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1 INTRODUCTION

The current development of the maritime domain is

showing applications of new automated systems as

well as the application of Maritime Remote Operation,

even going as far as autonomous or remotely operated

vessels already being in use [1]. These initiatives are

intensified due to various technological developments,

but also induced by the shortage of skilled labor in the

maritime industry [2]. For the remote operation of

vessels, it is especially important that the remote

operator is able to handle typical tasks in navigation,

such as avoiding collisions with other vessels or with

the maritime infrastructure. This can be hindered when

the remote operator is not able to assess the

environment of the vessel due to no sufficient data

being available, which is even more crucial in narrow

harbor areas or fairways. Misjudging the environment

and obstacles in harbor areas can lead to costly

incidents [3], potentially putting other participants and

the environment at danger. Using highly automated

systems without having information on the

surrounding environment is challenging, as it is harder

to safely navigate near these structures. This is also

Safeguarding Navigation in Automated Shipping

Through 3D Modelling and Reconstruction of Maritime

Objects Using Segmented LiDAR Point Clouds

D. Yacoub, C. Petersen & M. Steidel

German Aerospace Center (DLR), Oldenburg, Germany

ABSTRACT: The accurate perception of the environment of vessels is essential for the development of automated

maritime systems and remote operation, as it is important to ensure a safe navigation in narrow fairways and in

harbor areas. LiDAR (Light Detection and Ranging) scanners are widely used in object detection applications, as

they produce dense 3D point clouds. However, due to their line-of-sight limitations, only partial views of objects

are recorded, making a full shape reconstruction necessary for safe navigation and situational awareness. This

paper presents a method to reconstruct full object dimensions from incomplete LiDAR measurements. We

introduce an automated selection algorithm that chooses the most suitable model from segmented point clouds

based on geometric characteristics, aiming to reconstruct full object shapes. To improve modeling accuracy for

navigation, we evaluate three advanced models compared to the Box Model: Cylinder Model, L-Shape Box

Fitting, and Elliptic Cylinder Fitting. The reconstruction accuracy is quantified using the root mean squared error

(RMSE) by comparing the fitted models against ground-truth point clouds compiled from multi-view scans.

Furthermore, we compare the error of our proposed selection method to the box model, providing insight into its

advantages and limitations for maritime object modeling. Field tests with representative maritime objects from

two harbor locations are presented. The results show that the choice of reconstruction method plays a key role in

how accurately maritime objects can be modeled. Simple shapes such as buoys, pontoons and piles are well

represented by basic models, whereas complex or irregular structures require more flexible reconstruction

methods, such as Triangle Mesh. Adapting the modeling technique to object geometry reduces manual and

computational effort while supporting reliable navigation and autonomous operation.

http://www.transnav.eu

the International Journal

on Marine Navigation

and Safety of Sea Transportation

Volume 19

Number 4

December 2025

DOI: 10.12716/1001.19.04.24

1258

crucial in applications in which the vessel needs to fully

rely on the information from its sensors. As an

example, Figure 1 is showing a challenging situation in

the Jarßum Harbor in Emden. The research vessel is

approaching an area with a crane, which presents

several obstacles, notably the base of the crane, marked

in red. These maritime objects should be represented

precisely, also considering their shape and dimension.

While it is possible to view the surrounding

environment by looking at the camera picture, it is

challenging to fully understand the dimensions of

obstacles as well as to perceive the depth information.

This is crucial information that is needed to safeguard

navigation in automated and remote-controlled

applications.

Figure 1. Crane in the Jarßum Harbor in Emden, as seen from

the research vessel. The crane foundation on the left side is

marked in red.

Already used for sensing the environment and

detecting these objects are technologies such as radars,

cameras or LiDAR scanners [4], which are installed on

vessels. For example, LiDAR scanners can help to

provide the needed depth information as described

above. As unprocessed LiDAR data is complex, a

reliable solution is needed that can provide dimensions

or features of single objects, effectively supporting

remote operators and automated systems. LiDAR is

well-suited to object detection because it can measure

distances very precisely and capture a dense 3D image.

