This paper will be concerned with some fundamental properties of a line. In particular, fundamental ordering properties of a line segment are covered.

Este trabalho busca, num primeiro momento, caracterizar a problemática aprendizagem do número real na Escola Básica, aplicando questionários-sondagem, analisando livros didáticos e comparando-os com os Parâmetros Curriculares Nacionais. Num segundo momento desenvolvemos um efetivo estudo de Matemática: as maneiras mais comuns de se construir números reais e a equivalência entre todas elas. Mostramos também como, a partir de cada uma destas abordagens, chega-se à representação decimal de um número real positivo. Finalizamos com uma proposta pedagógica para o Ensino Fundamental, e uma experiência didática, numa 8ª série, de construção de um número real via medição exata de segmentos de reta. / The first part of this work is an attempt to characterize the problem of learning the concept of real number in Elementary School, making use of questionnaires and analyzing school books as well as the National Parameters for the teaching of Mathematics. The second part deals with the Mathematics involved in the construction of the real numbers, namely, different ways of constructing this set and also the equivalence between all those constructions. We also show how each one of those constructions leads to the decimal representation of a positive real number. The last part of this work consists of a pedagogic proposal for the construction of the real number making use of the (exact) measure of a line segment and the description and conclusions of its implementation in an 8th year of Elementary School.

Este trabalho busca, num primeiro momento, caracterizar a problemática aprendizagem do número real na Escola Básica, aplicando questionários-sondagem, analisando livros didáticos e comparando-os com os Parâmetros Curriculares Nacionais. Num segundo momento desenvolvemos um efetivo estudo de Matemática: as maneiras mais comuns de se construir números reais e a equivalência entre todas elas. Mostramos também como, a partir de cada uma destas abordagens, chega-se à representação decimal de um número real positivo. Finalizamos com uma proposta pedagógica para o Ensino Fundamental, e uma experiência didática, numa 8ª série, de construção de um número real via medição exata de segmentos de reta. / The first part of this work is an attempt to characterize the problem of learning the concept of real number in Elementary School, making use of questionnaires and analyzing school books as well as the National Parameters for the teaching of Mathematics. The second part deals with the Mathematics involved in the construction of the real numbers, namely, different ways of constructing this set and also the equivalence between all those constructions. We also show how each one of those constructions leads to the decimal representation of a positive real number. The last part of this work consists of a pedagogic proposal for the construction of the real number making use of the (exact) measure of a line segment and the description and conclusions of its implementation in an 8th year of Elementary School.

Este trabalho busca, num primeiro momento, caracterizar a problemática aprendizagem do número real na Escola Básica, aplicando questionários-sondagem, analisando livros didáticos e comparando-os com os Parâmetros Curriculares Nacionais. Num segundo momento desenvolvemos um efetivo estudo de Matemática: as maneiras mais comuns de se construir números reais e a equivalência entre todas elas. Mostramos também como, a partir de cada uma destas abordagens, chega-se à representação decimal de um número real positivo. Finalizamos com uma proposta pedagógica para o Ensino Fundamental, e uma experiência didática, numa 8ª série, de construção de um número real via medição exata de segmentos de reta. / The first part of this work is an attempt to characterize the problem of learning the concept of real number in Elementary School, making use of questionnaires and analyzing school books as well as the National Parameters for the teaching of Mathematics. The second part deals with the Mathematics involved in the construction of the real numbers, namely, different ways of constructing this set and also the equivalence between all those constructions. We also show how each one of those constructions leads to the decimal representation of a positive real number. The last part of this work consists of a pedagogic proposal for the construction of the real number making use of the (exact) measure of a line segment and the description and conclusions of its implementation in an 8th year of Elementary School.

