston Harbor, SC H11861 0.0 19.7 8.9 1:20,000
Narragansett Bay, RI H11988 0.4 21.9 7.6 1:20,000
Tampa Bay, FL H12018 1.5 18.2 7.4 1:40,000
Strait of Juan de Fuca, WA H12626 0.0 138 68 1:25,000
Table 3. Summary of input parameters for radius- and grid-based approaches.
Dataset
Minimum Radius
Length (mm, m)
Maximum Radius
Length (mm, m)
Fixed Radius
Length (mm, m)
Grid Cell Height
(mm, m)
Grid Cell Width
(mm, m)
Charleston Harbor, SC 1.91, 38.2 3.035, 60.7 1.91, 38.2 3.32, 66.4 3.82, 76.4
Narragansett Bay, RI 1.91, 38.2 3.035, 60.7 1.91, 38.2 3.32, 66.4 3.82, 76.4
Tampa Bay, FL 1.91, 76.4 3.035, 121.4 1.91, 76.4 3.32, 132.8 3.82, 152.8
Strait of Juan de Fuca, WA 1.91, 47.75 3.035, 75.875 1.91, 47.75 2.82, 70.5 3.82, 95.5
Table 2. Total quantity of soundings for each source dataset and the outputs of the radius- and grid-based methods
using traditional parameters.
Dataset Source Soundings Fixed Radius Variable Radius Grid-Based
Charleston Harbor, SC 221,494 59,907 41,955 113,569
Narragansett Bay, RI 496,433 120,006 65,455 184,101
Tampa Bay, FL 603,132 55,179 36,827 121,669
Strait of Juan de Fuca, WA 847,461 394,886 190,016 544,048
10 N. DYER ET AL.
Table 4 includes the total quantity of soundings
before and after the application of each generalization
method for each survey.
All of the generalization approaches resulted in signifi-
cantly fewer soundings than the original dataset. Our label-
based generalization process consistently resulted in the
least amount of soundings for each dataset and the grid-
based generalization resulted in the second least. The num-
ber of soundings for the grid-based approach is directly
related to the number of grid cells superimposed over the
data. The fixed radius approach resulted in more soundings
than the variable radius approach for all of the datasets.
This is due to the length of the radii, where the length
increases with depth for the variable radius approach,
which in turn increases the number of soundings general-
ized. Conversely, the fixed radius approach uses
a consistent radius length, resulting in fewer soundings
generalized.
Each of the generalized datasets were subsequently
assessed for adherence to the constraints of bathymetric
generalization for nautical charts: functionality (safety),
legibility, displacement, and shape.
The functionality, or safety, constraint states that
depth information on the chart must not appear
deeper than the source data. The IHO has an estab-
lished procedure for validating the shoal-bias nature
of a sounding selection, known as the triangle test
(International Hydrographic Organization, 2017b).
The triangle test states that no sounding in the
original bathymetry data should exist within
a triangle of charted soundings that is shallower
than the least depth of the soundings forming the
triangle. Violations of this constraint are assessed by
extracting a Delaunay triangulation of the hydro-
graphic selection, and for each triangle, comparing
the rounded depth values of the source soundings
within the triangle to the rounded depth value of
the shallowest sounding forming the triangle. If the
shallowest source depth value is less than the shal-
lowest sounding forming the triangle, the source
depth and the triangle containing it is marked as
a violation.
Violations of the legibility constraint occur when
symbolized features over-plot at scale, which makes
the chart difficult or impossible to read. The label of
each generalized sounding was calculated and used to
identify instances where the label intersected that of
a neighbor. If the generalized sounding overlapped
a neighbor, the legibility constraint violation count
was increased by one, resulting in a potential max-
imum of one violation for each generalized
sounding.
The displacement constraint is violated when
a sounding is displaced from its original location in
the source dataset. Violations of this constraint were
identified by assessing if the selected sounding exists in
the original source data at the same coordinates.
Finally, the shape constraint aims to ensure that the
seafloor morphology is preserved through generalization.
The constraint is considered more flexible than others
(Ruas & Plazanet, 1997), but it is also the most difficult to
evaluate, as different metrics of seafloor characteristics can
produce varying results. Moreover, as most relevant to
avoid dangers to navigation and maintain chart readability,
the other three constraints should take priority over pre-
serving shape. However, seafloor morphology can still be
useful for navigation. For example, surface roughness can
indicate underwater structures, such as marine habitats,
that should be avoided when casting an anchor. In this
work, we calculate the surface roughness using the average
root-mean square height (Shepard et al., 2001) before and
after generalization to assess the change in morphology.