Unlike a passive camera, it is not dependent on

ambient light conditions, making it a reliable choice for

sensing the environment. However, raw LiDAR point

clouds are unstructured and noisy. Therefore, it is

difficult to use it for navigation purposes in this

unprocessed state and it has to be processed and

enhanced in order to be used for information of the

vessel’s surrounding. For navigation, further

approaches exist to map the maritime environment in

harbors, such as in [5], aiming to improve conventional

Electronic Navigational Charts (ENC) by adding 3D

information from LiDAR scans, although mentioning

the need for retrieving the full shape of the detected

object from a single LiDAR scan.

Figure 2. Comparison between satellite image and ENC for

AeroWest, Airbus, CNES / Airbus, Maxar Technologies, Map

Professional+ chart data from Lloyd's Register/i4Insight in a

ChartServer solution from ChartWorld (right))

As can be seen in Figure 2, details in an ENC can

vary significantly compared to the actual shapes of

objects present. The crane in the satellite image is not

represented properly in the ENC, and relying on this

chart as a remote operator can be burdensome.

Retrieving the full shape of detected objects presents a

challenge due to factors such as varying object

geometries and incomplete point clouds, when objects

are only captured from one direction at a time. This

questions how LiDAR measurements in maritime

environments can be reconstructed to improve

awareness on the vessel’s surrounding.

Regarding the reconstruction of incomplete LiDAR

measurements, most previous work uses either

complete scans or simple box models for the

reconstruction of LiDAR point clouds. In practice,

especially in harbor environments, LiDAR scans are

often incomplete, and depending only on the box

models can lead to incorrect safety distances or

unnecessarily long routes during navigation. While

LiDAR nowadays is commonly used in the maritime

domain, incomplete measurements can be challenging

for navigation as already described. In these

applications, dimensions of objects and the depth

information are crucial. To address this problem, we

introduce an algorithm that automatically selects the

most suitable reconstruction method based on the

geometry of segmented LiDAR data. We investigate

three alternative modeling methods, namely Cylinder

Model, L-Shape Box Fitting and Elliptic Cylinder

Fitting compared to the Box Model, that are better

suited to maritime objects with rectangular, circular or

elliptical shapes in their XY projection. As no single

model is equally effective in all cases, our algorithm

determines the most suitable model. This approach

reduces manual effort and computation time while

improving reconstruction accuracy. We validate our

approach using various maritime objects recorded in

the Jarßum Harbor in Emden and the Oldenburg

Harbor, using root mean square error (RMSE) as

evaluation metric. The results demonstrate how

adaptive model selection can improve the reliability

and safety of LiDAR point clouds for remote and

autonomous vessel operation. While this study focuses

on regular-shaped objects, more complex maritime

structures may require alternative reconstruction

methods such as Triangle Mesh approaches, which are

discussed later in this paper.

2 RELATED WORK

Object reconstruction using LiDAR has been studied in

various fields, including autonomous driving [6, 7] and

autonomous maritime applications [9]. Working with

LiDAR point clouds often is dealing with incomplete

or irregular data, making it necessary to segment the

point cloud into clusters to improve the quality of 3D

reconstructions.

Automotive applications focus on object detection

and tracking as in [6], or approximating object shapes

and modeling obstacles [8] in order to improve the

safety of driver assistance systems. In the maritime

domain, applications include the sensor-supported

modeling and tracking of vessels and floating

structures as in [9], to be used in route planning and

collision avoidance.

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In these applications for the related literature

described above, several geometric models are applied

in order to estimate shapes of the objects. As an

example, the Box Model is a method in which objects

are approximated using rectangular volumes, making

it a standard approach for object modelling. Krämer [6]

uses box boundary surfaces for automatic detection

from LiDAR and approximates these surfaces by

adapting algorithms from [10]. This approach offers a

method that can also be used for detecting maritime

objects. Similarly, Ali et al. [7] extend the YOLO3D loss

function to include yaw angle, 3D box center, and

height for real-time oriented 3D bounding box

detection from LiDAR point clouds. The YOLO3D is a

variant of the popular YOLO algorithm, specifically

designed for 3D object detection, while traditional

YOLO models detect objects in 2D images.

For objects with cylindrical or round geometries,

the Cylindrical Model offers a more accurate

reconstruction than the Box Model. The study by

Nurunnabiet al. [11] proposes robust cylinder fitting

methods using point cloud data, which can be adapted

for detecting cylindrical maritime objects, even when

LiDAR data is noisy or incomplete.

