Experimental evaluation of segmentation algorithms for corner detection in sonar images

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F

ACULDADE DE

E

NGENHARIA DA

U

NIVERSIDADE DO

P

ORTO

Experimental evaluation of

segmentation algorithms for corner

detection in sonar images

Pedro Miguel Linhares Oliveira

Master in Electrical and Computers Engineering Supervisor: Bruno M. Ferreira PhD Co-Supervisor: Nuno A. Cruz PhD

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Resumo

O desenvolvimento de veículos submarinos autónomos (AUVs) representa uma das maiores con-quistas da engenharia e da ciência para a exploração do mundo subaquático. A utilização destes veículos facilita a recolha de dados e monitorização destes ambientes, permitindo-nos realizar operações outrora impossíveis.

Devido à elevada atenuação sofrida pelo Global Positioning System (GPS) e outros sinais de radiofrequência de baixo de água, a utilização de comunicações e sensores acústicos é predomi-nante.

Os sonares de imagem são capazes de medir a intensidade do eco retornado pelo varrimento de um sector. Essas medidas podem ser decompostas numa imagem acústica do ambiente, geralmente referida como uma imagem de sonar.

Dentro dos sonares de imagem, os sonares de varrimento mecânico (MSISs) são particular-mente interessantes para serem incorporados num AUV e obter informação do ambiente envol-vente. Devido à sua direccionalidade e largura de feixe, este tipo de sensor é ótimo para deteção e caracterização de obstáculos.

Geralmente, os cantos aparecem muito distintos do resto da imagem gerada pelo MSIS, nor-malmente caracterizados por intensidades agudas. A deteção de cantos é particularmente útil em ambientes estruturados, tais como tanques, porque o conhecimento da sua localização permite calcular a posição do veículo. A combinação de algumas operações básicas comummente usadas para segmentação de imagens tem grande potencial para detetar e localizar automaticamente os cantos em imagens de sonar.

Esta dissertação propõe e avalia com dados experimentais um conjunto de algoritmos de seg-mentação de imagens para deteção de cantos em scans de sonar. Os algoritmos desenvolvidos são avaliados com base num ground truth e o seu desempenho é analisado segundo algumas métricas relevantes para navegação autónoma.

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Abstract

The development of autonomous underwater vehicles (AUVs) represents one of the latest great achievements of engineering and science for the exploration of the underwater world. The use of these vehicles facilitates the collection of data and monitoring of these environments, allowing us to perform previously impossible operations.

Due to the high attenuation suffered by the GPS and other radio-frequency signals underwater, the use of acoustic communications and sensors is predominant.

Imaging sonars are capable of measuring the returning echo intensity values from a scanned area. These measurements can be decomposed into an acoustic image of the environment, gener-ally referred to as a sonar image.

Mechanically scanned imaging sonars (MSISs) are particularly interesting for being incorpo-rated into an AUV to acquire information in underwater environments. Because of their direction-ality and beam width, this type of sensor is well suited for obstacle detection and characterization. Corners usually appear very distinct from the rest of the scene in an MSIS image, gener-ally characterized by sharp intensities. The detection of corners is particularly useful in human-structured environments such as tanks because the knowledge on their location provides a way to compute the vehicle position. The combination of some basic operations typically used for image segmentation has great potential to detect and localize corners in sonar images automatically.

This dissertation proposes and evaluates with experimental data a set of image segmenta-tion algorithms for corner detecsegmenta-tion in sonar scans. The developed algorithms are evaluated with ground truth, and their performance is analyzed following a few relevant metrics for autonomous navigation.

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Acknowledgements

The accomplishment of this dissertation marks a significant period in my life because it culminates five years of studies, presenting itself as a test to my autonomy and preparing me to face the challenges that may arise in my professional life. I recognize that none of this could have been achieved without the help of the people mentioned in the following paragraphs.

First of all, I would like to express my gratitude to my supervisors, INESC senior researchers Bruno Ferreira and Nuno Cruz for granting me this opportunity, for all the support and guid-ance provided throughout the development of this dissertation and for the patience and dedication demonstrated.

I also want to thank INESC CRAS for providing the space and equipment necessary. Not forgetting their technician Jorge Barbosa for the helping hand provided and for the fellowship spirit.

I am eternally grateful to my parents for always believing and supporting me unconditionally. This dissertation is dedicated to them.

Lastly but not less important, I want to thank all my friends for the company and support provided during my years at FEUP and above all, for making my life worthwhile.

Pedro Linhares Oliveira

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“The journey of a thousand miles begins with one step”

Lao Tzu

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List of Figures

1.1 Sonar scan acquired in the middle of a tank with red rectangles marking the tank

corners. . . 3

1.2 Representation of fig.1.1sonar scan in the cartesian coordinate system. . . 3

2.1 A scheme of the localization and navigation methods applied to Autonomous Un-derwater Vehicle (AUV)s. Adapted from [11] . . . 6

2.2 (a):Short Baseline (SBL); (b):Ultrahort Baseline (USBL); (c):Long Baseline (LBL). Adapted from [11] . . . 8

2.3 An AUV is locating himself with a single beacon in a known location. Uncertainty grows between beacon pings. Upon the reception of a ping from the beacon, the uncertainty is reduced in the dimension coincident with the location of the beacon. Adapted from [11]. . . 9

2.4 Different types of sonar swath: (a) sidescan; (b) multibeam; (c) forward looking; (d) sector scan; (e) synthetic aperture. Adapted from [11]. . . 10

3.1 Sonar scan acquired in position 5 of fig.3.6with a selected maximum range of 10 m 16 3.2 Sonar scan of fig. 3.1in cartesian coordinates. . . 16

3.3 Photo of the tank showing a side wall with its windows. . . 17

3.4 Flow diagram describing the steps followed to obtain the results. . . 18

3.5 Photo of the SHAD AUV attached to the moveable bridge on INESC tank. . . 19

3.6 Tank positions and measurements. . . 20

3.7 Resulting binary images from threshold operations applied to a sonar scan ac-quired in position 5 of fig. 3.6with a selected maximum range of 5 m and a gain of 0,5. . . 23

3.8 Resulting binary images from derivative operations applied to the same scan of fig.3.7. . . 24

3.9 Representation of 8-direction connectivity. . . 25

3.10 Ground truth masks synthetized for raw image of fig. 3.7a. . . 26

3.11 Tritech Micron Mechanical Scanned Imaging Sonar (MSIS) vertical beam width characteristics. . . 27

4.1 Sonar scan taken in position one of fig. 3.6with a selected gain of 1.0 - Note the saturation of intensities that occur. . . 32

4.2 Sonar scan taken in position one of fig.3.6with a selected gain of 0.25. . . 32

4.3 Positive classification mask example in which corners regions are not placed cor-rectly. . . 33

4.4 Sum of correct corners detected - Top 20 results. . . 34

4.5 Average number of correct corners detected normalized - Top 20 results. . . 35

4.6 Average number of false corner detections normalized - Top 20. . . 37

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xii LIST OF FIGURES

4.7 Average ratio of positive / total corner detections - Top 20. . . 38

4.8 Average range error normalized - Top 20. . . 40

4.9 Average angle error normalized - Top 20. . . 41

4.10 Average execution time of each operation in seconds. . . 43

4.11 Average execution time of each operation normalized. . . 44

4.12 Top 20 results for scenario 1. . . 47

A.0 Graph of average number of corners detected normalized. . . 60

A.0 Graph of sum of correct corners detected. . . 63

A.0 Graph of average number of false corner detections normalized. . . 67

A.0 Graph of average error in range normalized. . . 71

A.0 Graph of average error in angle normalized. . . 74

A.0 Graph of combined metrics - 1. . . 78

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Abbreviations and Symbols

ASV Autonomous Surface Vehicle. AUV Autonomous Underwater Vehicle. CN Cooperative Navigation.