More cables will be installed owing to setting up more radio towers when it comes to 5G. However, a large proportion of radio units are constructed high in the open space, which makes it difficult for human technicians to maintain the systems. Under these circumstances, automatic detections of errors among radio cabinets are crucial. Cables and connectors are usually covered with weatherproofing tapes, and one of the most common problems is that the tapes are not closely rounded on the cables and connectors. This makes the tape go out of the cable and look like a waving flag, which may seriously damage the radio systems. The thesis aims at detecting this flagging-tape and addressing the issues. This thesis experiments two methods for object detection, the convolutional neural network as well as the OpenCV and image processing. The former uses YOLO (You Only Look Once) network for training and testing, while in the latter method, the connected component method is applied for the detection of big objects like the cables and line segment detector is responsible for the flagging-tape boundary extraction. Multiple parameters, structurally and functionally unique, were developed to find the most suitable way to meet the requirement. Furthermore, precision and recall are used to evaluate the performance of the system output quality, and in order to improve the requirements, larger experiments were performed using different parameters. The results show that the best way of detecting faulty weatherproofing is with the image processing method by which the recall is 71% and the precision reaches 60%. This method shows better performance than YOLO dealing with flagging-tape detection. The method shows the great potential of this kind of object detection, and a detailed discussion regarding the limitation is also presented in the thesis. / Fler kablar kommer att installeras på grund av installation av fler radiotorn när det gäller 5G. En stor del av radioenheterna är dock konstruerade högt i det öppna utrymmet, vilket gör det svårt för mänskliga tekniker att underhålla systemen. Under dessa omständigheter är automatiska upptäckter av fel bland radioskåp avgörande. Kablar och kontakter täcks vanligtvis med väderbeständiga band, och ett av de vanligaste problemen är att banden inte är rundade på kablarna och kontakterna. Detta gör att tejpen går ur kabeln och ser ut som en viftande flagga, vilket allvarligt kan skada radiosystemen. Avhandlingen syftar till att upptäcka detta flaggband och ta itu med frågorna. Den här avhandlingen experimenterar två metoder för objektdetektering, det invändiga neurala nätverket såväl som OpenCV och bildbehandling. Den förstnämnda använder YOLO (You Only Look Once) nätverk för träning och testning, medan i den senare metoden används den anslutna komponentmetoden för detektering av stora föremål som kablarna och linjesegmentdetektorn är ansvarig för utvinning av bandbandgränsen. Flera parametrar, strukturellt och funktionellt unika, utvecklades för att hitta det mest lämpliga sättet att uppfylla kravet. Dessutom används precision och återkallande för att utvärdera prestandan för systemutgångskvaliteten, och för att förbättra kraven utfördes större experiment med olika parametrar. Resultaten visar att det bästa sättet att upptäcka felaktigt väderbeständighet är med bildbehandlingsmetoden genom vilken återkallelsen är 71% och precisionen når 60%. Denna metod visar bättre prestanda än YOLO som hanterar markering av flaggband. Metoden visar den stora potentialen för denna typ av objektdetektering, och en detaljerad diskussion om begränsningen presenteras också i avhandlingen.

Real-time spatial awareness is essential in areas such as robotics and autonomous navigation. However, as environments expand and become increasingly complex, maintaining both a low computational load and high mapping accuracy remains a significant challenge. This thesis addresses these challenges by proposing a novel method for real-time construction of continuous Euclidean distance fields (EDF) using Gaussian process (GP) regression, hereafter referred to as GP-EDF, tailored specifically for large indoor environments. The proposed approach focuses on leveraging the inherent structural information of indoor spaces by partitioning them into rooms and constructing a local GP-EDF model for each, reducing the computational cost tied to large matrix operations in GPs. By also exploiting the geometric regularities commonly found in indoor spaces it detects walls and represents them as line segments. This information is integrated into the models’ priors to both improve accuracy and further reduce the computational expense. Comparison with two baselines demonstrated the proposed approach’s effectiveness. It maintained low computation times despite increasing amounts of sensor data, signifying a significant improvement in scalability. Results also confirmed that the EDF quality remains high and isn’t affected by partitioning the GP-EDF into local models. The method also reduced the influence of sensor noise on the EDF’s accuracy when incorporating the line segments into the model. Additionally, the proposed room segmentation method proved to be efficient and generated accurately partitioned rooms, with a high degree of independence between them. In conclusion, the proposed approach offers a scalable, accurate and efficient solution for real-time construction of EDFs, demonstrating significant potential in aiding autonomous navigation within large indoor spaces. / Realtidsrumslig medvetenhet är avgörande inom områden som robotik och autonom navigering. Emellertid, när miljöer expanderar och blir alltmer komplexa, kvarstår det en betydande utmaning att bibehålla både en låg beräkningsbelastning och hög kartläggningsnoggrannhet. Denna avhandling bemöter dessa utmaningar genom att föreslå en ny metod för realtidskonstruktion av kontinuerliga euklidiska avståndsfält (EDF) med hjälp av regression via gaussiska processer (GP), hädanefter benämnd GP-EDF, specifikt anpassad för stora inomhusmiljöer. Den föreslagna metoden fokuserar på att utnyttja den inneboende strukturella informationen i inomhusmiljöer genom att dela upp dem i rum och konstruera en lokal GP-EDF-modell för varje rum, vilket minskar den beräkningsbelastning som är kopplad till stora matrisoperationer i GP:er. Genom att även utnyttja de geometriska regelbundenheter som vanligtvis finns i inomhusutrymmen, detekterar den väggar och representerar dem som linjesegment. Denna information integreras sedan i modellernas a priori-fördelningar, både för att förbättra noggrannheten och ytterligare minska den beräkningsmässiga kostnaden. Jämförelse med två baslinjemodeller demonstrerade den föreslagna metodens effektivitet. Den bibehöll låga beräkningstider trots ökande mängder sensordata, vilket indikerar en betydande förbättring av skalbarheten. Resultaten bekräftade även att kvaliteten på EDF:en förblir hög och påverkas inte av uppdelningen av GP-EDF:en i lokala modeller. Metoden minskade även sensorbrusets inverkan på EDF:ens noggrannhet vid integrering av linjesegment i modellen. Dessutom visade sig den föreslagna rumsegmenteringsmetoden vara effektiv och genererade korrekt uppdelade rum, med en hög grad av oberoende mellan dem. Sammanfattningsvis erbjuder den föreslagna metoden en skalbar och effektiv lösning för realtidskonstruktion av EDF:er, och visar på betydande potential att underlätta autonom navigering inom stora inomhusutrymmen.