Additionally, the L-Shape fitting method is suitable

for modelling objects with L-shaped structures. In

related work, Zhang et al. [10] describe L-Shape fitting

as an optimization problem for vehicle detection using

laser scanners, while Shen et al. [8] present an efficient

algorithm that segments point clouds and fits them

with perpendicular lines. This technique can be

adapted for maritime objects with L-shaped or edged

features. In addition to L-Shape fitting, Lin et al. [9]

employ Elliptic Fitting specifically for maritime objects,

using LiDAR point clouds to model them as bounding

boxes or elliptic cylinders, thereby offering a different

approach for varied maritime geometries.

The models discussed work well for objects with

regular shapes, more complex maritime structures

often require different reconstruction methods. One

alternative solution in such cases is Triangle Mesh

reconstruction. Researchers such as Carlberg et al. [12],

Gopi and Krishnan [13] and Marton et al. [14] have

developed algorithms that generate triangular meshes

from disorganised point clouds, with a focus on mesh

initialisation, growth and refinement. Krämer [6] later

adapted these methods for automated driving.

However, these ideas could also be applied in a

maritime context to more accurately capture complex

maritime objects.

While these approaches provide valuable insights

into the applications of various geometric models to

maritime objects, a comprehensive evaluation of how

to effectively apply these models to maritime

structures remains incomplete. Further, a method that

can supply dimensions and depth information of

maritime objects to be used in navigation applications

is needed. This highlights the need for selecting and

adapting suitable models that can efficiently and

robustly reconstruct maritime objects from LiDAR

data, as information on the dimensions of maritime

objects or obstacles as well as the depth information is

necessary to have. Geometric models are differing in

their complexity, depending on the desired application

and object type. The following section therefore

presents our algorithm for selecting the most

appropriate reconstruction method based on the

geometry of the maritime object, while considering

different geometric models and their accuracy of

representation.

3 CONCEPT

3.1 Reconstruction of Maritime Objects using LiDAR

point clouds

As LiDAR scans from a single position only allow the

front side of objects to be captured, a reconstruction of

incomplete LiDAR point clouds is needed in order to

map current maritime environment conditions and to

enable a 3D perception of this environment. We

propose to fuse LiDAR and GNSS (Global Navigation

Satellite System) data in order to achieve a geo-

localization of the LiDAR scans. The complex geo-

referenced LiDAR point clouds will be processed with

different geometry-based methods in order to

reconstruct shapes and dimension of these objects. The

overall process is showcased in Figure 3, displaying all

needed steps in order to reconstruct objects from the

LiDAR point clouds.

Figure 3. Processing steps for LiDAR point cloud

reconstruction

LiDAR and GNSS data are the inputs needed for the

following processing steps. The step Point Cloud Data

Recording handles the processing of the LiDAR point

cloud, resulting in several point clouds with containing

single maritime objects. Here, the LiDAR and GNSS

data is fused, effectively leading to the point cloud

having a precise geo-position. Then, the point clouds

have to be filtered. This is done by selecting the area of

interest, so that only maritime objects are included in

the point cloud. Afterwards, all points below the water

surface are removed, as only objects above the water

surface can be reliable detected with the LiDAR

scanner and water reflections will hinder the

reconstruction process. Then, all objects are segmented

from the LiDAR point cloud and outliers are removed

to reduce noise. The next step Fitting Algorithm

(chapter 3.3) estimates shapes for the maritime objects

and applies models according to the step Fitting

Models (chapter 3.2). These processing steps are

applied and evaluated in chapter 4.

3.2 Geometric Models for the Reconstruction of Maritime

Objects from LiDAR Data

In maritime environments, accurate reconstruction of

object surfaces from LiDAR data depends on the

geometric characteristics of the object. Accordingly,

different surface fitting models can be applied. The

following models represent commonly used

approaches for approximating the shapes of maritime

objects based on incomplete segmented LiDAR point

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clouds. As these models are important for our

proposed algorithm, the models will be described first.

3.2.1 Box Model

The Box Surface Model has become the standard

geometric model for objects in automated driving [6].

This model approximates the object’s surface with a

box-shaped structure. The box surface

( )

, , , ,

Box

S c W L H



is represented by the dimensions of the Box W,L and H,

which are calculated as follows:

max min max min max min

,,W x x L y y H z z= − = − = −

where xmax, xmin, ymax, ymin, zmax, zmin are the minimum

and maximum coordinates of the segmented LiDAR

points along each axis.