DR Dead Reckoning. DVL Doppler Velocity Log. EKF Extended Kalman Filter. FLS Forward Looking Sonar. GIB GPS Intelligent Buoy. GPS Global Positioning System. INS Inertial Navigation System. LBL Long Baseline.

MSIS Mechanical Scanned Imaging Sonar. SAS Synthetic Aperture Sonar.

SBL Short Baseline. SFB Single Fixed Beacon.

SLAM Simultaneous Localization and Mapping. SONAR Sound Navigation and Ranging. TDMA Time-Division Multiple Access. TMS Tritech Micron Sonar.

TOF Time Of Flight. USBL Ultrahort Baseline. VLBL Virtual Long Baseline.

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Chapter 1 Introduction

1.1 Context

For a long time, the underwater marine and fluvial environments were only partially accessible to humans. Factors such as the human inability to breathe underwater, as well as the unsustainable pressure in depth, have always presented themselves as limiting factors for their exploration.

More than 2/3 of the earth’s surface is covered by the sea, containing about 97% of the total volume of water on Earth. The oceans are the habitat of a wide variety of life forms, many of which are yet to be cataloged. Furthermore, they play a vital role in the balance of the earth’s atmosphere, having a global impact on all life on the planet.

Recent scientific advances have made it possible a more in-depth exploration of this powerful medium. The development of autonomous underwater vehicles (AUVs) represents one of the latest great achievements of engineering and science for the exploration and monitoring of the under-water world, contributing to the development of some branches of science, mainly oceanography. The use of these vehicles facilitates the collection of data and monitoring of these environments, allowing us to perform previously impossible operations. However, the exploration of this world by autonomous vehicles continues to present many challenges. Underwater navigation is particu-larly difficult due to the high attenuation suffered by the GPS and other radio-frequency signals, making it challenging to communicate with vehicles.

1.2 Motivation

To ensure accurate data collection as well as the safety of the vehicle, the ability to navigate with precision is vital.

The use of acoustic communications and sensors underwater allows overcoming certain limi-tations imposed by methods that are often used for terrestrial navigation. Besides, the nature of the underwater realm coupled with the lack of visibility in dark areas, the turbidity of water and the frequent presence of various deposits such as mud, sand, algae, among others, justifies the search for more than reliable navigation techniques in these circumstances.

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2 Introduction

Sound Navigation and Ranging (SONAR) is a technique that uses sound propagation for map-ping of the surroundings, and it is now commonly used for AUV navigation. Despite being a robust and well-known technology, studies continue to be carried out in order to improve its relia-bility and accuracy. As such, there are different types of sonar sensors and different techniques and algorithms applied to their yielded scan data for the extraction of relevant features and its correct interpretation.

Imaging sonars are capable of measuring the returning echo intensity values from particular places within the sonar insonified area. These measurements can then be decomposed into an acoustic image of the environment, generally referred to as an acoustic image.

Mechanically scanned imaging sonars (MSISs) are particularly interesting for incorporation into an AUV to acquire information in underwater environments. Because of their directionality and beam width, this type of sonar sensor is well suited for obstacle detection and characterization. Figure1.1 shows the result of a sonar scan from a Tritech Micron MSIS in the middle of a rectangle shaped tank with dimensions 4.6 m (length) x 4.4 m (width) x 1.8 m (depth). As it can be seen, the way the MSIS maps the surroundings is by an array of bins (or cells) which are characterized by a distance (range), an angle and echo intensity. The mapping results from the rotation of the sensor head along with a given angle interval (a full 360o _{revolution in this}

case), yielding for each angular step the mentioned array. It can be represented directly in the polar coordinate system, as shown in fig.1.1but can also be converted to the cartesian coordinate system, as shown in fig. 1.2. The parabola-like formats seen in fig.1.1correspond to the walls of the tank, which are intuitively seen in fig.1.2.

As shown in figure1.1 (inside the red rectangles), corners usually appear very distinct from the rest of the scene in an MSIS scan, generally characterized by sharp intensities along with an angle interval for a specific range. A vertical intensity pattern is noticeable when looking at it as an image, instead of a set of distance and angle measures. The same vertical pattern does not appear in the cartesian coordinate system representation (fig. 1.2), a diagonal pattern appears instead.

Corner detection is particularly useful in human-structured environments such as water tanks because the knowledge on their position provides a way to compute the vehicle’s localization inside it.

Due to the presence of noise from multiple factors, and other variables such as multipath echoes, the potential for false detections in a raw sonar image is high. The use of image pro-cessing techniques, namely feature extraction, has much potential to help interpret sonar images more accurately, allowing to extract the relevant information from these scans automatically. This process should be as fast as possible because when the vehicle is in motion, it is required a fast vehicle localization update as well as a quick and reliable estimation of obstacles position in order to avoid them. Such operations on the resulting scan data can quickly become computationally demanding, so usually, a compromise must be set between the accuracy and the desired update time. An evaluation of the overall performance of different image segmentation algorithms for corner detection is of value for these purposes.

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1.2 Motivation 3

Figure 1.1: Sonar scan acquired in the middle of a tank with red rectangles marking the tank corners.

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4 Introduction

1.3 Objectives

In this work, it is intended to develop and evaluate with experimental data a set of segmentation algorithms to detect and locate corners in sonar images.

It is expected that these algorithms can be integrated into a navigation system to extend its capabilities by providing the relative position of corners in objects or structures present in the environment. This information can then be fed to an estimator such as an Extended Kalman Filter (EKF) to aid in estimating the vehicle position with more accuracy.

1.4 Document structure

The remainder of this document is composed of four chapters, each divided into sections.

Chapter 2 is dedicated to present an overview of the current state of AUV navigation tech-niques, the sensor technology, and briefly introduce the main image processing techniques utilized in the algorithms to detect the corners in sonar images.

Chapter 3 walks the reader through the many steps taken in the development of this dissertation to find solutions to the problem at hand and to get the desired results.

Chapter 4 critically analyzes the results obtained by different metrics that are considered rele-vant for autonomous navigation.