Surface roughness is computed by triangulating the sound-
ings using the Delaunay method, and for each vertex,
calculating the population standard deviation using the
vertex-vertex relationships. The value is reported as the
difference before and after generalization, not as
a discrete number of violations and should be interpreted
as such.
Table 5 summarizes the violations of the cartographic
constraints across each dataset and bathymetric general-
ization approach.
Our label-based generalization approach resulted in
the least violations of the functionality constraint across
all of the datasets. Conversely, the fixed radius approach
had the most (or tied for most) functionality violations
for the Charleston Harbor, Tampa Bay, and Strait of Juan
de Fuca datasets. The variable radius approach resulted in
the most functionality violations for Narragansett Bay.
The grid-based approach had the second least amount of
violations for all the datasets, except for Narragansett Bay,
where the fixed radius approach had less. Despite
Table 4. Total quantity of soundings for each source dataset and the outputs of the four generalization approaches.
Dataset Source Soundings Label-Based Fixed Radius Variable Radius Grid-Based
Charleston Harbor, SC 221,494 1,345 8,681 6,338 4,247
Narragansett Bay, RI 496,433 3,212 16,677 13,017 9,275
Tampa Bay, FL 603,132 830 5,466 3,879 2,337
Strait of Juan de Fuca, WA 847,461 2,946 21,367 13,524 8,465
CARTOGRAPHY AND GEOGRAPHIC INFORMATION SCIENCE 11
significantly more input points than the Charleston
Harbor and Narragansett Bay datasets, the Tampa Bay
dataset resulted in the least amount of functionality con-
straint violations across all generalization approaches.
The Tampa Bay dataset had the least level of depth
value precision (to the mm), which resulted in adjacent
soundings with the same depth as the assessed sounding.
These adjacent soundings were removed in favor of the
assessed sounding, which contributed to the generaliza-
tion of additional soundings and in turn, less overall
output soundings. The Strait of Juan de Fuca had the
highest number of input points overall and the highest
number of functionality violations across generalization
approaches.
Our label-based generalization approach resulted in
no violations of the legibility constraint. The fixed and
variable radius-based approaches resulted in legibility
violations for every generalized point in their respective
outputs. The grid-based approach only had three
soundings in the Narragansett Bay generalized dataset
that did not violate the legibility constraint. The number
of legibility violations for these approaches are related to
the values used for the radius length and grid cell size.
Shorter radii and smaller grid cell sizes can result in
under-generalization, which leads to increased legibility
violations; however, larger radii and grid cell sizes may
lead to over-generalization and increased safety viola-
tions (see, Figure 4). Moreover, as sounding labels can
increase in size within a specific depth range, e.g. the
difference in width between a label value of 21 and 21.5
and the other examples discussed throughout this paper,
it is practically impossible to generalize as a function of
depth without violating the legibility constraint using
the radius- and grid-based approaches. Figure 9 shows
the hydrographic selections from the four generalization
methods rendered at scale based on the S-52 presenta-
tion library, using version 4.3.0 of SevenC’s Analyzer
software (SevenCs, 2021).
As seen in the output for the label-based approach
(Figure 9d), the depth labels are legible and do not
overlap, which is not the case for any of the other
datasets. Additionally, as described in Section 3, the
additional spacing between depth labels for the label-
based approach results in soundings that are easily dis-
cernable from one another. This increased spacing can
result in a slight over-generalization; however, this is in
favor of legibility. As such, the increased spacing could
be reduced to fit user needs.
None of the approaches resulted in violations of the
displacement constraint. This is due to the fact that
none of the approaches extract interpolated soundings
and the generalized data is derived directly from the
source soundings.