The center position c of the box is defined as:

( )

/ 2, / 2, / 2c W L H=

Finally, the yaw angle 𝜓, which represents the

object's rotation around the vertical Z-axis, is estimated

by:

( )

2,atan L W



To determine an initial estimate for the Box Model

parameters from segmented LiDAR data, the box

fitting algorithm described by Zhang et al. [10] is used.

This method involves uniformly choosing the space of

possible box orientations (ψ) within the range [0, π),

taking advantage of the Box Model’s symmetry. For

each candidate angle, a closeness score 𝐶 is computed

to evaluate the fit:

( )

max ,

i min



where di is the distance from the i-th scan point to the

closest edge of the bounding box and dmin is the lower

cut-off distance threshold that reduces the influence of

points close to the object’s edge. The bounding box

with the highest closeness score provides an

approximate initial guess for the object’s position,

orientation, width, length, and height.

The box surface model provides a fast and simple

fit suitable for all object types, but it offers limited

shape accuracy. Therefore, in cases where maritime

objects have regular geometric forms such as cylinders,

elliptical cylinders or even cuboids, alternative

modeling methods including precise cuboid models

should be selected to ensure higher accuracy.

3.2.2 Cylinder Model

The Cylinder Model is important for many

applications of 3D point clouds, for example in

autonomous navigation [11]. The model is defined by:

( )

Cylinder

S c r H=

where c∈R

is the center of the cylinder, r is the radius

and H is the height along the Z-axis.

To compute the radius r, the 3D segmented point

cloud is projected onto the XY- plane. The minimum

enclosing circle is then determined using Welzl’s

algorithm [15]. This method returns the circle center (xc,

yc) and the radius r:

( )

min

EnclosingCircle

rP=

The height 𝐻 is calculated as:

max min

H z z=−

Finally, the 3D center 𝒄 is computed as:







The Cylinder Model is well suited for objects with

cylindrical geometries such as poles or pipes [11],

although provides lower accuracy for box-shaped,

angular, or elliptic cylindrical structures.

3.2.3 Shape-Fitting Method

L-Shape Box Fitting and Elliptic Cylinder Shape

Fitting are commonly used to approximate shapes [9].

Both methods start with a point set S∈R

n x 2

, defined by

x- and y-coordinates. The goal is to represent the

object’s geometry angular in L-Shape Fitting and

curved in Elliptic Fitting. In both methods, the height

of the Box or Elliptic Cylinder is determined by the

vertical distance between the highest and lowest z-

values.

1. L-Shape Box Fitting Method

An L-shaped rectangle is fitted, as described in [9],

to a 2D point cluster

( )

 

, 1,2, ,

S x y i n= = ∣

dividing it into two disjoint subsets P and Q, such that

, P Q S P Q =  =

. Each subset is associated with one

of two perpendicular lines:

1 1 2 2

: cos sin , : sin cos

i i i i

l x y c l x y c

   

+ = − + =

The optimal parameters θ, c1, c2 are found by

minimizing the sum of squared distances from the

points to their respective lines. The solution to this

optimization problem yields the parameters of the two

straight lines that best approximate the edges of the L-

shaped object. The rectangle’s corner points are then

determined by identifying the farthest associated

points along each fitted line, following the method

described by [9]. Two diagonal corner points P1 and P2

are identified, one with the minimum, the other with

the maximum x or y value. The third corner is the point

farthest from the diagonal line

, completing the L-

shape rectangle. The fitted 2D L-shape rectangle is

extended along the Z-axis to create a three-dimensional

L-Shaped Box Fitting.

2. Elliptic Cylinder Fitting

An ellipse in 2D can be described parametrically as

follows:

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( ) ( ) ( ) ( ) ( )

 

cos cos θ sin sin θ

cos sin θ sin cos θ ,

with 0,2

x t x a t b t

y t y a t b t



= + −

= + +



Here, a denotes the semi-major axis, b the semi-

minor axis, and θ the rotation angle of the ellipse with

respect to the X-axis. (xc, yc) represents the center of the

ellipse in the XY-plane. This formulation results from

applying a 2D rotation and translation to the standard

ellipse equation.

When fitting an ellipse to a point cloud, especially

when outliers exist, the RANSAC (Random Sample

Consensus) algorithm [16] is employed.