The last chapter presents the conclusions of this work, some thoughts on the potential next steps to take and highlights the main contributions of this work.

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Chapter 2 Literature Review

This dissertation focus is on the experimental evaluation of segmentation algorithms for corner detection in sonar images. Although the repercussions of this work apply to MSIS images in general, a particular emphasis is given to AUV navigation and localization, since it is the domain at which this work is directed and might have the most impact.

First, it is presented an overview of the state of the art in AUV navigation and sensor technol-ogy, emphasizing their essential features, advantages, and disadvantages. Then, a brief introduc-tion is made to the image segmentaintroduc-tion techniques required for this work.

2.1 AUV Navigation and Localization

The problem of navigation can be summarized by the following three questions: "Where am I?", " Where am I going?" and "How should I get there?" [8]. The first question is directly related to location: how do I know where I am, based on the knowledge I have and on what I can see. The other two are related to the goal and the way planned to achieve that goal, respectively.

Recent advances in the efficiency, size, and memory capacity of computers have been enhanc-ing the development of AUVs, resultenhanc-ing in the automation of operations that once required human control. Figure2.1illustrates in an organized manner the main techniques used for navigation and localization in AUVs.

AUVs have limited operating time due to energy consumption and tend to have dynamic con-straints, such as loss of controllability at very low speeds, which requires fast access to information around the environment for navigation to be safe [8].

The navigation and location of AUVs is a challenge that continues to this day. The main techniques utilized are divided into three categories by the sensor technology utilized:

• Inertial;

• Acoustic navigation systems; • Geophysical.

These techniques are described in the following sections.

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6 Literature Review

Figure 2.1: A scheme of the localization and navigation methods applied to AUVs. Adapted from [11]

2.1.1 Dead Reckoning and Inertial Navigation

Dead Reckoning (DR) is the process of computing the current position without any external sup-port. It is one of the most well known and used methods.

Using inertial sensors such as a compass and a Doppler Velocity Log (DVL) the current posi-tion of the vehicle is computed based on a previously determined posiposi-tion and the moposi-tion detected by the inertial sensors.

The Inertial Navigation System (INS) attempts to improve the position estimated through DR by integrating the measurements of accelerometers and gyroscopes, providing the estimation of the full state of the vehicle (position, velocity, acceleration, attitude and angular rate) continuously and at high frequencies [12].

Some pros of proprioceptive inertial sensors (compass, pressure sensor, DVL) are that they can provide measurements at a much higher frequency than acoustic sensors since these are dependent on Time Of Flight (TOF). Thus, these sensors can reduce the growth rate of the error in the position estimate.

The main disadvantage of this method of navigation is that the position error is cumulative and can grow unbounded with the distance traveled by the vehicle.

These sensors are considered to be the basis of a precise navigation system and are usually combined with other navigation techniques [11].

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2.1 AUV Navigation and Localization 7

2.1.2 Acoustic Navigation Systems

Acoustic navigation systems comprehend techniques of navigation which are based on the TOF of acoustic signals emitted by beacons or modems. The length of the baseline generally classifies them, i.e., the distance between the active transceivers [15]. The most common methods are described in the following sections.

2.1.2.1 Ultrashort Baseline (USBL)

The USBL technology allows obtaining the location of the AUV relative to a surface vehicle. The beacons are placed closely together, usually on a ship hull. The distance and attitude are determined based on the TOF and the phase difference of the emitted acoustic signals, respectively, thanks to an array of transducers that allow the computation of the transceiver position in the coordinate reference of the vehicle [10].

The major limitation of USBL is the reduced operating area.

2.1.2.2 Short Baseline (SBL)

SBL technology has the same operating principle of the USBL except that the beacons are placed more distanced apart, usually at the opposing ends of a ship hull. The distance is calculated by triangulation [11]. The baseline size depends on the length of the support vehicle (see fig.2.1(a)). So, in addition to the need for a support vehicle, the accuracy of the system is dependent on the length of the ship hull.

2.1.2.3 Long Baseline (LBL)

In LBL systems, localization is achieved by triangulating the acoustic signals emitted by beacons spaced apart with a baseline in the order of 100-6000 m and fixed to the ocean floor [15] (fig.2.1

(c)). In most cases, beacons are globally referenced by another vehicle before the beginning of a mission [11].

For high accuracy position detection, a high-frequency LBL system offers very good results [15]. LBL systems are among the most robust, reliable, and accurate localization systems avail-able. A 300 kHz system can achieve a precision of less than 1cm in a range of 1-100 m, while a system operating at 12 kHz may achieve a range of 5-10 km with an accuracy of 0.01-10 m [15].

The major disadvantage of this system is the cost and time required to install the beacons and georeferencing them. However, this may be slightly mitigated if the locations of the beacons are not globally referenced and are either capable of self-locating [1] or localized by an AUV. Another shortcoming is the limited range imposed by the distance between the beacons as well as the dependence on precise knowledge about the velocity of sound propagation on the water column [6].

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8 Literature Review

Figure 2.2: (a):SBL; (b):USBL; (c):LBL. Adapted from [11]

2.1.2.4 GPS Intelligent Buoy (GIB)

The operating principle of GIBs is identical to that of LBL except that they do not require the installation of beacons in the ocean floor, instead these are buoying on the surface, thus reducing installation costs and the difficulty of recovering them [11].

2.1.2.5 Single Fixed Beacon (SFB)

Instead of building a network of beacons, it is possible to reduce these infrastructure requirements if a single beacon is used. The baseline is simulated by estimating the distance to the beacon until the next update is received. This technique is called Virtual Long Baseline (VLBL) [7].

The trajectory of an AUV has a significant impact on the observability of the vehicles state. Long strokes toward the beacon or in the opposite direction will cause an unlimited growth in position error. As a result, the vehicle trajectories must be planned to be tangent to the acoustic waves emitted by the beacons transceiver [11].

In figure2.3it is represented the navigation of an AUV based on a single beacon. It is assumed that the vehicle has prior knowledge of the beacon location. The AUV receives three pings. The dashed ellipse surrounding the vehicle represents the position uncertainty in a given dimension. Upon the reception of a beacon ping, the uncertainty in position is reduced in the dimension coincident with the location of the beacon.

2.1.2.6 Acoustic Modem

The acoustic modem follows the advances in the field of acoustic communications. It allows simultaneous acoustic communication of small packets and ranging based on TOF. It has had a significant impact in the performance of Cooperative Navigation (CN) as it supports inter-AUV communication, enabling teams of AUVs to localize cooperatively [11].

The transmitter can share its position with the receiver allowing it to bind its position to a sphere centered on the transmitter. As such, there is no need to georeference the beacons before the mission and their reposition during it is allowed.

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Figure 2.3: An AUV is locating himself with a single beacon in a known location. Uncertainty grows between beacon pings. Upon the reception of a ping from the beacon, the uncertainty is reduced in the dimension coincident with the location of the beacon. Adapted from [11].