Finally, adherence to the shape constraint is directly
related to the number of points in the generalized data-
set. Across each dataset, the generalization approach
that resulted in the largest quantity of soundings had
the lowest difference in surface roughness before and
after generalization, i.e. surface roughness increased
with less selected soundings. The fixed radius approach
performed the best in this category, as it resulted in the
highest number of soundings, followed by the variable
radius and grid-based approaches. Our label-based
approach performed the worst, as it consistently had
the lowest number of selected soundings. There is
a clear trade-off between adhering to the legibility and
shape constraints. More selected soundings results in
less legibility but an improved representation of mor-
phology and vice-versa. However it should be empha-
sized that the hydrographic sounding selection from
each approach requires further generalization before
being used to update an ENC. This will reduce the
number of soundings and in turn increase the difference
in surface roughness before and after generalization.
The greater the number of soundings from the hydro-
graphic sounding selection, the greater the degree of
Table 5. Summary of cartographic constraint violations.
Dataset Method Functionality Legibility Displacement Shape
Charleston Harbor, SC Fixed Radius 128 8,861 0 0.1764
Variable Radius 122 6,338 0 0.1895
Grid-Based 90 4,247 0 0.2505
Label-Based 68 0 0 0.4587
Narragansett Bay, RI Fixed Radius 88 16,677 0 0.1179
Variable Radius 102 13,017 0 0.1305
Grid-Based 94 9,272 0 0.1610
Label-Based 80 0 0 0.2885
Tampa Bay, FL Fixed Radius 68 5,466 0 0.2063
Variable Radius 68 3,879 0 0.2309
Grid-Based 53 2,337 0 0.3015
Label-Based 19 0 0 0.5169
Strait of Juan de Fuca, WA Fixed Radius 352 21,367 0 0.9546
Variable Radius 342 13,524 0 1.0659
Grid-Based 167 8,465 0 1.5198
Label-Based 150 0 0 2.9008
12 N. DYER ET AL.
generalization that is required for the final cartographic
selection, thus, the greater the effect to the surface
roughness. Our approach will require the least general-
ization, as it results in the fewest number of soundings.
Figure 10 illustrates the need for additional general-
ization of the hydrographic selection during the carto-
graphic sounding selection for an area of the Strait of
Juan de Fuca dataset. Figure 10a shows the hydro-
graphic sounding selection produced from our label-
based approach and Figure 10b shows the distribution
of the soundings on the current ENC. As explained in
this work, the subsequent cartographic selection of
Figure 10b is currently a manual process, where the
cartographer selects soundings from the hydrographic
selection (Figure 10a) based on the particular region and
presence of cartographically relevant navigation fea-
tures, e.g. depth contours, shoreline, rocks, wrecks, etc.
It is noted that depth values in Figure 10a and
Figure 10ab are different in some regions due to newer
bathymetry superseding the survey data used in this
work and potential selection issues (as described with
the support of Figure 5) from the extremely dense
hydrographic selection that was utilized for the produc-
tion of the chart in Figure 10b.
Figure 9. Sounding label distributions of generalization approaches for the Strait of Juan de Fuca dataset: a) fixed radius; b) variable
radius; c) grid-based; and d) label-based.
CARTOGRAPHY AND GEOGRAPHIC INFORMATION SCIENCE 13
5. Concluding remarks
This work presented an algorithm for hydrographic
sounding selection using the dimensions of sounding
labels rendered at scale. The output of the proposed algo-
rithm along with outputs of existing approaches were
compared by assessing their adherence to cartographic
constraints. Although there exists trade-offs between satis-
fying all of the cartographic constraints, the proposed
label-based algorithm performed the best with respect to
the two most fundamental constraints in nautical carto-
graphy: safety and legibility. Moreover, the proposed algo-
rithm only requires the scale of the target chart as an input
parameter, where the output from radius- and grid-based
approaches are highly dependent on input parameters.
We found that the precision of depth measurements
can affect the adherence to cartographic constraints for all
of the compared approaches. The complication arises from
adjacent soundings that have the same depth, where
a sounding is retained because it is not technically deeper
than the assessed sounding. The datasets used in this work
have depths to the millimeter value or less, which helps
avoid the issue as depth values with millimeter precision
are less likely to be equal. Moreover, the problem was
mitigated in this work by removing the neighbor sounding
with the same depth; however, this can be a more relevant
issue for datasets with less precision.
We also noted that many of the existing approaches in
the literature for both hydrographic and cartographic
sounding selection lack cartographic constraint-based
validations for assessing the quality of the output. As
such, the validation approaches presented in this study
were used to address this gap. Future work will include
building on these validation methods in an effort to better
assess the quality of sounding selections derived from
different approaches.
