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1

Implementation and evaluation of medical imaging techniques based on conformal geometric algebra

Franchini Silvia, Gentile Antonio, Vassallo Giorgio, Vitabile Salvatore

International Journal of Applied Mathematics and Computer Science

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2020

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Vol. 30, no. 3

415--433

EN

Medical imaging tasks, such as segmentation, 3D modeling, and registration of medical images, involve complex geometric problems, usually solved by standard linear algebra and matrix calculations. In the last few decades, conformal geometric algebra (CGA) has emerged as a new approach to geometric computing that offers a simple and efficient representation of geometric objects and transformations. However, the practical use of CGA-based methods for big data image processing in medical imaging requires fast and efficient implementations of CGA operations to meet both real-time processing constraints and accuracy requirements. The purpose of this study is to present a novel implementation of CGA-based medical imaging techniques that makes them effective and practically usable. The paper exploits a new simplified formulation of CGA operators that allows significantly reduced execution times while maintaining the needed result precision. We have exploited this novel CGA formulation to re-design a suite of medical imaging automatic methods, including image segmentation, 3D reconstruction and registration. Experimental tests show that the re-formulated CGA-based methods lead to both higher precision results and reduced computation times, which makes them suitable for big data image processing applications. The segmentation algorithm provides the Dice index, sensitivity and specificity values of 98.14%, 98.05% and 97.73%, respectively, while the order of magnitude of the errors measured for the registration methods is 10-5.

2

MD-jeep: a New Release for Discretizable Distance Geometry Problems with Interval Data

Mucherino Antonio, Gonçalves Douglas S., Liberti Leo, Lin Jung-Hsin, Lavor Carlile, Maculan Nelson

Annals of Computer Science and Information Systems

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2020

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Vol. 21

289--294

EN

With the most recent releases of MD-JEEP, new relevant features have been included to our software tool. MD-JEEP solves instances of the class of Discretizable Distance Geometry Problems (DDGPs), which ask to find possible realizations, in a Euclidean space, of a simple weighted undirected graph for which distance constraints between vertices are given, and for which a discretization of the search space can be supplied. Since its version 0.3.0, MD-JEEP is able to deal with instances containing interval data. We focus in this short paper on the most recent release MD-JEEP 0.3.2: among the new implemented features, we will focus our attention on three features: (i) an improved procedure for the generation and update of the boxes used in the coarse-grained representation (necessary to deal with instances containing interval data); (ii) a new procedure for the selection of the so-called discretization vertices (necessary to perform the discretization of the search space); (iii) the implementation of a general parser which allows the user to easily load DDGP instances in a given specified format. The source code of MD-JEEP 0.3.2 is available on GitHub, where the reader can find all additional details about the implementation of such new features, as well as verify the effectiveness of such features by comparing MD- JEEP 0.3.2 with its previous releases.

3

An Exact Two-Phase Method For Optimal Camera Placement In Art Gallery Problem

Alihodzic Adis, Delalic Sead, Hasic Damir

Annals of Computer Science and Information Systems

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2020

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Vol. 21

215--222

EN

It is well-known that determining the optimal number of guards which can cover the interior of a simple nonconvex polygon presents an NP-hard problem. The optimal guard placement can be described as a problem which seeks for the smallest number of guards required to cover every point in a complex environment. In this paper, we propose an exact twophase method as well as an approximate method for tackling the mentioned issue. The proposed exact approach in the first phase maps camera placement problem to the set covering problem, while in the second phase it uses famous state-of-the-art CPLEX solver to address set covering problem. The performance of our combined exact algorithm was compared to the performance of the approximate one. According to the results presented in the experimental analysis, it can be seen that the exact approach outperforms the approximate method for all instances.

4

Estimation of the localisation and geometric parameters of the semi-solid zone of steel samples

Dębiński T.

Technical Transactions

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2018

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Vol. 115, iss. 6

145--154

EN

This paper presents the use of computer graphics methods for the initial estimation of the shape, position and volume of the semi-solid zone in samples from the Gleeble 3800 physical simulator. Simulations were performed for the verification of the heating and deformation process of steel with a semi-solid zone. The numerical model consists of three separate subsystems for describing the deformation of the solid and semi-solid zones: mechanical, thermal and predictive densities. Taking into consideration the specific localisation of these zones, the initial estimation of the location of the melting zone is very helpful in understanding the process and may be the starting point for further research. This article describes the technique of selecting areas in samples that meet the thermal criteria. This allows us to approximate the location and shape of the semi-solid zone and this information can be used at a later stage to further refine its parameters.