Due to the limited bandwidth underwater, the communication channel is usually shared using a Time-Division Multiple Access (TDMA) scheme in which each member in the group is allotted a time slot to broadcast information. The primary drawback of such scheme is that the total cycle time grows with group size.

The modem can also be deployed into an Autonomous Surface Vehicle (ASV) as in [2], thereby increasing the autonomy of the process and potentially providing longer-term autonomous navi-gation capabilities.

2.1.3 Geophysical Navigation

Geophysical navigation systems, also known as terrain navigation systems, refer to any method that uses observable physical characteristics of the surrounding environment to obtain an estimate of the AUV position.

The purpose of geophysical navigation is to provide navigation performance similar to the GPS system. It can be accomplished by providing a map of the area to the AUV or by constructing one along with the vehicle’s mission (also known as Simultaneous Localization and Mapping (SLAM)) [16]. The success of any geophysical method of navigation and location is, therefore, dependent on the presence of suitable features in the environment and the ability of the system to extract useful information from the sensor data.

The following sections describe the most relevant technologies in this domain.

2.1.3.1 Optical Sensors

Optical systems use a stereo or monocular camera to capture images of the seabed and then match those images to navigate. They allow the performance of visual odometry, which is the process of determining the robot pose by analyzing subsequent camera images [11].

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10 Literature Review

Figure 2.4: Different types of sonar swath: (a) sidescan; (b) multibeam; (c) forward looking; (d) sector scan; (e) synthetic aperture. Adapted from [11].

In underwater environments, images are prone to scattering and inadequate lighting. The reduced camera range (typically less than 10 m [5]) is another significant detractor to the utilization of this navigation method.

The use of optical underwater navigation methods relies on the existence of features. There-fore, they are particularly suited for small-scale mapping of feature-rich environments [11].

2.1.3.2 Sonar Sensors

The use of sonar devices for underwater imaging is a fairly robust technology.

Active sonars can both transmit an acoustic signal and receive its reflected echo. Therefore, they can extract information from their surroundings. They are designed to operate at specific frequencies, depending on the range and resolution required and can be classified into two major categories, depending on whether they produce only a set of range and bearing measures (ranging sonars) or an acoustic image of the scene (imaging sonars) [14]. Figure2.4shows the sonic swaths emitted by the different types of sonar analyzed.

Ranging sonars are not capable of measuring the returning echo intensity value from partic-ular places within the insonified area. They produce only a set of range and bearing measures. Therefore, they are not well suited for capturing the corner echo intensity characteristics. The most commonly used ranging sonars are:

• Echo sounder: It is one of the most straightforward ranging systems. It operates by emitting a pulse from its transducer. If this pulse reflects off a surface, it returns to the sensor head, and the distance can be estimated based on the TOF [14].

Such devices are usually mounted in a downward-facing position to measure the depth be-low the transducer.

• Mechanically scanned profiler: This sensor is composed of a mechanically actuated echo sounder that can be sequentially oriented to different angles and produce a series of distance

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measurements. It can be used for obstacle detection tasks, or to acquire bathymetric data when mounted on a down-looking position [14].

• Multibeam echo sounder: Instead of just one transducer pointing down, this sensor is composed of arrays of transducers that can emit multiple fan-shaped beams towards the bottom [14]. It is specifically designed to generate bathymetric maps of the seabed. Figure

2.4(b) shows the acoustic swath of this device.

Imaging sonars emit acoustic pulses and then listen with an array of transducers to their return, sampling the acoustic energy returned from different directions. The sampling of the transducers is periodic and provides TOF, azimuth angle, and intensity for each sample. The combination of the returns from all the elements provides an acoustic representation of the environment, generally referred to as an acoustic image.

Although an imaging sonar scan returns an array of echo intensities, these echo intensities are usually represented in 8 bits and can be displayed as images. On the course of this document, echo intensity matrices and sonar images will be referred interchangeably.

The most common types of imaging sonars are:

• Sidescan sonar: The sonic swath of a sidescan sonar is shown in figure2.4(a). It emits multiple beams directed perpendicular to travel direction. The intensity of the acoustic returns from the ocean floor is recorded in a series of cross-sections. When coupled along the direction of the vehicle, these combined slices form a 2D image of the ocean floor within the emitted range. Each ping echo return is processed independently. The along-track resolution (also known as azimuth resolution) becomes weaker as the range increases. The transmitter and receiver horizontal beam widths are small (typically 1o_{) [}₄_{]. This type}

of sonar is usually used for bathymetry and is not suited for obstacle detection tasks.

• Synthetic Aperture Sonar (SAS): SAS is an enhancement of sidescan sonar, producing a more faithful optical-like image of the seafloor [4].

Synthetic aperture techniques use coherent addition of consecutive displaced returns to cre-ate a virtual array (aperture) whose extent can be increased with range to maintain a constant along-track resolution. So, instead of using a large static array of transducers like the sides-can, it uses the sensors along-track displacement to synthesize a sizeable virtual array. The resulting resolution is independent of the distance between the sensor and the target [11]. The transmitter and receiver horizontal beam widths are larger than the sidescan (typically > 30o_{), implying shorter physical apertures or lower center frequencies as well as some}

means of storing the received echoes from many pings and processing data [4]. SAS swath is depicted in figure2.4(e).

• Forward Looking Sonar (FLS): Also known as multibeam imaging sonar, this sensor is similar in principle to a sidescan sonar, only beams are directed forward. It is equipped with an array of hydrophones which allow producing a full acoustic image of the insonified area

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with the emission of a single pulse. This area is usually limited to a small sector in front of the sensor (fig.2.4(c)).

The vertical width of the beam is higher than the horizontal, hence this type of sonar is most often used to map vertical features and is optimal for obstacle avoidance tasks [11]. It could be used as well for detecting corners in a human-structured environment. Its main drawback is its cost, which can be around ten times more than an MSIS [14].

• Mechanically scanned imaging sonar (MSIS): Because of their reduced size and price compared to other sonar imaging devices, MSISs are among the most studied imaging sonars for integration into AUVs.

Its form of operation is identical to that of the FLS, but instead of multiple beams, a single fan-shaped beam is rotated through the desired scanning sector at a predefined angular step (fig. 2.4(d)). For each angular step, it yields an array of cells characterized by a distance and an echo intensity value. This information accumulated over a full 360o_{scan produces}

an acoustic image of the surroundings.

It may take about 7-8 s to make a complete revolution. Consequently, the refresh rate is slow, and it can not be assumed that the position of the AUV remains constant over a full scan cycle [11].

The transducer geometry typically has a large vertical width making it possible to detect obstacles at different heights as well as a narrow horizontal width, which increases the resolution of the device and improves the acuity of the acoustic images [13].

The operation of this type of sonar is of major importance as it was the sensor utilized to acquire data during the elaboration of this dissertation.

