Mathematical models of generalized diffusion

We discuss in this paper equations describing processes involving non-linear and higher-order diffusion. We focus on a particular case (u(t) = 2 lambda (2)(uu(x))(x) + lambda (2)u(xxxx)), which is put into analogy with the KdV equation. A balance of nonlinearity and higher-order diffusion enables the existence of self-similar solutions, describing diffusive shocks. These shocks are continuous solutions with a discontinuous higher-order derivative at the shock front. We argue that they play a role analogous to the soliton solutions in the dispersive case. We also discuss several physical instances where such equations are relevant.

Mathematical models for Isoptera (Insecta) mound growth

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Test systems and mathematical models for transmission network expansion planning

The data of four networks that can be used in carrying out comparative studies with methods for transmission network expansion planning are given. These networks are of various types and different levels of complexity. The main mathematical formulations used in transmission expansion studies-transportation models, hybrid models, DC power flow models, and disjunctive models are also summarised and compared. The main algorithm families are reviewed-both analytical, combinatorial and heuristic approaches. Optimal solutions are not yet known for some of the four networks when more accurate models (e.g. The DC model) are used to represent the power flow equations-the state of the art with regard to this is also summarised. This should serve as a challenge to authors searching for new, more efficient methods.

Surface reconstruction using multiple light sources and perspective projection

This paper presents a method to recover 3D geometry of Lambertian surfaces by using multiple images taken from the same view point and with the scene illuminated from different positions. This approach differs from Stereo Photometry in that it considers the light source at a finite distance from the object and the perspective projection in image formation. The proposed model allows local solution and recovery of 3D coordinates, in addition to surface orientation. A procedure to calibrate the light sources is also presented. Results of the application of the algorithm to synthetic images are shown.

Estimation of crowd density using image processing

Human beings perceive images through their properties, like colour, shape, size, and texture. Texture is a fertile source of information about the physical environment. Images of low density crowds tend to present coarse textures, while images of dense crowds tend to present fine textures. This paper describes a new technique for automatic estimation of crowd density, which is a part of the problem of automatic crowd monitoring, using texture information based on grey-level transition probabilities on digitised images. Crowd density feature vectors are extracted from such images and used by a self organising neural network which is responsible for the crowd density estimation. Results obtained respectively to the estimation of the number of people in a specific area of Liverpool Street Railway Station in London (UK) are presented.

Demodulação de sinais interferométricos de saída de sensor eletro-óptico de tensões elevadas utilizando processador digital de sinais

Pós-graduação em Engenharia Elétrica - FEIS

Assessment of the mechanics of a tissue-engineered rat trachea in an image-processing environment

OBJECTIVES: Despite the recent success regarding the transplantation of tissue-engineered airways, the mechanical properties of these grafts are not well understood. Mechanical assessment of a tissue-engineered airway graft before implantation may be used in the future as a predictor of function. The aim of this preliminary work was to develop a noninvasive image-processing environment for the assessment of airway mechanics.METHOD: Decellularized, recellularized and normal tracheas (groups DECEL, RECEL, and CONTROL, respectively) immersed in Krebs-Henseleit solution were ventilated by a small-animal ventilator connected to a Fleisch pneumotachograph and two pressure transducers (differential and gauge). A camera connected to a stereomicroscope captured images of the pulsation of the trachea before instillation of saline solution and after instillation of Krebs-Henseleit solution, followed by instillation with Krebs-Henseleit with methacholine 0.1 M (protocols A, K and KMCh, respectively). The data were post-processed with computer software and statistical comparisons between groups and protocols were performed.RESULTS: There were statistically significant variations in the image measurements of the medial region of the trachea between the groups (two-way analysis of variance [ANOVA], p<0.01) and of the proximal region between the groups and protocols (two-way ANOVA, p<0.01).CONCLUSIONS: The technique developed in this study is an innovative method for performing a mechanical assessment of engineered tracheal grafts that will enable evaluation of the viscoelastic properties of neo-tracheas prior to transplantation.