PL

W artykule przedstawiono wykorzystanie metod grafiki komputerowej do wstępnego oszacowania kształtu, położenia i objętości strefy półciekłej w próbkach z symulatora fizycznego Gleeble 3800. W celu weryfikacji procesu nagrzewania i odkształcania stali w strefie półciekłej przeprowadzono wiele symulacji. Model numeryczny składa się z trzech odrębnych części: mechanicznej, termicznej i przewidującej zmiany gęstości opisujących odkształcenie dla strefy stałej i półciekłej. Biorąc pod uwagę specyficzną lokalizację tych stref, wstępna ocena położenia strefy przetopienia jest bardzo pomocna w zrozumieniu procesu i może być punktem wyjścia do dalszych badań. W artykule opisano technikę wybierania obszarów w próbkach, które spełniają wyznaczone kryteria, co pozwala na przybliżenie lokalizacji, kształtu i parametrów geometrycznych strefy półciekłej, co można wykorzystać w celu dalszego poprawiania jej parametrów oraz dokładności samego modelu.

5

Generating placated random shapes for an area estimation study

Almowanes A., Kakiashvili T., Koczkodaj W. W.

Journal of Applied Mathematics and Computational Mechanics

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2013

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Vol. 12, nr 2

5--13

EN

Random but visually nice shapes are often needed for cognitive experiments and processes. This study describes a heuristic for generating random but nice shapes. We call them placated shapes. These shapes are produced by applying the Gaussian blur to randomly generated polygons. Subsequently, the threshold is set to transform pixels to black and white from different shades of gray. This transformation produces placated shapes for easier estimation of areas. Randomly generated placated shapes are used for testing the accuracy of cognitive processes by pairwise comparisons. They can also be used in many other areas such as computer games or software testing. Such shapes could also be used for camouflaging heavy army equipment.

6

Estymacja objętości obiektów o złożonej geometrii na podstawie pomiarów naziemnym skaningiem laserowym

Tymków P.

Archiwum Fotogrametrii, Kartografii i Teledetekcji

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2012

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Vol. 24

383--391

PL

W pracy przedstawiono propozycję automatycznej metody zgrubnego modelowania 3D obiektów o skomplikowanej geometrii na potrzeby szybkiej estymacji parametrów geometrycznych tych obiektów, a zwłaszcza objętości. Badania w terenie obejmowały wykonanie pomiarów skanerem laserowym zabytkowej kutej kraty stanowiącej osłonę studni w Nysie (woj. opolskie). Przedstawiona metodyka modelowania opiera się o warstwową metodę convex-hull, która zakłada podział chmury punktów pomiarowych na segmenty. W obrębie każdego segmentu dokonywana jest segmentacja w oparciu o minimalne odległości między punktami. Otrzymane zbiory punktów modelowane są następnie jako bryły wypukłe. Dzięki zastosowaniu segmentacji chmury punktów w każdym segmencie oraz integracji uzyskanych otoczek wypukłych uzyskano model obiektu, który umożliwia oszacowanie takich parametrów geometrycznych jak objętość i pole powierzchni obiektu. Zaletą proponowanej metody jest ograniczenie liczby parametrów do dwóch: grubości segmentu oraz parametru maksymalnej odległości między punktami w procesie segmentacji chmury w obrębie segmentu. Dzięki zastosowaniu metody convex-hull dokonywana jest selektywna filtracja punktów dzięki czemu model 3D oparty jest na znacznie mniejszej liczbie werteksów i trójkątów niż początkowa liczba punktów w chmurze. Wadą proponowanego algorytmu jest natomiast nieregularność siatki trójkątów wpływająca na gładkość powierzchni oraz wrażliwość na błędy pomiarowe.

EN

The paper presents an automatic, coarse method for 3D modelling of metal objects with complex geometry for a need of volume estimation. The field research were conducted on a historic wrought iron bar that covers the historic well in Nysa (city In southern Poland). The presented modelling methodology is based on a layered convex-hull method, which involves dividing of a point cloud on the segments. Within each segment, segmentation is performed based on the minimum distance between points. The resulting sets of points are then modelled as a convex solids. Thanks to the segmentation of point clouds in each segment and the integration of convex shells a detailed object model can be obtained. That allows to estimate the geometric parameters such as volume and surface area of the object. The advantage of the proposed method is that it has a small number of parameters: a thickness of segment and the parameter of maximum distance between points in the process of segmentation of clouds within the segment. Applying the convex hull algorithm causes a selective filtering point clouds, thus resulting 3D model is based on a much smaller number of vertexes than the initial number of points in the cloud. The disadvantage of the proposed algorithm is an irregular triangle mesh models, resulting in low surface regularity and larger items, and sensitivity to measurement errors (noise, ghost points).