2.2 Feature Extraction and Image Processing Techniques

The detection of objects in sonar images is challenging because several factors affect the intensity of the acoustic reflections of objects in a water column. Some of these factors include the size, material, and geometry of the object relative to the sonar sensor head as well as interferences from other acoustic sensors and the acoustic background composition (such as the background type and amount of sediment) [9]. Once an obstacle is detected, image processing algorithms can be applied to measure their size and calculate their location within the navigational frame.

While locating objects through the ranging and bearing data embedded in the resulting sonar scan image is a straightforward process, estimating its actual size is very difficult.

The automatic recognition of natural features present in underwater environments is one of the most significant challenges to geophysical navigation due to reliance on the identification of suitable elements which can not be easily described by simple geometric forms.

The performance of feature extraction algorithms is dependent on both the quantity and quality of the features present in the environment.

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2.2 Feature Extraction and Image Processing Techniques 13

As the nature of the reference points varies according to the sensors and the operating envi-ronment in which the AUV is inserted, the methods frequently proposed are usually only suitable for particular situations [16].

2.2.1 Image Segmentation

Image segmentation subdivides an image into its regions or composing objects. The level of detail in the subdivision depends on the problem at hand. That is, the segmentation should stop when the objects or regions of interest in an application are detected [3].

Most of the segmentation algorithms are based on one of two basic properties of intensity values: discontinuity and similarity [3]. In the first category, the approach is to partition the image based on abrupt changes in intensity, such as edges. The primary strategy of the second category is to partition the image into similar regions according to a predefined criterion. Thresholding, and region growing are examples of methods in this category.

Segmentation performance can be improved by combining different methods, such as tech-niques where edge detection is combined with thresholding.

The most commonly used segmentation techniques are:

• Thresholding: Thresholding techniques are very popular because they are intuitive, sim-ple to imsim-plement, and computationally fast. It consists of partitioning images directly into regions based on intensity values, resulting in a binary image.

It is useful to eliminate irrelevant regions in an image while keeping the relevant ones.

• Edge-based segmentation: This method is based on the detection of acute changes in local intensity.

Derivatives of first and second order are particularly suitable for this purpose:

– Gradient: First derivatives in image processing are implemented using the magnitude of the gradient. For a function f (x,y), the gradient of f at coordinates (x,y) is defined as the two-dimensional column vector

∇f ="gx gy # = "_∂_f ∂x ∂f ∂y # (2.1)

This vector has the geometrical property that it points in the direction of the greatest rate of change of f at location (x,y). The magnitude of vector ∇ f , denoted as M(x,y) where

M(x,y) =qg2

x+g2y (2.2)

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– Laplacian: The Laplacian is a second-order derivative operator defined as ∇2f = ∂

2_f

∂x2 + ∂2f

∂y2 (2.3)

Being a second-order derivative operator, it is superior in enhancing fine detail. How-ever, this causes it to produce noisier results than the gradient.

• Region Growing: It is a procedure that groups pixels or subregions into larger regions based on predefined criteria for growth.

The basic approach is to start with a set of "seed" points and from these grow regions by appending to each seed those neighboring pixels that have predefined properties similar to the seed (such as specific ranges of intensity).

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Chapter 3 Methodology

Throughout this chapter, a walkthrough of the developed work will be done, explaining the thought and actions taken to solve the problem in hands and to get the results.

3.1 Work Introduction

The Tritech Micron [18], [17] is a mechanically scanned imaging sonar (MSIS) that can be pro-grammed to continuously cover sectors of varying amplitude from few degrees up to full 360o_{. It}

has a maximum range of 75 m and a minimum range of 30 cm, a beam vertical and horizontal width of 35o _{and 3}o _{respectively, and a configurable mechanical resolution (angle step) of 0.45}o_,

0.9o_{or 1.8}o_.

The matrix returned by a full 360o_{Tritech Micron Sonar (TMS) scan has dimensions 200 lines}

x 399 columns. The 200 lines result from the division of the revolution angle by the angle step, that is

revolutionAngle/angleStep = numberO f Lines (3.1) The 399 columns is a fixed value and determine the bin length when divided by the selected maximum range

binLength = 399/selectedMaximumRange (3.2) The matrix can be directly represented in the polar coordinate system (fig. 3.1) where each point holds an intensity between 0 and 255, characterizing the strength of the return signal on that distance and angle, and it can be converted to the cartesian coordinate system (fig.3.2).

Figure3.1was yielded by the TMS in a rectangle shaped tank with dimensions 4.6 m (length) x 4.4 m (width) x 1.8 m (depth). The first line of horizontal parabola-like formats correspond to the walls of the tank. The parabolas above the 6 m range mark result from multipath echoes. It happens because the selected maximum range with which the scan was performed was 10 m, and the diagonal length of the tank is approximately 6.35 m, which is the maximum tank length.

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16 Methodology

Figure 3.1: Sonar scan acquired in position 5 of fig.3.6with a selected maximum range of 10 m

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3.1 Work Introduction 17

Figure 3.3: Photo of the tank showing a side wall with its windows.

Therefore, multiple reflections of the emitted sonar beam occur between the walls before returning to the sonar head. The sensor interprets them as obstacles in a longer range. As seen before (fig.

1.1) multipath echoes do not occur when the selected maximum range is 5 m, but in this case, the sonar cannot capture all the tank corners in some tank positions (see fig. 3.6). It is also observed that these multipath returns can be characterized by higher intensities than the first returns, which can complicate the process of automatically detecting corners in these scans.

Sharp vertical intensities located on transitions between two walls in figure 3.1 correspond to tank corners while sharp vertical intensities along the walls are usually associated with the small corners of the existing windows on the walls of the tank (see fig. 3.3). As this sharp vertical intensities stand out on the eye, they shall also be easily spotted automatically using some derivative-based image processing operations (will be explained in a later section). The developed algorithms focus on the detection of these patterns. It must be emphasized that they only occur in the directly acquired sonar scan, not on the cartesian coordinate converted scan. Therefore, the algorithms developed were only performed to the first and not the latter.

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18 Methodology

Figure 3.4: Flow diagram describing the steps followed to obtain the results.

3.2 Data Acquisition

In order to get experimental data to test the different algorithms, the TMS was mounted on the SHAD AUV (Small Hovering AUV with Differential Actuation).

The movement of the vehicle induces a distortion in the acoustic images obtained. Therefore, the AUV was static and fixed to a moveable bridge (see fig. 3.5) during the procedure. There was no object floating on the tank, and the scans were made with the AUV on the surface. The procedure was to perform 360o _{sonar scans at six different positions in the tank, each of which}

measured with measuring tape relative to the tank walls (see fig.3.6).

Before running the scan, a few sonar settings had to be set. These settings include the maxi-mum scan range, the gain, and the angle step increment.

