Rebuilding convex sets in graphs

The usual distance between pairs of vertices in a graph naturally gives rise to the notion of an interval between a pair of vertices in a graph. This in turn allows us to extend the notions of convex sets, convex hull, and extreme points in Euclidean space to the vertex set of a graph. The extreme vertices of a graph are known to be precisely the simplicial vertices, i.e., the vertices whose neighborhoods are complete graphs. It is known that the class of graphs with the Minkowski–Krein–Milman property, i.e., the property that every convex set is the convex hull of its extreme points, is precisely the class of chordal graphs without induced 3-fans. We define a vertex to be a contour vertex if the eccentricity of every neighbor is at most as large as that of the vertex. In this paper we show that every convex set of vertices in a graph is the convex hull of the collection of its contour vertices. We characterize those graphs for which every convex set has the property that its contour vertices coincide with its extreme points. A set of vertices in a graph is a geodetic set if the union of the intervals between pairs of vertices in the set, taken over all pairs in the set, is the entire vertex set. We show that the contour vertices in distance hereditary graphs form a geodetic set

Structure and properties of maximal outerplanar graphs.

Outerplanar graphs are planar graphs that have a plane embedding in which each vertex lies on the boundary of the exterior region. An outerplanar graph is maximal outerplanar if the graph obtained by adding an edge is not outerplanar. Maximal outerplanar graphs are also known as triangulations of polygons. The spine of a maximal outerplanar graph G is the dual graph of G without the vertex that corresponds to the exterior region. In this thesis we study metric properties involving geodesic intervals, geodetic sets, Steiner sets, different concepts of boundary, and also relationships between the independence numbers and domination numbers of maximal outerplanar graphs and their spines. In Chapter 2 we find an extension of a result by Beyer, et al. [3] that deals with Hamiltonian degree sequences in maximal outerplanar graphs. In Chapters 3 and 4 we give sharp bounds relating the independence number and domination number, respectively, of a maximal outerplanar graph to those of its spine. In Chapter 5 we discuss the boundary, contour, eccentricity, periphery, and extreme set of a graph. We give a characterization of the boundary of maximal outerplanar graphs that involves the degrees of vertices. We find properties that characterize the contour of a maximal outerplanar graph. The other main result of this chapter gives characterizations of graphs induced by the contour and by the periphery of a maximal outerplanar graph. In Chapter 6 we show that the generalized intervals in a maximal outerplanar graph are convex. We use this result to characterize geodetic sets in maximal outerplanar graphs. We show that every Steiner set in a maximal outerplanar graph is a geodetic set and also show some differences between these types of sets. We present sharp bounds for geodetic numbers and Steiner numbers of maximal outerplanar graphs

Co-registration of three-dimensional building models with image\ud features from infrared video sequences

In the European Union (EU) countries buildings consume 40% of the energy and cause 36% of CO2 emissions.\ud The thermal information of facades and roofs are important for building inspection and energy saving. Texturing\ud the existing three-dimensional (3D) building models with infrared (IR) images enriches the model database and\ud enables analysis of energy loss of buildings.\ud The main purpose of the presented thesis is to investigate methods for automatic extraction of the IR textures for\ud roofs and facades of the existing building model. The correction of the exterior orientation parameters of the IR\ud camera mounted on mobile platform is studied. The developed method bases on a point-to-point matching of the\ud features extracted from IR images with a wire frame building model.\ud Firstly, extraction of different feature types is studied on a sample IR image; Förstner and intersection points are\ud chosen for representation of the image features. Secondly, the 3D building model is projected into each frame of\ud the IR video sequence using orientation parameters; only coarse exterior orientation parameters are known. Then\ud the automatic co-registration of a 3D building model projection into the image sequence with image features is\ud carried out. The matching of a model and extracted features is applied iteratively and exterior orientation\ud parameters are adjusted with least square adjustment. The method is tested on a dataset of dense urban area.\ud Finally, an evaluation of developed method is presented with fiv

Ground Profile Recovery from Aerial 3D LiDAR-based Maps

The paper presents the study and implementation of the ground detection methodology with filtration and removal of forest points from LiDAR-based 3D point cloud using the Cloth Simulation Filtering (CSF) algorithm. The methodology allows to recover a terrestrial relief and create a landscape map of a forestry region. As the proof-of-concept, we provided the outdoor flight experiment, launching a hexacopter under a mixed forestry region with sharp ground changes nearby Innopolis city (Russia), which demonstrated the encouraging results for both ground detection and methodology robustness.Comment: 8 pages, FRUCT-2019 conferenc

Semi-supervised Learning with the EM Algorithm: A Comparative Study between Unstructured and Structured Prediction

Semi-supervised learning aims to learn prediction models from both labeled and unlabeled samples. There has been extensive research in this area. Among existing work, generative mixture models with Expectation-Maximization (EM) is a popular method due to clear statistical properties. However, existing literature on EM-based semi-supervised learning largely focuses on unstructured prediction, assuming that samples are independent and identically distributed. Studies on EM-based semi-supervised approach in structured prediction is limited. This paper aims to fill the gap through a comparative study between unstructured and structured methods in EM-based semi-supervised learning. Specifically, we compare their theoretical properties and find that both methods can be considered as a generalization of self-training with soft class assignment of unlabeled samples, but the structured method additionally considers structural constraint in soft class assignment. We conducted a case study on real-world flood mapping datasets to compare the two methods. Results show that structured EM is more robust to class confusion caused by noise and obstacles in features in the context of the flood mapping application