Ce mémoire de maîtrise présente une nouvelle approche non supervisée pour détecter et segmenter les régions urbaines dans les images hyperspectrales. La méthode proposée n ́ecessite trois étapes. Tout d’abord, afin de réduire le coût calculatoire de notre algorithme, une image couleur du contenu spectral est estimée. A cette fin, une étape de réduction de dimensionalité non-linéaire, basée sur deux critères complémentaires mais contradictoires de bonne visualisation; à savoir la précision et le contraste, est réalisée pour l’affichage couleur de chaque image hyperspectrale. Ensuite, pour discriminer les régions urbaines des régions non urbaines, la seconde étape consiste à extraire quelques caractéristiques discriminantes (et complémentaires) sur cette image hyperspectrale couleur. A cette fin, nous avons extrait une série de paramètres discriminants pour décrire les caractéristiques d’une zone urbaine, principalement composée d’objets manufacturés de formes simples g ́eométriques et régulières. Nous avons utilisé des caractéristiques texturales basées sur les niveaux de gris, la magnitude du gradient ou des paramètres issus de la matrice de co-occurrence combinés avec des caractéristiques structurelles basées sur l’orientation locale du gradient de l’image et la détection locale de segments de droites. Afin de réduire encore la complexité de calcul de notre approche et éviter le problème de la ”malédiction de la dimensionnalité” quand on décide de regrouper des données de dimensions élevées, nous avons décidé de classifier individuellement, dans la dernière étape, chaque caractéristique texturale ou structurelle avec une simple procédure de K-moyennes et ensuite de combiner ces segmentations grossières, obtenues à faible coût, avec un modèle efficace de fusion de cartes de segmentations. Les expérimentations données dans ce rapport montrent que cette stratégie est efficace visuellement et se compare favorablement aux autres méthodes de détection et segmentation de zones urbaines à partir d’images hyperspectrales. / This master’s thesis presents a new approach to urban area detection and segmentation in hyperspectral images. The proposed method relies on a three-step procedure. First, in order to decrease the computational complexity, an informative three-colour composite image, minimizing as much as possible the loss of information of the spectral content, is computed. To this end, a non-linear dimensionality reduction step, based on two complementary but contradictory criteria of good visualization, namely accuracy and contrast, is achieved for the colour display of each hyperspectral image. In order to discriminate between urban and non-urban areas, the second step consists of extracting some complementary and discriminant features on the resulting (three-band) colour hyperspectral image. To attain this goal, we have extracted a set of features relevant to the description of different aspects of urban areas, which are mainly composed of man-made objects with regular or simple geometrical shapes. We have used simple textural features based on grey-levels, gradient magnitude or grey-level co-occurence matrix statistical parameters combined with structural features based on gradient orientation, and straight segment detection. In order to also reduce the computational complexity and to avoid the so-called “curse of dimensionality” when clustering high-dimensional data, we decided, in the final third step, to classify each individual feature (by a simple K-means clustering procedure) and to combine these multiple low-cost and rough image segmentation results with an efficient fusion model of segmentation maps. The experiments reported in this report demonstrate that the proposed segmentation method is efficient in terms of visual evaluation and performs well compared to existing and automatic detection and segmentation methods of urban areas from hyperspectral images.