In order to evaluate the algorithms in different sonar settings, for each of the six positions, eight different 360o _{scans were performed, varying the range and the gain. The angle step increment}

was set constant to 1.8o_{throughout the whole procedure.}

Selected maximum ranges were 5 and 10m, and the gain was varied from 0.25 to 1.0 in 0.25 increments, totaling 48 different sonar images. Despite the maximum dimension of the tank being approximately 6.35 m, a maximum range of 5 m was considered because it is of interest to test the algorithms in a shorter range, the reason being that the shorter the range, the more detail in the sonar image, and less noise and multipath interference. Ranges longer than 10 m were not considered because the maximum dimension of the tank is substantially shorter and therefore it was not appropriate.

For each position, the sonar device generated a log file containing the data gathered. All the log files were downloaded to the computer via ssh wireless connection. A MATLAB script was used to process the files, and obtain the echo intensity matrix, also known as the raw sonar image.

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3.2 Data Acquisition 19

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20 Methodology

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3.3 Corner Detection 21

3.3 Corner Detection

A set of algorithms were applied to the raw sonar image in MATLAB (see fig. 3.7a). These algorithms consist of individual combinations of the following operations:

• Thresholding (Th);

• _{Horizontal and vertical gradient (Gx, Gy);} • Horizontal and vertical Laplacian (Lx, Ly).

These operations were selected for a reason. As the goal is to isolate the corners, and it is noticeable that the corners generally hold higher intensities than the rest of the scene (fig. 3.1), the function of thresholding is to discard the unwanted low-intensity regions, while keeping the high-intensity ones.

It is also noticeable that corners appear as an abrupt horizontal transition of intensity. There-fore, the horizontal gradient and horizontal Laplacian have the same function, that is, to capture this abrupt horizontal transitions.

The vertical gradient and vertical Laplacian have a different function. It was observed that the vertical change in a corner region is low. Therefore these operators are meant to detect spots with a relatively low-intensity vertical transition.

The result of a thresholding operation is a binary image/matrix in which pixels in the raw image with a value greater than or equal to the threshold value have the value of 1, and the others have 0 (see fig.3.7).

The result of a gradient and a Laplacian applied to the raw image is a matrix in which each pixel holds the resulting value of the respective operation at that position.

All the combining matrices had to be composed of logic ones and zeros to enable their com-bination. Therefore, after performing the horizontal gradient and Laplacian, the resulting matrix was binarized with a tolerant threshold of 20% of the maximum value in the resulting matrix. For the same reason, and in order to capture the low vertical changes, values greater than 20% of the maximum value present in the resulting matrix of the vertical derivatives performed were set to zero, while lesser or equal values were set to one (see fig.3.8).

Multiple threshold values were tested. This threshold values were selected as a percentage of the maximum intensity present in the raw echo-intensity matrix. Percentages considered were in the interval 40% to 90% in 5% increments.

Gradient and Laplacian were performed with MATLAB built-in function imgradientxy(). This function computes both directional gradients in each matrix position. The horizontal Laplacian is given by performing imgradientxy() to the horizontal gradient computed earlier, while the vertical Laplacian is computed in the same way with the vertical gradient.

All these operations were performed individually and then combined with AND operators, i.e., after performing an operation to the raw matrix, the resulting binary matrix was combined with the rest. All the possible combinations of the mentioned operations were tested, from a single

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22 Methodology

threshold operation up to a combination of T h. ∗ Gx. ∗ Gy. ∗ Lx. ∗ Ly, the operator ".∗" denotes multiplication or in this case a logical AND.

A total of 157 different combinations were performed to each image. For each possible combi-nation, the resulting binary matrix and corresponding image were saved. Figure3.7and3.8shows the resulting binary matrices of the different single operations applied to the same image. The white regions seen correspond to ones in the binary matrix. The goal is to discard all the white regions, except for the ones within each corner zone, that is, to isolate the corners.

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3.3 Corner Detection 23

(a) Raw sonar image (b) Threshold 40% (Th40)

(c) Threshold 45% (Th45) (d) Threshold 50% (Th50)

(e) Threshold 55% (Th55) (f) Threshold 60% (Th60)

(g) Threshold 65% (Th65) (h) Threshold 70% (Th70)

(i) Threshold 75% (Th75) (j) Threshold 80% (Th80)

(k) Threshold 85% (Th85) (l) Threshold 90% (Th90)

Figure 3.7: Resulting binary images from threshold operations applied to a sonar scan acquired in position 5 of fig.3.6with a selected maximum range of 5 m and a gain of 0,5.

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24 Methodology

(a) Horizontal gradient (Gx) (b) Vertical gradient (Gy)

(c) Horizontal Laplacian (Lx) (d) Vertical Laplacian (Ly)

Figure 3.8: Resulting binary images from derivative operations applied to the same scan of fig.

3.7.

3.4 Clustering

An 8-connected component labeling was performed in the binary image to assess the number of pixel regions whose centroid (geometric center) is inside each corner. 8-connected component labelling consists in the labeling of pixels which are in an eight direction neighborhood (see fig.

3.9).

To further isolate the corners and reduce the number of detections, clustering was performed to every 8-connected region labeled. It consists simply in the aggregation of objects or regions following a defined criteria.

The goal was to compute the centroids (geometric center) of the resulting clusters and compare it with the real corner locations.

The clustering procedure was to group every 8-connected region within a range of 4 lines x 2 columns in the binary matrix and compute the combined centroid. This range corresponds approximately to a tolerance of 7.2o_{and 2.52 cm for a selected maximum sonar range of 5 m and}

7.2o_{, 5.02 cm for 10 m. The centroid of grouped regions A and B was computed as}

CentroidAB=AreaA×Centroid_AreaA+AreaB×CentroidB

A+AreaB (3.3)

Where the area is the number of ones in the corresponding binary image region. The centroid is the location (line, column) of the geometric center of the same region.

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3.5 Ground Truth 25

Figure 3.9: Representation of 8-direction connectivity.

3.5 Ground Truth

The point of ground truth is to evaluate the accuracy of the different algorithms by comparing their results with the exact measures. Ground truth was needed to test the effectiveness of the algorithms for corner detection.

With all the measurements taken (fig. 3.6) the exact position of the sonar relative to the tank walls and corners was known. So, it was possible to synthesize an image mask with the exact position of the corners marked within a defined tolerance. The sonar parameter range and angle step increment had to be taken into account in the generation of these masks.

It was possible to synthesize three masks for each acquired image automatically (see fig.3.10). One of the masks marks all the corners exact position in each image (fig.3.10a), i.e., the positive detections. Each corner was marked correctly inside a tolerance of 8 lines x 4 columns. This dimension was found to be the most suitable for the uncertainty caused by the concavity of the corners. A size of 8 lines x 4 columns in the matrix corresponds sensibly to a tolerance interval of 14,4o_{in bearing and 5,04 cm in range for a 5 m selected maximum range and 10.04 cm for a 10 m}

selected maximum range. These intervals are acceptable since the MSIS has a beam width of 3o

horizontal and 35o_{vertical (figs.}_3.11_{). It is important to note that this tolerance has the limitation}

of not being able to distinguish different corners within an 8x4 range but for the scenario tested there was no risk of that happening as the tank corners were far away from each other.