1. Sampling: Random subsets of points in the XY-

plane are selected.

2. Model Estimation: Each subset is used to estimate

an ellipse (center, axes, angle).

3. Model Evaluation: The remaining points within a

threshold are inliers; others are outliers.

4. Optimization: The ellipse with the most inliers is

chosen.

The 2D ellipse is then extended along the Z-axis into

an elliptical cylinder, where the height is determined

by the lowest and highest points in the z-values.

3.3 Fitting Method Selection Algorithm Based on Object

Geometry

Since the characteristics of the described models can

affect their accuracy when applied to point clouds, it is

essential to select an appropriate geometric model for

each object. This is particularly important because it is

often difficult to determine the exact shape of an object

based only on its point cloud representation. Manual

selection of geometric models entails the risk of

inaccurate reconstruction, particularly when only

partial point clouds are available. Therefore, an

automated approach is required to identify the most

suitable geometric model for the reconstruction of

maritime objects.

In this section, we address these challenges by

proposing an automated algorithm that determines

whether an object is best represented by an L-Shape

Box, a Cylinder Model, or an Elliptical Cylinder, based

on the geometry of its 2D projection from the point

cloud. These three geometric models were chosen

because they accurately represent the most common

shapes found in maritime environments, while also

ensuring that the object’s height can be derived

consistently from LiDAR observations. The proposed

algorithm operates through the following steps:

3.3.1 Point Cloud Projection:

As a first step, the segmented 3D point cloud is

projected onto the XY-plane. This projection reduces

the dimensionality of the data and simplifies the

analysis of the object’s ground projection. However,

since LiDAR measurements in maritime environments

are often incomplete, the projected shape is not always

clearly defined. Therefore, the ground projection must

be further examined to determine whether it is best

fitted as rectangular, circular, or elliptical.

3.3.2 Rectangularity Test:

To identify rectangular shapes, the convex hull of

the projected points is first analysed. A line is estimated

using the RANSAC algorithm [16, 17], which estimates

model parameters by repeatedly selecting random

subsets of points and evaluating the model that best fits

the largest consensus set of inliers. After this step, the

inliers of the first line are removed, and a second line is

estimated using RANSAC on the remaining points. If

both lines are nearly orthogonal and each is supported

by a sufficient number of inliers, the object is classified

as rectangular. In this case, the selected geometric

model is the L-Shape Box.

3.3.3 Roundness Test (Circle vs. Ellipse)

If the rectangularity test fails and as we are only

considering maritime objects with regular shapes, the

object is considered to be round. Two parallel

RANSAC procedures are applied:

− RANSAC_circle: tests for circularity using small

random point subsets.

− RANSAC_ellipse: tests for ellipticity in the same

manner.

Both follow the Efficient-RANSAC strategy [18],

which robustly detects shapes by repeatedly sampling

small random subsets and selecting the model

supported by the greatest number of inliers. Once the

best candidate is identified, the corresponding inliers

are refitted using least-squares methods for improved

accuracy:

− For circles: classical least-squares circle solvers [17],

which minimize the distance of the points to an

ideal circular model.

− For ellipses: direct least-squares ellipse solvers [19],

which formulate the problem as a generalized

eigenvalue problem to estimate ellipse parameters.

− To further distinguish between circular and

elliptical shapes, the following additional criterion

is used.

3.3.4 The Axis Ratio (Eigenvalue Ratio):

As an additional criterion, the Principal Component

Analysis (PCA) is applied to the 2D shape obtained

from the roundness test [20]. PCA rotates the point

cloud so that one axis corresponds to the direction of

greatest variation in the points, while the other axis

corresponds to the least variation. The eigenvalues λ1

and λ2 representing the variance along the principal

directions. The Axis Ratio is defined as:

, λλ

R =

− If R ≈ 1, the shape is close to a circle, and the

selected geometric model is the Cylinder Model.

− If R > 1, the shape is elongated, representing an

ellipse, and the corresponding model is the

Elliptical Cylinder Fitting.

The proposed algorithm is specifically designed for

regular geometries, i.e., objects that can be

approximated by rectangular, circular, or elliptical

projections. In cases where objects consist of irregular

or complex geometries, the method becomes less

suitable, and a more generalized approach, such as

triangulated mesh reconstruction or convex hull

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approximation, is required. To test and validate the

proposed reconstruction methods, field experiments

were conducted at different locations with various

maritime objects. The following section in chapter 4

describes the acquired data and evaluation.