The resulting hydrographic selection derived from the
proposed algorithm will not contain legibility constraint
violations and guarantees that no deeper soundings exist
within the label of the portrayed sounding. As such, could
be used as input for any manual or automated carto-
graphic sounding selection approach. The cartographic
sounding selection further generalizes the hydrographic
selection, where the final ENC-ready sounding distribu-
tion is based on transportation routes, dangers to naviga-
tion, and existing chart features. Utilizing our label-based
hydrographic selection as input to the cartographic selec-
tion process will result in less cartographic constraint
violations, particularly legibility, compared to the other
approaches that result in significantly more soundings
and constraint violations. Future work will utilize the
label-based hydrographic selection as a preliminary gen-
eralization method toward a final selection of soundings
that complements the other chart features in the repre-
sentation of the seafloor topography on charts.
Disclosure statement
The authors do not report any conflicts of interest.
Funding
The work of Christos Kastrisios was supported by the
National Oceanic and Atmospheric Administration under
grant number NA15NOS4000200. The work of Leila De
Floriani was partially supported by the National Science
Foundation under grant number NSF IIS-1910766.
Figure 10. Sounding label distributions of the a) label-based hydrographic sounding selection and b) cartographic sounding selection
present on the current ENC for the Strait of Juan de Fuca dataset.
14 N. DYER ET AL.
ORCID
Noel Dyer http://orcid.org/0000-0002-9184-9055
Christos Kastrisios http://orcid.org/0000-0001-9481-3501
Leila De Floriani http://orcid.org/0000-0002-1361-2888
Data availability
The data that support the findings of this study are available in
figshare at https://doi.org/10.6084/m9.figshare.14474082.v1.
These data were derived from the following resources avail-
able in the public domain: National Centers for Environmental
Information (NCEI) bathymetric data viewer portal (https://
maps.ngdc.noaa.gov/viewers/bathymetry)
References
Arundel, S. T., & Sinha, G. (2020). Automated location cor-
rection and spot height generation for named summits in
the coterminous United States. International Journal of
Digital Earth, 3(12), 1570–1584. https://doi.org/10.1080/
17538947.2020.1754936
Cavanagh, G. (2019). Evaluation of current automated BE
compilation tools and prospects for improvement. Study
Report. Canadian Hydrographic Service.
Haigang, S., Li, H., Haitao, Z., & Yongli, Z. (2005). A fast algo-
rithm of cartographic sounding selection. Geo-Spatial
Information Science, 8(4), 262–268. https://doi.org/10.1007/
BF02838660
Haigang, S., Penggen, C., Anming, Z., & Jianya, G. (1999). An
algorithm for automatic cartographic sounding selection.
Geo-spatial Information Science, 2(1), 96–99. https://doi.
org/10.1007/BF02826726
Human Factors and Ergonomics Society (HFES). (2007).
ANSI/HFES 100-2007 Human Factors Engineering of
Computer Workstations. Santa Monica, CA, USA.
International Hydrographic Organization. (2014). IHO
transfer standard for digital hydrographic data.
Supplementary Information for the Encoding of S-57.,
Edition 3.1. Monaco, International Hydrographic
Bureau. (International Hydrographic Organization
Special Publication, S-57).
International Hydrographic Organization. (2017a). IHO
ECDIS Presentation Library. Edition 4.0. (2). Publication
S-52. ANNEX A. International Hydrographic Organization
Secretariat. Monaco.
International Hydrographic Organization. (2017b).
Regulations of the IHO for International (INT) charts and
chart specifications of the IHO, Edition 4.7. International
Hydrographic Organization Secretariat. Monaco.
International Hydrographic Organization. (2021). S-100
geospatial information registry. Portrayal Register.
Retrieved 2 March, 2021, from http://registry.iho.int/por
trayal/list.do
Kastrisios, C., & Calder, B. (2018). Algorithmic implementation
of the triangle test for the validation of charted soundings. In
Proceedings of the 7th International Conference on
Cartography and GIS, Sozopol, Bulgaria, June, Bulgarian
Cartographic Association. (pp. 18–23). https://doi.org/10.
13140/RG.2.2.12745.39528
Lakshminarayanan, V. (2015). Visual Acuity. In J. Chen, W.
