A New Estimator of Intrinsic Dimension Based on the Multipoint Morisita Index

The size of datasets has been increasing rapidly both in terms of number of variables and number of events. As a result, the empty space phenomenon and the curse of dimensionality complicate the extraction of useful information. But, in general, data lie on non-linear manifolds of much lower dimension than that of the spaces in which they are embedded. In many pattern recognition tasks, learning these manifolds is a key issue and it requires the knowledge of their true intrinsic dimension. This paper introduces a new estimator of intrinsic dimension based on the multipoint Morisita index. It is applied to both synthetic and real datasets of varying complexities and comparisons with other existing estimators are carried out. The proposed estimator turns out to be fairly robust to sample size and noise, unaffected by edge effects, able to handle large datasets and computationally efficient

Fractal and morphological processing for phase contrast MRI image of the aortic lumen

Магнітно-резонансна томографія (МРТ) – це метод відображення внутрішньої структури матеріальних об'єктів, заснований на явищі ядерного магнітного резонансу і широко застосовуваний у задачах медичної діагностики. Переваги МРТ перед рентгенівською комп'ютерною томографією складаються з можливості отримання необов'язково паралельних перерізів, з більш високою роздільною здатністю, та у відсутності шкідливого жорсткого променевого впливу на пацієнтів і обслуговуючий персонал. У цій роботі ми представляємо технології сегментацiï та шумоподавлення, розроблені для 3D MRТ-зображень, що базуються на методах фрактальної фільтрації та математичної морфології.Magnetic resonance imaging (MRI) is a method of displaying the internal structure of material objects, based on the phenomenon of nuclear magnetic resonance and widely used in the tasks of medical diagnostics. Advantages of MRI before X-ray computed tomography include the possibility of obtaining optionally parallel cross sections, with higher resolution, and in the absence of harmful rigid radiation effects on patients and attendants. In this work, we present segmentation and noise reduction technologies developed for 3D MRT images based on fractal filtration and mathematical morphology

Texture analysis of aggressive and nonaggressive lung tumor CE CT images

This paper presents the potential for fractal analysis of time sequence contrast-enhanced (CE) computed tomography (CT) images to differentiate between aggressive and nonaggressive malignant lung tumors (i.e., high and low metabolic tumors). The aim is to enhance CT tumor staging prediction accuracy through identifying malignant aggressiveness of lung tumors. As branching of blood vessels can be considered a fractal process, the research examines vascularized tumor regions that exhibit strong fractal characteristics. The analysis is performed after injecting 15 patients with a contrast agent and transforming at least 11 time sequence CE CT images from each patient to the fractal dimension and determining corresponding lacunarity. The fractal texture features were averaged over the tumor region and quantitative classification showed up to 83.3% accuracy in distinction between advanced (aggressive) and early-stage (nonaggressive) malignant tumors. Also, it showed strong correlation with corresponding lung tumor stage and standardized tumor uptake value of fluoro deoxyglucose as determined by positron emission tomography. These results indicate that fractal analysis of time sequence CE CT images of malignant lung tumors could provide additional information about likely tumor aggression that could potentially impact on clinical management decisions in choosing the appropriate treatment procedure

Modeling of process of wastewater treatment by electrocoagulation in non-isothermal conditions

Проаналізовано проблеми моделювання процесу очищення води в електрокоагуляційній камері в неізотермічних умовах. Визначено основні параметри для розрахунку тепло- та масопереносу в електрокоагуляторі. Побудовано математичну модель, що описує закономірності протікання процесів в електрокоагуляційній установці із уточненням оптимальних параметрів. Знайдено розв'язки відповідної модельної задачі з використанням асимптотичного наближення розв'язку відповідної крайової задачі та наведені результати комп'ютерного експерименту.The problems of modeling the process of water treatment in an electrocoagulation chamber in nonisothermal conditions are analyzed. The basic parameters for calculating the mass and heat transferin the electrocoagulator are determined. The mathematical model describing the patterns of process flow in the electrocoagulation installation with the specification of the optimal parameters of the process is constructed. The solutions of the corresponding model problem are found using the asymptotic approximation of the solution of the corresponding boundary value problem and the results of the computer experiment are given