4 APPLICATION & EVALUATION

This chapter focuses on applying the described process

model on real world data. For this, point cloud data

from field tests are used. Maritime objects are

segmented from these LiDAR scans and the Fitting

Method Selection Algorithm is applied on this data.

The accuracy of the results is evaluated by comparing

single LiDAR scans to a combined LiDAR ground

truth.

4.1 Field tests

In order to apply the shape fitting methods, sufficient

LiDAR data from the real world is needed that

represents relevant maritime objects. For this, field

tests are conducted in three different test locations,

containing different maritime objects of interest. The

specifications of these test locations are displayed in

Table 1. Used in this measuring campaign is a high-

resolution LiDAR scanner stationed on the quay walls

to record comprehensive data from multiple angles of

each test location. A vessel-based sensor setup is not

used at this stage, as the focus on these maritime

objects allows a high-resolution scanner to fully scan

these objects from the quay walls in a controlled

environment. These LiDAR scans are georeferenced by

using GNSS data, with the accuracy being increased by

correctional measurements of Real-Time Kinematic-

GPS. By georeferencing each single LiDAR scan, the

foundation is set to combine the single scans of a

location in order to obtain a full representation of the

specific location. This setup allows for the creation of a

ground truth dataset through combination of the

collected data, so that objects in each location are fully

captured from all angles.

Table 1. Field test locations

Test location

Location type

Scan positions

Emden

Seaport

Oldenburg (South)

Waterway

Oldenburg (North)

Inland Port

In the Jarßum Harbor in Emden, the most relevant

object is the crane, which is also visible in the satellite

image in Figure 2. Further, a vessel is available in the

data, which was present at the time of recording

LiDAR data in the harbor area. For the two locations in

Oldenburg (Figure 4), the southern area includes data

of a bridge and buoys, while the northern area includes

different mooring facilities. Overall, the recordings

result to about 18.4 GB of LiDAR and GNSS data from

these three locations.

Figure 4. Aerial image of both test locations in Oldenburg

4.2 Evaluation data

For further usage, maritime objects of interest are

segmented from the LiDAR point clouds. First, the area

of interest is filtered. As a next step, single objects are

segmented from the area of interest. For the LiDAR

data from the test locations a manual segmentation is

conducted. The LiDAR point clouds for separated

maritime objects are filtered in order to remove

outliers, aiming to further reduce noise. This same

procedure is applied to multiple objects captured in the

field tests. With the data from these point clouds for

maritime objects it is now possible to apply the fitting

algorithm in order to find fitting models and evaluate

the accuracy of the selected models. Used for the

evaluation purposes of the Fitting Method Selection

Algorithm are maritime objects from these LiDAR

scans, namely the buoy (scanned in Oldenburg) as well

as the vessel and the two parts of the base of the crane

(scanned in Emden).

Figure 5. Unfiltered LiDAR point cloud of the crane in the

Jarßum Harbor in Emden.

Figure 5 is showing a combined point cloud of

multiple LiDAR scans for the crane in the Jarßum

Harbor in Emden. The data is unfiltered and therefore

including several objects nearby. The data in Figure 6

has been filtered and only the base of the crane is

visible. In this case, only a single LiDAR scan is shown.

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Figure 6. Area of interest for a single scan for the crane in the

Jarßum Harbor in Emden.

4.3 Validation on Maritime Objects

We validated the Fitting Method Selection Algorithm

based on object geometry in field tests implemented in

Oldenburg and Emden. For the evaluation of maritime

objects, four different object types that met the selection

criteria were selected, as already described in chapter

4.2. Tables 2 to 5 show these objects, with the buoy

being scanned in Oldenburg and the other objects

scanned in Emden. Tables 2 and 4 show the foundation

of the crane in the Jarßum Harbor in Emden, which can

reconstruct the full foundation of the crane when the

results for the reconstructed models are combined. For

the crane base (see Table 2), running two-line RANSAC

on the convex hull points yields two nearly orthogonal

directions supported by many points, the

rectangularity test is therefore passed and the

suggested 3D model is an L-shaped box.