Cranton, M. Fihn (Eds.), Handbook of visual display technol-
ogy (pp. 1–6). Springer Berlin Heidelberg. https://doi.org/10.
1007/978-3-642-35947-7_6-2
Lecours, V., Dolan, M. F., Micallef, A., & Lucieer, V. L. (2016).
A review of marine geomorphometry, the quantitative study
of the seafloor. Hydrology and Earth System Sciences, 20(8),
3207–3244. https://doi.org/10.5194/hess-20-3207-2016
Lovrinčević, D. (2019). The development of a new methodology
for automated sounding selection on nautical charts. Nase
More, 66(2), 70–77. https://doi.org/10.17818/NM/2019/2.4
Lu, X., Yan, H., Li, W., Li, X., & Wu, F. (2019). An algorithm
based on the weighted network Voronoi Diagram for point
cluster simplification. ISPRS International Journal of Geo-
Information, 8(3), 105. https://doi.org/10.3390/ijgi8030105
MacDonald, G. (1984). Computer-assisted sounding selection
techniques. The International Hydrographic Review, 61(1),
93–109. https://journals.lib.unb.ca/index.php/ihr/article/down
load/23513/27286
McMaster, R. B., & Shea, K. S. (1992). Generalization in digital
cartography. Association of American Geographers.
National Centers for Environmental Information (NCEI).
(2021). Bathymetric data viewer. https://maps.ngdc.noaa.gov/
viewers/bathymetry/
Oraas, S. R. (1975). Automated sounding selection. The
International Hydrographic Review, 52(2), 103–115 https://
journals.lib.unb.ca/index.php/ihr/article/download/23255/
27030
Putnam, G. R. (2013). Nautical Charts. Project Gutenberg. J.
Wiley & Sons. (Original work published 1908).
Rocca, L., Jenny, B., & Puppo, E. (2017). A continuous
scale-space method for the automated placement of spot
heights on maps. Computers & Geosciences, 109, 216–227.
https://doi.org/10.1016/j.cageo.2017.09.003
Ruas, A., & Plazanet, C. (1997). Strategies for automated
generalization. In M. J. Kraak, M. Molenaar (Eds.), Advances
in GIS research II (Proceedings Seventh International
Symposium on Spatial Data Handling (pp. 319–36). Taylor
and Francis.
Rytz, A., Bantel, E., Hoinkes, C., Merkle, G., & Schelling, G.
(1980). Cartographic generalization: Topographic maps.
Cartographic Publication Series (English translation of
publication No. 1). Swiss Society of Cartography.
Samet, H. (1984). The quadtree and related hierarchical data
structures. ACM Computing Surveys (CSUR), 16(2),
187–260. https://doi.org/10.1145/356924.356930
SevenCs. (2021). 7Cs Analyzer version 4.3.0. https://www.
sevencs.com/
Shepard, M. K., Campbell, B. A., Bulmer, M. H., Farr, T. G.,
Gaddis, L. R., & Plaut, J. J. (2001). The roughness of natural
terrain: A planetary and remote sensing perspective.
Journal of Geophysical Research: Planets, 106(E12),
32777–32795. https://doi.org/10.1029/2000JE001429
Skopeliti, A., Stamou, L., Tsoulos, L., & Pe’eri, S. (2020).
Generalization of Soundings across Scales: From DTM to
Harbour and Approach Nautical Charts. ISPRS International
Journal of Geo-Information, 9(11), 11. https://doi.org/10.3390/
ijgi9110693
Stoter, J., Post, M., van Altena, V., Nijhuis, R., & Bruns, B. (2014).
Fully automated generalization of a 1: 50k map from 1: 10k
data. Cartography and Geographic Information Science, 41(1),
1–13. https://doi.org/10.1080/15230406.2013.824637
CARTOGRAPHY AND GEOGRAPHIC INFORMATION SCIENCE 15
Tsoulos, L., & Stefanakis, K. (1997). Sounding selection for
nautical charts: An expert system approach. Paper pre-
sented at 18th International Cartographic Conference,
June 23–27, Stockholm, Sweden: International
Cartographic Association.
University of Utah. (2001). Average character widths.
Retrieved April 3, 2021, from https://www.math.utah.
edu/~beebe/fonts/afm-widths.html
Wang, Z., & Müller, J. C. (1998). Line generalization based on
analysis of shape characteristics. Cartography and
Geographic Information Systems, 25(1), 3–15. https://doi.
org/10.1559/152304098782441750
Ware, C. (2013). Information Visualization. Elsevier.
https://doi.org/10.1016/B978-0-12-381464-7.00002-8.