Use of mathematical models in the study of bodily growth in GIFT strain Nile tilapia

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Cephalometric evaluation of surgical mandibular advancement

The treatment of Class II adult individuals with mandibular deficiency has been the combination of orthodontic treatment and orthognathic surgery. Therefore, a study was conducted in which cephalometric analysis was used to evaluate the influence of dentoalveolar decompensation in Class II patients submitted to orthodontic and surgical treatment for mandibular advancement, by bilateral osteotomy of the mandibular ramus. A sample of 15 leukoderma adult female patients were selected and three cephalometric radiographs of each patient, taken before the orthodontic treatment, before surgery and after at least 6 months postoperatively, were analyzed in a total of 45 roentgenograms. The tracings were made by the manual method and the points were digitalized using software. The results showed that values of SNB increased from 75.6 to 78.6°. The measures BNP and PGNP were reduced from -12.7 to -7.7 mm and -12.7 to -6.6 mm, respectively. For ANB there was a reduction of 3.23° (from 8.1° to 4.9°). Likewise, the values of AOBO were diminished by 6.3 mm (from 7.6 to 1.3 mm), and in the values of OJ there was a reduction of 5.7 mm (from 9 to 3.3 mm). It was concluded that the pre-surgical orthodontic treatment promoted minimal and variable dental and skeletal changes in the final result. The surgical treatment caused significant skeletal changes, especially in the measurements related to the mandible (SNB, BNP, PGNP and SNPM) or indirectly to it (ANB, AOBO and OJ).

Modelos matemáticos para o retoque digital de imagens

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Image registration and image interpolation in volume rendering of cross sections

We outline a method for registration of images of cross sections using the concepts of The Generalized Hough Transform (GHT). The approach may be useful in situations where automation should be a concern. To overcome known problems of noise of traditional GHT we have implemented a slight modified version of the basic algorithm. The modification consists of eliminating points of no interest in the process before the application of the accumulation step of the algorithm. This procedure minimizes the amount of accumulation points while reducing the probability of appearing of spurious peaks. Also, we apply image warping techniques to interpolate images among cross sections. This is needed where the distance of samples between sections is too large. Then it is suggested that the step of registration with GHT can help the interpolation automation by simplifying the correspondence between points of images. Some results are shown.

Morphological routine proposal to extraction of highways in digital images of high resolution

This research proposes to apply techniques of Mathematics Morphology to extract highways in digital images of high resolution, targeting the upgrade of cartographic products. Remote Sensing data and Mathematical Morphological techniques were integrated in the process of extraction. Mathematical Morphology's objective is to improve and extract the relevant information of the visual image. In order to test the proposed approach some morphological operators related to preprocess, were applied to the original images. Routines were implemented in the MATLAB environment. Results indicated good performances by the implemented operators. The integration of the technologies aimed to implement the semiautomatic extraction of highways with the purpose to use them in processes of cartographic updating.

Geometric modeling from the medical images in the CAD system to support prosthesis design

This paper presents an individual designing prosthesis for surgical use and proposes a methodology for such design through mathematical extrapolation of data from digital images obtained via tomography of individual patient's bones. Individually tailored prosthesis designed to fit particular patient requirements as accurately as possible should result in more successful reconstruction, enable better planning before surgery and consequently fewer complications during surgery. Fast and accurate design and manufacture of personalized prosthesis for surgical use in bone replacement or reconstruction is potentially feasible through the application and integration of several different existing technologies, which are each at different stages of maturity. Initial case study experiments have been undertaken to validate the research concepts by making dimensional comparisons between a bone and a virtual model produced using the proposed methodology and a future research directions are discussed.

Image segmentation using morphological watershed applied to cartography

Image segmentation is a process frequently used in several different areas including Cartography. Feature extraction is a very troublesome task, and successful results require more complex techniques and good quality data. The aims of this paper is to study Digital Image Processing techniques, with emphasis in Mathematical Morphology, to use Remote Sensing imagery, making image segmentation, using morphological operators, mainly the multi-scale morphological gradient operator. In the segmentation process, pre-processing operators of Mathematical Morphology were used, and the multi-scales gradient was implemented to create one of the images used as marker image. Orbital image of the Landsat satellite, sensor TM was used. The MATLAB software was used in the implementation of the routines. With the accomplishment of tests, the performance of the implemented operators was verified and carried through the analysis of the results. The extration of linear feature, using mathematical morphology techniques, can contribute in cartographic applications, as cartographic products updating. The comparison to the best result obtained was performed by means of the morphology with conventional techniques of features extraction. © Springer-Verlag 2004.

Analysis of tectonic-controlled fluvial morphology and sedimentary processes of the western Amazon Basin: an approach using satellite images and digital elevation model

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)