For the buoy, crane pile, and vessel (see Tables 3–5),

no pair of perpendicular edges is detected, so their

cross-sections are treated as round. We then perform a

model competition (circle vs. ellipse) using Efficient

RANSAC, followed by least-squares refitting of the

selected curve. For the buoy and crane pile, the PCA

axis ratio R ≈1, and the circle is selected as the best fit,

the recommended 3D model is a Cylinder. For the

vessel, R >1; indicates elongation, therefore the

ellipse is chosen, yielding an Elliptical Cylinder.

Table 2. From left to right: (1) photo of the crane base; (2) its

3D point cloud; (3) XY-plane projection with a bounding; (4)

resulting suggested model (L-shape box).

Table 3. From left to right: (1) photo of the buoy; (2) its 3D

point cloud; (3) XY-plane projection with a bounding and

the eigenvalues; (4) resulting suggested model (Cylinder).

Table 4. From left to right: (1) photo of the crane pile; (2) its

3D point cloud; (3) XY-plane projection with a bounding

and the eigenvalues; (4) resulting suggested model

(Cylinder).

Table 5. From left to right: (1) photo of the crane base; (2) its

3D point cloud; (3) XY-plane projection with a bounding

and the eigenvalues; (4) resulting suggested model (Elliptic

Cylinder).

In summary, results for the selected objects show

that the proposed algorithm is suited for segmented

LiDAR point clouds of maritime objects, where cross-

sections can be represented by simple shapes such as

rectangles, circles, or ellipses, and the appropriate 3D

model can be assigned. However, the algorithm is not

intended to handle very complex objects in a single

step. In such cases, the object should first be divided

into simpler parts, and the fitting method can then be

applied to each part. For highly irregular or detailed

structures, alternative approaches such as triangle

mesh reconstruction are required. Additionally, the

processing time is strongly influenced by the

complexity of the object and the number of points in

the LiDAR dataset. Simpler shapes with fewer points,

like buoys or piles, can be reconstructed much faster

since they require fewer optimization steps and

simpler calculations. In contrast, large or complex

structures, such as vessels or cranes with detailed

components, need more time for segmentation,

filtering, and model fitting because of their more

detailed surfaces and higher point densities.

4.4 Evaluation of maritime objects from field test

Now that the shape of the maritime objects has been

determined from the point cloud data as described in

the Fitting Method Selection Algorithm, the accuracy

of these fits can get evaluated. The geometric accuracy

of reconstructed maritime objects from incomplete

LiDAR point clouds is evaluated using the Root Mean

Square Error (RMSE). In this context, RMSE quantifies

how closely the reconstructed model matches the

actual geometry of the object. By scanning an object

from all sides and using these scans as ground truth, it

is possible to accurately determine the geometric

deviation between the reconstructed model and the

original object. The distance from each point on the

original point cloud to the surface of the fitted model is

calculated using the following formula:

RMSE



Here, di represents the shortest distance from the i-

th point in the ground truth point cloud to the surface

of the fitted model, and N denotes the total number of

points in the ground truth cloud. A lower RMSE value

denotes a more accurate reconstruction.

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For evaluation, the four object types introduced

above are used. The model chosen by the selection

algorithm is compared against the Box Surface Model,

the model with the lower RMSE is considered more

accurate.

Table 6. Evaluation results for crane base object

For the crane- base, the algorithm selected L-Shape

Box fitting, reducing RMSE to 0.70 m compared with

1.65 m for the Box Model.

Table 7. Evaluation results for buoy object

Table 8. Evaluation results for crane pile object

For the buoy and the crane-pile (R ≈ 1), the

algorithm proposed a cylinder model, yielding lower

RMSEs than the Box Model 0.43 m versus 0.57 m for the

buoy and 0.76 m versus 0.84 m for the crane pile. This

improved performance shows that the accuracy of the

geometric representation is increased, as the algorithm

determines a better fit for a cylindrical shape.

Table 9. Evaluation results for vessel object

For the vessel (R >1), an elliptic-cylinder fit achieved

an RMSE of 5.88 compared with 14.78 for the Box

Model.

The results show that the choice of an appropriate

reconstruction model depends on the detected shape

and therefore used model by the Fitting Method

Selection Algorithm that has been validated by the

RMSE score. An adaptive model choice offers a clear

advantage over a Box Model, as it provides a more

accurate geometric representation of regular maritime

objects and ensures an essential requirement for robust

applications in navigation and remote operation.