Weintrit, A. (2018). Clarification, systematization and general
classification of electronic chart systems and electronic
navigational charts used in marine navigation. Part
2-electronic navigational charts. TransNav: International
Journal on Marine Navigation and Safety of Sea
Transportation, 12(4). https://doi.org/10.12716/
1001.12.04.17
Wolfe, E., & Pacheco, P. (2020). Gross benefit estimates from
reductions in allisions, collisions and groundings due to
Electronic Navigational Charts. Journal of Ocean and
Coastal Economics, 7(1), 3. https://doi.org/10.15351/2373-
8456.1121
Yan, H., & Weibel, R. (2008). An algorithm for point cluster
generalization based on the Voronoi diagram. Computers &
Geosciences, 34(8), 939–954. https://doi.org/10.1016/j.
cageo.2007.07.008
Yan, J., Guilbert, E., & Saux, E. (2017). An ontology-driven
multi-agent system for nautical chart generalization.
Cartography and Geographic Information Science, 44(3),
201–215. https://doi.org/10.1080/15230406.2015.1129648
Yu, W., Zhang, Y., Ai, T., & Chen, Z. (2021). An integrated
method for DEM simplification with terrain structural fea-
tures and smooth morphology preserved. International
Journal of Geographical Information Science, 35(2),
273–295. https://doi.org/10.1080/13658816.2020.1772479
Yu, W. (2018). Automatic sounding generalization in nautical
chart considering bathymetry complexity variations.
Marine Geodesy, 41(1), 68–85. https://doi.org/10.1080/
01490419.2017.1393476
Zhang, X., & Guilbert, E. (2011). A multi-agent system approach
for feature-driven generalization of isobathymetric line. In
A. Ruas (Ed.), Advances in cartography and GIScience.
Volume 1: Selection from ICC 2011, Paris (pp. 477–495).
Springer Berlin Heidelberg. https://doi.org/10.1007/978-
3-642-19143-5_27
Zoraster, S., & Bayer, S. (1992). Automated cartographic sound-
ing selection. The International Hydrographic Review, 69(1).
https://journals.lib.unb.ca/index.php/ihr/article/view/23255.
16 N. DYER ET AL.
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Information Classification: General
Appendix A
ENC data are attributed according to IHO S-57 standards (IHO, 2014), which are then referenced
by the ECDIS to symbolize features. The ECDIS calls a dedicated conditional symbology
procedure (SNDFRM04 in S-52) to symbolize sounding depth values. Font style and size are not
customizable in ECDISs, as S-52 symbology uses a consistent mono-spaced typeface for depth
labels.
The depth value is passed to the symbology procedure and the conditional logic determines
the symbol. There are six depth value representation algorithms in the workflow that render the
label based on the depth (see SNDFRM04 in S-52 for a detailed explanation of the algorithms). A
depth of 20.7 m, for example, is processed as follows:
1. Isolate the leading digit of the depth value. Create symbol name by adding “20” to the
leading digit to get the symbol prefix, which is used for the call to the lookup table or
conditional procedure. The 20.7 m depth, for example, the conditional symbology isolates
the “2” and creates either SOUNDS22 (if the depth is shallower than the safety depth) or
SOUNDG22 when deeper than the safety depth. The difference is the font color of the
portrayed label; black for SOUNDS and gray for SOUNDG.
2. Isolate the second digit of the depth value. Create symbol name by adding “10” to the
second digit in order to get the symbol prefix (e.g., for the “0” in the 20.7 meters that
would be “SOUNDS10” or “SOUNDG10”).
3. Isolate the decimal of the depth value by multiplying by 10 and truncating all digits after
the decimal without rounding up. Create symbol name by adding “50” to fraction to get the
symbol prefix for the fraction part of the depth value (e.g. for the “7” in the 20.7 meters
that would be “SOUNDS57” or “SOUNDG57”).