La lecture automatique de plaques d’immatriculation de véhicule est considérée comme une approche de surveillance de masse. Elle permet, grâce à la détection /localisation ainsi que la reconnaissance optique, d’identifier un véhicule dans les images ou les séquences d’images. De nombreuses applications comme le suivi du trafic, la détection de véhicules volés, le télépéage ou la gestion d’entrée / sortie des parkings utilise ce procédé. Or malgré d’important progrès enregistré depuis l’apparition des premiers prototypes en 1979 accompagné d’un taux de reconnaissance parfois impressionnant, notamment grâce aux avancés en recherche scientifique et en technologie des capteurs, les contraintes imposés pour le bon fonctionnement de tels systèmes en limitent les portées. En effet, l’utilisation optimale des techniques de localisation et de reconnaissance de plaque d’immatriculation dans les scénarii opérationnels nécessite des conditions d’éclairage contrôlées ainsi qu’une limitation dans de la pose, de vitesse ou tout simplement de type de plaque. La lecture automatique de plaques d’immatriculation reste alors un problème de recherche ouvert. La contribution majeure de cette thèse est triple. D’abord une nouvelle approche robuste de localisation de plaque d’immatriculation dans des images ou des séquences d’images est proposée. Puis, l’amélioration de la qualité des plaques localisées est traitée par une adaptation de technique de super-résolution. Finalement, un modèle unifié de localisation et de super-résolution est proposé permettant de diminuer la complexité temporelle des deux approches combinées. / Automatic reading of vehicle license plates is considered an approach to mass surveillance. It allows, through the detection / localization and optical recognition to identify a vehicle in the images or video sequences. Many applications such as traffic monitoring, detection of stolen vehicles, the toll or the management of entrance/ exit parking uses this method. Yet in spite of important progress made since the appearance of the first prototype sin 1979, with a recognition rate sometimes impressive thanks to advanced science and sensor technology, the constraints imposed for the operation of such systems limit laid. Indeed, the optimal use of techniques for localizing and recognizing license plates in operational scenarios requiring controlled lighting conditions and a limitation of the pose, velocity, or simply type plate. Automatic reading of vehicle license plates then remains an open research problem. The major contribution of this thesis is threefold. First, a new approach to robust license plate localization in images or image sequences is proposed. Then, improving the quality of the plates is treated with a localized adaptation of super-resolution technique. Finally, a unified model of location and super-resolution is proposed to reduce the time complexity of both approaches combined.

Ce mémoire de maîtrise présente une nouvelle approche non supervisée pour détecter et segmenter les régions urbaines dans les images hyperspectrales. La méthode proposée n ́ecessite trois étapes. Tout d’abord, afin de réduire le coût calculatoire de notre algorithme, une image couleur du contenu spectral est estimée. A cette fin, une étape de réduction de dimensionalité non-linéaire, basée sur deux critères complémentaires mais contradictoires de bonne visualisation; à savoir la précision et le contraste, est réalisée pour l’affichage couleur de chaque image hyperspectrale. Ensuite, pour discriminer les régions urbaines des régions non urbaines, la seconde étape consiste à extraire quelques caractéristiques discriminantes (et complémentaires) sur cette image hyperspectrale couleur. A cette fin, nous avons extrait une série de paramètres discriminants pour décrire les caractéristiques d’une zone urbaine, principalement composée d’objets manufacturés de formes simples g ́eométriques et régulières. Nous avons utilisé des caractéristiques texturales basées sur les niveaux de gris, la magnitude du gradient ou des paramètres issus de la matrice de co-occurrence combinés avec des caractéristiques structurelles basées sur l’orientation locale du gradient de l’image et la détection locale de segments de droites. Afin de réduire encore la complexité de calcul de notre approche et éviter le problème de la ”malédiction de la dimensionnalité” quand on décide de regrouper des données de dimensions élevées, nous avons décidé de classifier individuellement, dans la dernière étape, chaque caractéristique texturale ou structurelle avec une simple procédure de K-moyennes et ensuite de combiner ces segmentations grossières, obtenues à faible coût, avec un modèle efficace de fusion de cartes de segmentations. Les expérimentations données dans ce rapport montrent que cette stratégie est efficace visuellement et se compare favorablement aux autres méthodes de détection et segmentation de zones urbaines à partir d’images hyperspectrales. / This master’s thesis presents a new approach to urban area detection and segmentation in hyperspectral images. The proposed method relies on a three-step procedure. First, in order to decrease the computational complexity, an informative three-colour composite image, minimizing as much as possible the loss of information of the spectral content, is computed. To this end, a non-linear dimensionality reduction step, based on two complementary but contradictory criteria of good visualization, namely accuracy and contrast, is achieved for the colour display of each hyperspectral image. In order to discriminate between urban and non-urban areas, the second step consists of extracting some complementary and discriminant features on the resulting (three-band) colour hyperspectral image. To attain this goal, we have extracted a set of features relevant to the description of different aspects of urban areas, which are mainly composed of man-made objects with regular or simple geometrical shapes. We have used simple textural features based on grey-levels, gradient magnitude or grey-level co-occurence matrix statistical parameters combined with structural features based on gradient orientation, and straight segment detection. In order to also reduce the computational complexity and to avoid the so-called “curse of dimensionality” when clustering high-dimensional data, we decided, in the final third step, to classify each individual feature (by a simple K-means clustering procedure) and to combine these multiple low-cost and rough image segmentation results with an efficient fusion model of segmentation maps. The experiments reported in this report demonstrate that the proposed segmentation method is efficient in terms of visual evaluation and performs well compared to existing and automatic detection and segmentation methods of urban areas from hyperspectral images.