Another mask covers the uncertain regions (fig. 3.10c), i.e., regions that might also possess corners belonging to the windows, but because they are not always well defined or distinguishable from the walls, they will be treated specially. This mask covers the walls in every image.

The false detections mask (fig. 3.10e) meant to assess all the false-positive detections. This mask is very important for the evaluation of the algorithms as it covers all the regions in which a corner detection is considered to be a false detection. Thereby, allowing to differentiate a good detection from a bad one.

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26 Methodology

(a) Positive classification mask synthetized.

Each white rectangle delimits a corner area. (b) Positive classification mask overlaid to theraw sonar image.

(c) Uncertain classification mask synthetized

covering the walls of the tank. (d) Uncertain classification mask overlaid to theraw sonar image.

(e) Negative classification mask synthetized

covering the false-detection regions. (f) Negative classification mask overlaid to theraw sonar image.

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3.6 Classification 27

Figure 3.11: Tritech Micron MSIS vertical beam width characteristics.

3.6 Classification

After the clustering procedure, the number of corners detected was computed as the number of corner regions in the positive classification mask (see fig. 3.10a) that have a cluster centroid within their encompassed area. These cluster centroid locations were used to compare the location of the detected corners with each corner real location. The procedure was:

1. Pick all the cluster centroids localized within each corner region (with ground truth);

2. Compute their combined centroid;

3. Convert each centroid to polar coordinates (ρ,θ);

4. Associate each centroid polar coordinates with the closest corner.

In the same manner, the number of false and uncertain detections was computed as the number of cluster centroids inside the respective regions.

3.6.1 Measuring computational performance

Each operation performed was isolated in a function to test its execution time with MATLAB built-in function timeit() for every image. It operates by calling a specified function multiple times and computing the median of the measurements. These tests were taken in a computer which has an Intel Core I7-6700HQ CPU with a base frequency of 2.6 GHz and 16 GB of RAM.

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28 Methodology

3.6.2 Data Processing

All the operations and evaluations performed to an image were saved in an organized matrix to be able to write it directly and automatically into an Excel .xlsx file. This was performed using the xlswrite MATLAB function.

Each image accounted for one Excel worksheet and was identified by the position in which it was acquired, and the respective sonar settings gain and maximum range utilized to acquire it.

All the values to be compared between different algorithms were re-scaled to interval [0,1] with min-max normalization (eq. 3.4).

normalizedValueM=_{maxValue − minValue}value − minValue (3.4)

Variables in which the interest is to minimize such as the number of false detections were also re-scaled in same way and then subtracted to one (eq.3.5).

normalizedValuem=1 − value − minValue

maxValue − minValue (3.5)

3.6.3 Procedure Automation

The complete process from reading the .dst files up to writing the results in Excel was automated with MATLAB code. All the .dst files were kept in a folder, each one identified by the position in the tank in which it was acquired and the respective sonar settings gain and maximum range respectively. A MATLAB script performed the following steps:

1. Read .dst file;

2. Create folder with same name;

3. Copy file to the folder;

4. Execute MATLAB scripts while inside folder:

(a) Process .dst file;

(b) Execute segmentation algorithms; (c) Perform evaluation;

(d) Generate Excel matrices.

5. Leave folder, create Excel file and write the matrices in the respective worksheet.

3.6.4 Defined Metrics

A set of metrics were defined to evaluate the developed algorithms performance by different cri-teria:

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3.6 Classification 29

• Number of correct corner detections: This metric is of importance as the navigation algo-rithm should be able to correctly detect as many corners as possible. It should provide safer vehicle navigation.

• Number of false corner detections: By considering a cluster detection as corner detection, it is possible to assert the number of clusters in the false detection mask region and compute the number of false corner detections. This metric is of importance as the minimization of these detections improves the quality of the algorithms.

• Accuracy of the corners detected: The error in the detected corner position is another useful criteria as it is useless to detect corners if the error in position is too large. This metric compares the position of the cluster centroids localized in the defined corner region (explained in section3.5), with the real corner location obtained through measurements on site (fig.3.6). The average of all images corner relative range and angle error was computed. That is, for each operation performed to an image, it was computed the relative range and bearing error for each individual corner detected, then it was averaged for the respective operation and averaged again for all images.

• Computational demand: Computational performance is of critical importance as the ca-pacities of different on board computers vary a lot and it is required that the developed algorithms execute as fast as possible to update the moving vehicle position in real time. All the metric results were normalized to the interval [0,1] with equations 3.4 and 3.5. In cases where it is desirable to maximize the result equation3.4 was applied while in cases where the minimum value is preferred, equation3.5 was applied. The normalization allows combining the results from different metrics. By associating different weights to each metric, it is possible to provide a score for each developed algorithm for a particular scenario of interest where certain metrics can be prioritized over others.

Four different weights were defined, one for each defined metric, such that

4

∑

i wi

=1;wi∈ [0,1] (3.6)

where wiis the defined weight of metric i.

The score was computed for each algorithm as

Score = w1×c1+w2×c2+w3×c3+w4×c4 (3.7)

where each ciis the normalized result of an algorithm for the metric i.

The normalized accuracy result was computed as the average of the normalized range and angle relative errors:

caccuracy= relErrorrange+relErrorangle

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Chapter 4 Analysis of results

In this chapter, a thorough analysis will be done emphasizing certain aspects that are considered relevant for the application in mind, which is AUV navigation.

It is important to note that the threshold percentages utilized should be adapted to each sonar sensor and its settings, in particular, the gain. Therefore, although analysis will be made judging the effects of different threshold percentages, the focus is on the derivatives whose performance is independent of those factors.

Only the top 20 results for each metric are displayed in this chapter. The complete results are shown in appendixA.

4.1 Algorithm Performance Difficulties

First, it is important to mention some algorithm performance difficulties observed in the images acquired. Namely, having to do with the sonar scan settings, selected gain, and maximum range. As it can be observed, comparing figure4.1 acquired with a selected maximum gain of 1.0 with figure4.2acquired with a 0.25 gain, intensity saturation occurs in the first image, which attenuates the transitions of intensity between pixels, and will, therefore, impact the performance of the derivatives operation.

Another struggle happens when the selected maximum range is beyond the tank length (fig.

3.1). In this case, it will occur multipath echoes, which can shadow the real features in which we are interested. Also, these multipath echoes might be characterized by higher intensities than the real echoes as it happens in the example mentioned. Therefore it will impact the performance of the algorithms.

It was also observed that some of the corner regions were not correctly placed in the positive classification masks that were automatically synthesized (see4.3, for example). That might be due to small errors in the tank measurements in conjunction with the uncertainty associated with corner returns due to their convex nature. It will, of course, impact the positive detections in some images.

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32 Analysis of results

Figure 4.1: Sonar scan taken in position one of fig. 3.6 with a selected gain of 1.0 - Note the saturation of intensities that occur.