4. Truncate the symbols.
Figure A1 shows the symbol diagrams of SOUNDS22, SOUNDS10, and SOUNDS57
utilized for the symbology of the 20.7 m sounding as provided in the Addendum of Part I of S-52
publication. The bounding box that encloses every label has as point of origin in the upper left
corner, with the column number (x-coordinate) being positive to the right and the row number (y-
2
Information Classification: General
coordinate) being positive downwards. The pivot point, illustrated with a cross in a circle, is the
actual geographic position of the sounding being symbolized.
Figure A1. Symbol diagram examples for a depth of 20.7 m.
When depth values are integers, the height of the bounding box remains the same, as the
glyphs are always the same height. However, when a decimal value is present, the decimal value is
shifted downward. This can be seen in Figure A1, where the decimal value of “7” is vertically offset
in relation to the pivot point. This offset is a long-lasting practice in nautical cartography bequeathed
to ENCs from paper charts. As a result, the depth label footprint can be polygonal or rectangular in
shape depending on whether it contains a decimal or not.
Under general mapping practices, labels are rendered directly on top of an elevation or depth
measurement, where the measurement is the centroid of the label bounding box. However, this is
not the case in digital nautical cartography, where label placement is much more complicated, being
determined by the number of glyphs and presence of decimal values composing the sounding label
(IHO, 2017a).
The calculation of the sounding label footprint requires the glyph (digit) height (D
H
in Figure
6), glyph width (D
W
), stroke width (S
W
), and spacing between glyphs (L
S
). According to the S-52
Presentation Library (IHO 2017a), each glyph is contained within a bounding box of dimensions 2.5
mm by 1.25 mm, including the narrower glyph “1”. Nevertheless, when “1” is the first digit (e.g.,
12, 100), the decimal (e.g., 9.1, 20.1), or the last digit in whole numbers (e.g., 31, 51), we must
account for the narrower width of the glyph “1” to accurately calculate the dimensions of the
portrayed label, the space it occupies on the ECDIS display, and how this is perceived by the human
eye. Additionally, from the symbol diagram in Figure 6, it can be extrapolated that the spacing
between glyphs is 1 mm. The width and height of the glyph bounding box do not include the line
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Information Classification: General
weight/width. The line weight, as used in the symbol descriptions in S-52 for S-57 and S-101 charts,
is derived from the requirement for screen resolution given in S-52, section 5.1. In detail, minimum
lines per mm (L) is given by L = 864/s, where s is the smaller dimension of the chart display area
(e.g., for the minimum chart area, s = 270 mm and resolution L = 3.20 lines per mm, thus a pixel
size of 0.312 mm). For the calculations in this work, the line width of 0.32mm in the S-100 registry
is utilized (IHO, 2021).
Furthermore, two neighboring labels must maintain a minimum spacing to avoid confusion
between them. There is no provision for the spacing between two labels in the aforementioned IHO
publications. According to the American National Standard for Human Factors Engineering of
Visual Display Terminal Workstations (HFES, 2007), the spacing between words should exceed the
spacing between glyphs, and preferably be at least half the width of an uppercase sans-serif letter
“H”.
The average upper-case letter-width to digit-width ratio is approximately 1.2 (a list of the
average glyph widths for 3,993 fonts is available from The University of Utah (2001)). Thus, for
glyphs with a 1.25 mm width, the “H” width is 1.5 mm and the minimum distance between labels
must be at least 0.75 mm, excluding stroke width. Considering that the minimum spacing between
glyphs in IHO S-52 is nearly the same, i.e., 0.68 mm (excluding the stroke width), this value seems
relatively small. The glyph spacing of 0.68 mm is 54% the glyph width which is over twice the
minimum and approximately equal to the maximum recommended in HFES (i.e., 25% and 60% the
glyph width, respectively). Accordingly, label spacing twice the minimum would be justified,
especially considering the factors that ECDIS screen is often viewed from an angle and under low
luminance conditions.
Based on the above, a label spacing twice the minimum recommended in HFES for two
vertically neighboring letters (that is 15% of H height) equals 0.75 mm. On the other hand, increasing
the label spacing will result in fewer soundings, thus the optimal value must be found to maintain
the balance between legibility and maximum density of soundings for the scale. Further research
should be performed in the specific application of maritime navigation to determine the label
spacing, both in the x and y-axis, but, after several trials, a uniform 0.75mm value was selected for
this paper (LS in Figure 6). It is noted that the above values apply to ENCs; the font height and width
values, along with glyph and label spacing should be modified accordingly for any other mapping
product or application.