5 TECHNOLOGICAL CHALLENGES

This chapter will discuss identified challenges for the

reliable reconstruction of maritime objects captured by

LiDAR scanners. One major challenge is how complex

object shapes can be reconstructed in the future, aiming

at precisely representing their true shapes.

5.1 Reconstruction of complex and irregular shapes

When maritime objects with complex shapes need to be

reconstructed, the geometric models described in

chapter 3.2 can be insufficient for these objects. The

Triangle Mesh Method has been studied as an

approach for reconstructing 3D surfaces from LiDAR

point clouds, particularly in the automotive domain

[6]. However, its application in maritime contexts has

received little attention. This section discusses the 3D

Delaunay Mesh Method for reconstructing maritime

objects, especially irregular and complex structures,

from LiDAR point clouds. A 3D Delaunay

Triangulation connects points in a 3D space to form

non-overlapping tetrahedra that represent the surface

of the object. In practice, the Delaunay property alone

is not sufficient, and it is necessary to impose quality

constraints governing the shape, size, and angles of the

elements. This process is called Delaunay mesh

refinement, as introduced by [21]. The Delaunay

Refinement ensures that the points are connected in

such a way that no point is inside the circumsphere (in

3D) of any of the tetrahedra. In 2D, this would be the

circumcircle of the triangles. Further, the Delaunay

refinement also aims to improve the shape quality of

the mesh elements by maximizing the minimum angle

of the tetrahedra triangles (or triangles in 2D). These

criteria ensure that the resulting Delaunay

triangulation is well-shaped and connected, which is

all important for accurately modelling objects in 3D.

Figure 7 shows an example for two maritime objects.

Figure 7. Two examples of Triangle Mesh applications on

maritime objects. Left (1): A simple object where applying a

mesh adds little value. Right (2): A complex object where

meshing enables a more detailed and precise reconstruction.

This approach is particularly useful for irregularly

shaped maritime objects, when a more precise

reconstruction is needed that cannot be achieved with

the models described above. However, these detailed

models may require more computational resources.

For regular structures, the Triangle Mesh method may

not be necessary, and simpler geometric models may

be more practical and efficient.

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5.2 Selection of technologies

Challenging as well is the selection of technologies in

order to capture the maritime environment and to

process LiDAR point clouds for the reconstruction.

Used for the evaluation of this work was a high-

resolution LiDAR scanner stationed on the quay wall,

while mobile LiDAR scanners on vessels are likely to

have a lower resolution of the resulting point clouds.

Here, it is important to consider how far away the

scanned maritime objects are, as closer objects will be

captured in a higher resolution. Further, how many

points of an object exist in the point cloud will have an

impact on the processing speed for the LiDAR

reconstruction, as more points describe a more

computationally demanding problem.

6 CONCLUSION AND FUTURE WORK

In this study, several methods were evaluated for

reconstructing 3D models of maritime objects based on

incomplete LiDAR point cloud data, with the goal of

supporting reliable object representation in

autonomous systems and maritime navigation. For

reconstruction, LiDAR data was used from field trials

in two locations. Results from evaluating the Fitting

Method Selection Algorithm showed that the

reconstruction method decides how accurately

maritime objects are modeled and that our proposed

method is able to detect the shapes of the geometries in

the LiDAR point clouds. The comparison of Box-,

Cylinder-Model, L-Shape Box- and Elliptic Cylinder-

Fitting, as well as the outlook towards Triangle Mesh

approaches showed that each method has specific

advantages depending on the object’s geometry and

complexity. The results confirm the importance of

choosing a modelling method that aligns

reconstruction accuracy with the geometric

characteristics of the object. Future work will aim to

extend the modelling methods to a wider range of

maritime object classes. This includes improving the

representation of complex structures, such as

modelling a crane as a single object rather than as

multiple components. Triangle Mesh Methods will be

applied for modelling irregular shapes and fully

reconstructing of detailed objects. In the future, these

advanced modelling techniques can be integrated into

maritime systems. Their deployment in navigational

applications and for Remote Operation is expected to

enhance Situation Awareness and aid in safeguarding

automated systems. Further future use cases include

route planning and collision avoidance applications in

both autonomous and remotely operated maritime

environments.

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