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4.2 Number of Correct Corner Detections 33

Figure 4.3: Positive classification mask example in which corners regions are not placed correctly.

4.2 Number of Correct Corner Detections

Figure4.5shows the top 20 normalized results for the average number of corners detected in all the acquired images. Full results are shown in figureA.0.

For the considered metric, there is no significant difference between the top 20 results. The combination of thresholding with horizontal and vertical Laplacian yielded the best result. The horizontal Laplacian is the major contributor to this. Despite this, the combination of thresholding with horizontal and vertical gradients is statistically similar, and it has the computational advantage that only one derivative is being performed in each direction.

Considering only single operations, it is noticeable that horizontal derivatives are the major contributors to a better score, in particular, the horizontal Laplacian. This observation makes sense because as it was noted before, given the abrupt horizontal transition of intensity that characterizes corners, it is not surprising that horizontal derivatives are very efficient at detecting corners alone. FigureA.0 considers all the combinations tested. The results were divided into three pages for better visibility and page size reasons. All combinations follow the trend that the higher the threshold value considered, the less amount of corners are correctly detected. It is evident that the lower threshold values tested in combination with two different direction derivatives yield better results, and below the 50% threshold mark, the results are constant.

To give a more intuitive view, fig. 4.4shows the top 20 results for the sum of correct corner detections, that is, the total corners detected by each combination for all the images considered. FigureA.0shows the complete results. Knowing that in the total of the 48 images acquired, there are 184 detectable corners, the best three combinations resulted in the detection of 67.4% of the total corners detectable.

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4.2 Number of Correct Corner Detections 35

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4.3 Number of False Corner Detections

Figure 4.6 shows the top 20 results for this metric. The results shown were normalized with equation3.5. FigureA.0shows all the results. Once again, the graph was divided into three pages for the same reason mentioned in the last section.

In terms of this metric, there is no significant difference between the top 20 results. It is no coincidence that the combinations that result in less false detections are the ones that combine a higher threshold value. A higher threshold value results in fewer detections overall and conse-quently less false detections, but also, less correct corner detections as noted in the last section.

Overall the differences in score across all the algorithms tested are not critical, except for the isolated horizontal gradient and Laplacian operations.

The combination of thresholding with an horizontal and a vertical Laplacian consistently yielded the best results for each threshold mark, but once again, the difference is not significant.

To provide a better understanding of the results, figure4.7 shows the top 20 results for an average ratio of positive to total detections, not normalized, for each combination. It is observable that the number of false detections is significantly larger than the number of correct detections because the best result yielded by the combination "Th80 .* Gy .* Ly", yielded an average of approximately 7.4% ratio of correct to total corner detections, that is, in a total of 100 detections, approximately 7 will be correct, on average.

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4.3 Number of False Corner Detections 37

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4.4 Accuracy of the Detected Corners 39

4.4 Accuracy of the Detected Corners

The bar graph on figure4.8and figureA.0displays the top 20 results for the range error and angle error, respectively. The complete graphs are shown in figuresA.0andA.0.

First of all, it is observed that the results for the two errors analyzed go hand in hand. There-fore, they can be analyzed together. Also, in general, both errors decrease with the threshold percentage value, although this trend stops at the 50% mark as the error for each combination re-mains constant below that mark. That happens probably because below the 50% threshold mark, corner regions and their neighborhood are no longer affected by the threshold operation as these regions are characterized by a relatively high intensity. Therefore, below the 50% mark, corner regions maintain their full characteristics and can only be influenced by the derivative operations which affect them equally. It is important to notice that in general, for threshold values above the 50% mark, the scores get a lot worse.

The combination of two different directional derivatives consistently yielded the best results for each threshold mark, with no benefit in adding more operations to that mix. The combination T h. ∗ Lx. ∗ Ly is a bit more accurate than the T h. ∗ Gx. ∗ Gy, but this difference is not significant. The horizontal Laplacian is once again, the single operation that has greater influence in achieving a better score. A single horizontal Laplacian or horizontal gradient yielded better results than all the combinations with threshold mark equal or above the 75% mark, with the horizontal Laplacian having a significant 10% advantage over the gradient in this regard.

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4.4 Accuracy of the Detected Corners 41

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4.5 Computational Demand

Figure4.10compares the average execution time taken for each operation. The unit of time in which the results are displayed is the second (s). Once again, it is important to note that every execution and measurement was performed in the same machine at the same conditions. Although the results cannot be replicated in any other system, they still serve the purpose of giving a general idea about the relative computational performance of each algorithm.

As it is observable, a simple thresholding operation is so fast that its effect on the execution time of the other combinations is negligible.

The time it took for the gradient operation is on average twice the amount taken for the Lapla-cian, which makes sense because the Laplacian is simply the gradient performed two times.

Combination execution time grows by the same amount of the added individual operation execution times considered.

The combinations Th .* Gx .* Gy .* Lx .* Ly and Th .* Lx .* Ly have no significant time performance difference because for both, the same derivative operations are performed and matrix multiplications are fast and not time significant.

The results were normalized with equation3.5to combine with the other metrics. Figure4.11

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4.5 Computational Demand 43

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4.6 Individual Metric Analysis Summary 45

4.6 Individual Metric Analysis Summary

It was observed that the threshold values utilized have a significant impact on segmentation algo-rithms performance. Therefore, the threshold percentages should be adapted to each sonar sensor and its settings. It is recommended to test different threshold percentages with the suggested algorithms for a scenario of interest before a mission.

For the number of correct corner detections, vertical derivatives alone are useless, while single horizontal derivatives yield the best result. In general, the higher the threshold value considered, the less amount of corners are correctly detected. The combination of thresholding with horizontal and vertical derivatives is a safe choice. Combining the results of more than one derivative in the same direction has no added advantage.

The number of false detections, in general, decreases with the threshold percentage increment, as a higher threshold value results in fewer detections overall. The differences in score across all the algorithms tested are not critical, except for the single horizontal gradient and Laplacian operations.

Regarding algorithms accuracy, both range and bearing errors decrease with the threshold value. This trend stops at the 50% mark. Once again, the combination of two different direction derivatives yields better results with no benefit in adding more operations. It is noticeable that combinations with a threshold percentage above the 50% mark performed considerably worse.

Regarding computational performance, a thresholding operation has no significant impact on combination execution time. The time it took for the gradient operation is on average double the amount taken for the Laplacian, as expected. The combinations execution time grow almost equal to the sum of the individual operation execution times in consideration.

Overall, horizontal derivatives are the most effective single operations for corner detection in raw MSIS scans.

4.7 Combining Metrics

Following the analyze made for each metric score, all the metrics were then combined with as-sociated weights in order to assess the best overall algorithm score for a particular scenario. The notation for the different weights is the following:

• wdc: Weight of the metric number of correct corner detections.

• w_{f d}: Weight of the metric number of false detections. • w_accu: Weight of the accuracy metric.

• wcd: Weight of the computational demand metric.