Unknown Radial Distortion Centers in Multiple View Geometry Problems

The radial undistortion model proposed by Fitzgibbon and the radial fundamental matrix were early steps to extend classical epipolar geometry to distorted cameras. Later minimal solvers have been proposed to find relative pose and radial distortion, given point correspondences between images. However, a big drawback of all these approaches is that they require the distortion center to be exactly known. In this paper we show how the distortion center can be absorbed into a new radial fundamental matrix. This new formulation is much more practical in reality as it allows also digital zoom, cropped images and camera-lens systems where the distortion center does not exactly coincide with the image center. In particular we start from the setting where only one of the two images contains radial distortion, analyze the structure of the particular radial fundamental matrix and show that the technique also generalizes to other linear multi-view relationships like trifocal tensor and homography. For the new radial fundamental matrix we propose different estimation algorithms from 9,10 and 11 points. We show how to extract the epipoles and prove the practical applicability on several epipolar geometry image pairs with strong distortion that - to the best of our knowledge - no other existing algorithm can handle properly.

Preservice teachers' knowledge on elementary geometry concepts

This text is based on a research, which is still in progress, whose main objective is to identify and understand what are the main difficulties of future mathematics teachers of basic education are, regarding their content knowledge in geometry in the context of the curricular unit of Geometry during their undergraduate degree. We chose a qualitative approach in the form of case study, in which data collection was done through observation, interviews, a diverse set of tasks, a diagnostic test and other documents. This paper focuses on the test given to prospective teachers at the beginning of the course. The preliminary analysis of the data points to a weak performance of preservice teachers in the test issues addressing elementary knowledge of Geometry

Drilling tool geometry evaluation for reinforced composite laminates

In this work, a comparative study on different drill point geometries and feed rate for composite laminates drilling is presented. For this goal, thrust force monitoring during drilling, hole wall roughness measurement and delamination extension assessment after drilling is accomplished. Delamination is evaluated using enhanced radiography combined with a dedicated computational platform that integrates algorithms of image processing and analysis. An experimental procedure was planned and consequences were evaluated. Results show that a cautious combination of the factors involved, like drill tip geometry or feed rate, can promote the reduction of delamination damage.

Strength improvement of adhesively-bonded joints using a reverse-bent geometry

Adhesive bonding of components has become more efficient in recent years due to the developments in adhesive technology, which has resulted in higher peel and shear strengths, and also in allowable ductility up to failure. As a result, fastening and riveting methods are being progressively replaced by adhesive bonding, allowing a big step towards stronger and lighter unions. However, single-lap bonded joints still generate substantial peel and shear stress concentrations at the overlap edges that can be harmful to the structure, especially when using brittle adhesives that do not allow plasticization in these regions. In this work, a numerical and experimental study is performed to evaluate the feasibility of bending the adherends at the ends of the overlap for the strength improvement of single-lap aluminium joints bonded with a brittle and a ductile adhesive. Different combinations of joint eccentricity were tested, including absence of eccentricity, allowing the optimization of the joint. A Finite Element stress and failure analysis in ABAQUS® was also carried out to provide a better understanding of the bent configuration. Results showed a major advantage of using the proposed modification for the brittle adhesive, but the joints with the ductile adhesive were not much affected by the bending technique.

Preservice teachers' knowledge on elementary geometry concepts

This text is based on a research, which is still in progress, whose main objective is to identify and understand what are the main difficulties of future mathematics teachers of basic education are, regarding their content knowledge in geometry in the context of the curricular unit of Geometry during their undergraduate degree. We chose a qualitative approach in the form of case study, in which data collection was done through observation, interviews, a diverse set of tasks, a diagnostic test and other documents. This paper focuses on the test given to prospective teachers at the beginning of the course. The preliminary analysis of the data points to a weak performance of preservice teachers in the test issues addressing elementary knowledge of Geometry.

A theoretical study on modelling the respiratory tract with ladder networks by means of intrinsic fractal geometry

Fractional order modeling of biological systems has received significant interest in the research community. Since the fractal geometry is characterized by a recurrent structure, the self-similar branching arrangement of the airways makes the respiratory system an ideal candidate for the application of fractional calculus theory. To demonstrate the link between the recurrence of the respiratory tree and the appearance of a fractional-order model, we develop an anatomically consistent representation of the respiratory system. This model is capable of simulating the mechanical properties of the lungs and we compare the model output with in vivo measurements of the respiratory input impedance collected in 20 healthy subjects. This paper provides further proof of the underlying fractal geometry of the human lungs, and the consequent appearance of constant-phase behavior in the total respiratory impedance.

Full analysis of suspension geometry and chassis performance of Formula Student racing car

Formula Student events gather engineering students, who compete, designing, building and racing single-seater cars. The team of ISEP is working on its first car that soon will take part in this competition. This work aims to analyze the current design’s chassis, focusing on suspension geometry and frame’s performance. After analyzing results of the tests planned suggestions, that can be taken into consideration during design process of next cars will be presented. As the car has not been tested yet this work can also be helpful to explain its performance on the track later.