Backscatter Gain and Array Modeling for a Large-Aperture High-Power Radar

A robust software package was developed for modeling the far field radiation pattern of phased array radars. The application of this package will assist SRI International’s Geospace Division model the radiation pattern of their AMISR arrays. With this package, SRI will be able to calibrate their measurements of phenomena occurring in the upper atmosphere. Additionally, tools have been developed for beam analysis and radiation pattern characterization. Methods of validation for the computed radiation pattern’s accuracy are included in the package

Maakoore vertikaalliikumised Eestis täppisnivelleerimiste andmetel

The aim of this study was to detect vertical crustal movements in Estonia and find out possible changes of vertical crustal movements in time. Vertical velocities of the benchmarks were calculated from the precise levellings between 1933 and 2011 of the Estonian levelling network using the joint weighted kinematic least squares adjustment of the levelling campaigns. Two different mathematical models, the “heights included” and the “heights eliminated” model, were used in the adjustment. Different options of the computer software Surfer were used for modelling of the vertical crustal movements. Accuracy of the models was estimated by finding differences between the velocities interpolated from the models and adjusted vertical velocities of the benchmarks, using the cross validation technique, and by comparing models with the results from other geodetic measurements (continuously operating GNSS stations, tide gauges, other land uplift models). From the variance component estimation, it appeared that levelling errors of the First levelling campaign were ~3 times larger than estimated a priori. Final adjustment was performed with the re-scaled weights according to the results of the variance component estimation. Models of the vertical crustal movements EST2013LU and EST2015LU were created based on the vertical velocities of the benchmarks. According to the models, rates of the land uplift in Estonia range from −0.7 mm/yr in SE Estonia to +2.8 mm/yr in the island of Hiiumaa in NW Estonia. Accuracy of the models was estimated to be ±0.4 mm/yr on average. The comparison of the models with the velocities from the independent measurement methods revealed best fit with the velocities of the GNSS permanent stations where residual differences remained within ±0.3 mm/yr on average. The discrepancies between the velocities of the coastal tide gauges and the velocities from the models were ±0.7…±1.0 mm/yr on average. Obtained differences implied to the systematic biases in tide gauge velocities. Comparison with the historical vertical crustal movement maps of Estonia showed that differences remained within ±0.7 mm/yr on average. The fit between the most recent Fennoscandian LU map NKG2005LU and the models obtained in the present study was very good. Differences remained within ±0.3 mm/yr on average. It appeared also that vertical velocity of the benchmarks has been significantly changed between the levelling periods. Results of the study can be used to estimate the risks to the coastal areas coming from the global warming related rise of the sea level.Doktoritöö eesmärk oli leida maakoore vertikaalliikumiste kiirused Eestis nelja kordusnivelleerimise (1933-2011) andmete põhjal ja välja selgitada reeperite kiiruste muutumine ajas. Reeperite vertikaalliikumise kiirused leiti nivelleerimiste ühisest kaalutud kinemaatilisest tasandusest vähimruutude meetodil. Tasandusel kasutati kahte matemaatilist mudelit: nn „kõrgustega“ ja „kõrgusteta“ mudelit. Maakoore vertikaalliikumiste modelleerimiseks kasutati tarkvara Surfer erinevaid võimalusi. Mudelite täpsust hinnati mudelist interpoleeritud ja reeperite tasandatud kiiruste vaheliste erinevuste leidmise, ristvalideerimise ja sõltumatute mõõtmistulemustega (GNSS-püsijaamad, veemõõdujaamad, teised mudelid) võrdlemise teel. Dispersioonikomponentide hindamisest selgus, et esimese nivelleerimiskampaania vead on ~3 korda suuremad kui a priori eeldati. Lõplik tasandus teostati dispersioonikomponentide hindamise tulemuste põhjal ümberskaleeritud kaaludega. Reeperite kiiruste põhjal loodi Eesti maakoore vertikaalliikumiste mudelid EST2013LU ja EST2015LU. Mudelite põhjal ulatuvad maatõusu kiirused Eestis alates −0.7 mm/a Kagu-Eestis kuni +2.8 mm/a Hiiumaal. Mudelite täpsuseks hinnati keskmiselt ±0.4 mm/a. Võrdluses sõltumatutest meetoditest määratud maatõusu kiirustega selgus, et parim oli sobivus GNSS-püsijaamade kiirustega, keskmiselt ±0.3 mm/a. Halvim oli sobivus ranniku veemõõdujaamade kiirustega: ±0.7….±1.0 mm/a. Saadud erinevused viitasid süstemaatilistele nihetele veemõõdujaamade kiirustes. Võrdlus Eesti varasemate maakoore vertikaalliikumiste kaartidega näitas, et erinevused jäid keskmiselt ±0.7 mm/a piiridesse. Mudelite sobivus viimase Fennoskandia maatõusu mudeliga NKG2005LU oli aga väga hea, erinevused jäid keskmiselt ±0.3 mm/a piiridesse. Samuti selgus, et nivelleerimisperioodide vahel on reeperite kiirus statistiliselt oluliselt muutunud. Uurimistöö tulemusi saab kasutada kliimasoojenemisest tulenevate meretõusu riskide hindamiseks rannikualadel