Geometry based visualization with OpenCL

Dissertação para obtenção do Grau de Mestre em Engenharia Informática

In situ measured cross section geometry of old timber structures and its influence on structural safety

Old timber structures may show significant variation in the cross section geometry along the same element, as a result of both construction methods and deterioration. As consequence, the definition of the geometric parameters in situ may be both time consuming and costly. This work presents the results of inspections carried out in different timber structures. Based on the obtained results, different simplified geometric models are proposed in order to efficiently model the geometry variations found. Probabilistic modelling techniques are also used to define safety parameters of existing timber structures, when subjected to dead and live loads, namely self-weight and wind actions. The parameters of the models have been defined as probabilistic variables, and safety of a selected case study was assessed using the Monte Carlo simulation technique. Assuming a target reliability index, a model was defined for both the residual cross section and the time dependent deterioration evolution. As a consequence, it was possible to compute probabilities of failure and reliability indices, as well as, time evolution deterioration curves for this structure. The results obtained provide a proposal for definition of the cross section geometric parameters of existing timber structures with different levels of decay, using a simplified probabilistic geometry model and considering a remaining capacity factor for the decayed areas. This model can be used for assessing the safety of the structure at present and for predicting future performance.

Development of a satellite based PM10 concentration product for urban areas

Dissertação para obtenção do Grau de Doutor em Engenharia do Ambiente

Mobile image processing to support educational geometry games

The mobile IT era is here, it is still growing and expanding at a steady rate and, most of all, it is entertaining. Mobile devices are used for entertainment, whether social through the so-called social networks, or private through web browsing, video watching or gaming. Youngsters make heavy use of these devices, and even small children show impressive adaptability and skill. However not much attention is directed towards education, especially in the case of young children. Too much time is usually spent in games which only purpose is to keep children entertained, time that could be put to better use such as developing elementary geometric notions. Taking advantage of this pocket computer scenario, it is proposed an application geared towards small children in the 6 – 9 age group that allows them to consolidate knowledge regarding geometric shapes, forming a stepping stone that leads to some fundamental mathematical knowledge to be exercised later on. To achieve this goal, the application will detect simple geometric shapes like squares, circles and triangles using the device’s camera. The novelty of this application will be a core real-time detection system designed and developed from the ground up for mobile devices, taking into account their characteristic limitations such as reduced processing power, memory and battery. User feedback was be gathered, aggregated and studied to assess the educational factor of the application.

A GIS extension model to calculate urban heat island intensity based on urban geometry

This paper presents a simulation model, which was incorporated into a Geographic Information System (GIS), in order to calculate the maximum intensity of urban heat islands based on urban geometry data. The method-ology of this study stands on a theoretical-numerical basis (Okeâ s model), followed by the study and selection of existing GIS tools, the design of the calculation model, the incorporation of the resulting algorithm into the GIS platform and the application of the tool, developed as exemplification. The developed tool will help researchers to simulate UHI in different urban scenarios.

Aortic stenosis. Gender influence on left ventricular geometry and function in patients under 70 years of age

OBJECTIVE: To verify if adaptive left ventricle (LV) characteristics are also present in individuals under 70 years of age with severe aortic stenosis (AS). METHODS: The study comprised 40 consecutive patients under 70 years of age with AS and no associated coronary artery disease, referred for valve surgery. Out of the 40 patients, 22 were men and 18 women, and the mean age was 49.8±14.3 years. Cardiac symptoms, presence of systemic hypertension (SH), functional class according to the New York Heart Association (NYHA), and valve lesion etiology were considered. LV cavity dimensions, ejection fraction (EF), fractional shortening (FS), mass (MS), and relative diastolic thickness (RDT) were examined by Doppler echocardiography. RESULTS: Fourteen (63.6%) men and 11 (61.6%) women were classified as NYHA class III/IV (p=0.70). There was no difference in the frequency of angina, syncope or dyspnea between genders. The incidence of SH was greater in women than in men (10 versus 2, p=0.0044). Women had a smaller LV end-diastolic diameter index (32.1±6.5 x 36.5±5.3mm/m², p=0.027), LV end-systolic diameter index (19.9±5.9 x 26.5±6.4mm/m², p=0.0022) and LV mass index (MS) (211.4±71.1 x 270.9±74.9g/m², p=0.017) when compared with men. EF (66.2±13.4 x 52.0±14.6%, p=0.0032), FS (37.6±10.7 x 27.9±9.6%, p=0.0046) and RDT (0.58±0.22 x 0.44±0.09, p=0.0095) were significantly greater in women than in men. CONCLUSION: It is the patient gender rather than age that influences left ventricular adaptive response to AS.

Left Ventricular Diastolic Function in Essential Hypertensive Patients: Influence of Age and Left Ventricular Geometry

PURPOSE - To evaluate diastolic dysfunction (DD) in essential hypertension and the influence of age and cardiac geometry on this parameter. METHODS - Four hundred sixty essential hypertensive patients (HT) underwent Doppler echocardiography to obtain E/A wave ratio (E/A), atrial deceleration time (ADT), and isovolumetric relaxation time (IRT). All patients were grouped according to cardiac geometric patterns (NG - normal geometry; CR - concentric remodeling; CH- concentric hypertrophy; EH - eccentric hypertrophy) and to age (<40; 40 - 60; >60 years). One hundred six normotensives (NT) persons were also evaluated. RESULTS - A worsening of diastolic function in the HT compared with the NT, including HT with NG (E/A: NT - 1.38±0.03 vs HT - 1.27±0.02, p<0.01), was observed. A higher prevalence of DD occurred parallel to age and cardiac geometry also in the prehypertrophic groups (CR). Multiple regression analysis identified age as the most important predictor of DD (r²=0.30, p<0.01). CONCLUSION - DD was prevalent in this hypertensive population, being highly affected by age and less by heart structural parameters. DD is observed in incipient stages of hypertensive heart disease, and thus its early detection may help in the risk stratification of hypertensive patients.