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Image segmentation with a finite element method

Blaise Bourdin (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The Mumford-Shah functional for image segmentation is an original approach of the image segmentation problem, based on a minimal energy criterion. Its minimization can be seen as a free discontinuity problem and is based on Γ-convergence and bounded variation functions theories. Some new regularization results, make possible to imagine a finite element resolution method. In a first time, the Mumford-Shah functional is introduced and some existing results are quoted. Then, a discrete formulation...

Implementing Dynamic Visualization as an Alternative Interface to a Digital Mathematics Library

Nevěřilová, Zuzana (2010)

Towards a Digital Mathematics Library. Paris, France, July 7-8th, 2010

This paper presents an alternative interface for browsing in the Czech Digital Mathematics Library (DML-CZ) using our Visual Browser web browsing tool. Using dynamic visualization, we have created a tool for browsing the library graphically. Visualization can help users orient themselves in complex data and at the same time reveal sometimes unexpected relationships among units; it at least speeds up browsing. This work follows the metadata processing undertaken on DML-CZ and visualizes all reasonable...

Impulse noise removal based on new hybrid conjugate gradient approach

Morteza Kimiaei, Majid Rostami (2016)

Kybernetika

Image denoising is a fundamental problem in image processing operations. In this paper, we present a two-phase scheme for the impulse noise removal. In the first phase, noise candidates are identified by the adaptive median filter (AMF) for salt-and-pepper noise. In the second phase, a new hybrid conjugate gradient method is used to minimize an edge-preserving regularization functional. The second phase of our algorithm inherits advantages of both Dai-Yuan (DY) and Hager-Zhang (HZ) conjugate gradient...

Innovative applications of associative morphological memories for image processing and pattern recognition.

Manuel Graña, Peter Sussner, Gerhard Ritter (2003)

Mathware and Soft Computing

Morphological Associative Memories have been proposed for some image denoising applications. They can be applied to other less restricted domains, like image retrieval and hyperspectral image unsupervised segmentation. In this paper we present these applications. In both cases the key idea is that Autoassociative Morphological Memories selective sensitivity to erosive and dilative noise can be applied to detect the morphological independence between patterns. Linear unmixing based on the sets of...

INSPIRE: Realizing the Dream of a Global Digital Library in High-Energy Physics

Holtkamp, Annette, Mele, Salvatore, Šimko, Tibor, Smith, Tim (2010)

Towards a Digital Mathematics Library. Paris, France, July 7-8th, 2010

High-Energy Physics (HEP) has a long tradition in pioneering infrastructures for scholarly communication, and four leading laboratories are now rolling-out the next-generation digital library for the field: INSPIRE. This is an evolution of the extraordinarily successful, 40-years old SPIRES database. Based on the Invenio software, INSPIRE already provides seamless access to almost 1 million records, which will be expanded to cover multimedia, data, software, wikis. Services offered include citation...

Instability of the eikonal equation and shape from shading

Ian Barnes, Kewei Zhang (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In the shape from shading problem of computer vision one attempts to recover the three-dimensional shape of an object or landscape from the shading on a single image. Under the assumptions that the surface is dusty, distant, and illuminated only from above, the problem reduces to that of solving the eikonal equation |Du|=f on a domain in ℝ 2 . Despite various existence and uniqueness theorems for smooth solutions, we show that this problem is unstable, which is catastrophic for general numerical algorithms. ...

Local detection of defects from image sequences

Ewaryst Rafajłowicz, Marek Wnuk, Wojciech Rafajłowicz (2008)

International Journal of Applied Mathematics and Computer Science

Our aim is to discuss three approaches to the detection of defects in continuous production processes, which are based on local methods of processing image sequences. These approaches are motivated by and applicable to images of hot metals or other surfaces, which are uniform at a macroscopic level, when defects are not present. The first of them is based on the estimation of fractal dimensions of image cross-sections. The second and third approaches are compositions of known techniques, which are...

Mathematical Communication and Representation in a Virtual Learning Environment

Córcoles, César, Huertas, Antonia (2010)

Towards a Digital Mathematics Library. Paris, France, July 7-8th, 2010

Abstract. At an exclusively online university such as the UOC the necessity for communicating mathematics in the web is pressing. In an environment that does not allow for face to face communication, things implicitly communicated when using a blackboard, such as the canonical verbalization or handwriting of formulae, are lost and become a big obstacle. Also, the editorial process for the creation of learning/teaching resources is suited for a generalist approach and, consequently, needs such as...

Mathematical Formulae Recognition and Logical Structure Analysis of Mathematical Papers

Suzuki, Masakazu (2010)

Towards a Digital Mathematics Library. Paris, France, July 7-8th, 2010

In most cases the current on-line journals in mathematics are supplied in the form of PDF with print images of papers in the front and OCR’ed hidden texts behind to provide with search facilily using key words. The embedded hidden texts usually does not include good information about mathematical formulae in the papers. We can say that, for the future development of DML, it is desirable to include, in the digitised journals, more structured information of the content of mathematical papers, e.g....

Medical image – based computational model of pulsatile flow in saccular aneurisms

Stéphanie Salmon, Marc Thiriet, Jean-Frédéric Gerbeau (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Saccular aneurisms, swelling of a blood vessel, are investigated in order (i) to estimate the development risk of the wall lesion, before and after intravascular treatment, assuming that the pressure is the major factor, and (ii) to better plan medical interventions. Numerical simulations, using the finite element method, are performed in three-dimensional aneurisms. Computational meshes are derived from medical imaging data to take into account both between-subject and within-subject anatomical...

Medical image – based computational model of pulsatile flow in saccular aneurisms

Stéphanie Salmon, Marc Thiriet, Jean-Frédéric Gerbeau (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Saccular aneurisms, swelling of a blood vessel, are investigated in order (i) to estimate the development risk of the wall lesion, before and after intravascular treatment, assuming that the pressure is the major factor, and (ii) to better plan medical interventions. Numerical simulations, using the finite element method, are performed in three-dimensional aneurisms. Computational meshes are derived from medical imaging data to take into account both between-subject and within-subject anatomical...

Metadata Editing and Validation for a Digital Mathematics Library

Filej, Miha, Růžička, Michal, Šárfy, Martin, Sojka, Petr (2010)

Towards a Digital Mathematics Library. Paris, France, July 7-8th, 2010

For preparing and validating metadata for the Digital Mathematics Library DML-CZ, a new tool, the Metadata Editor, has been developed. This paper outlines the procedures for Linguistic and geographical localizations its components. Also mentioned are such aspects as dynamic generation of form editing based on the XML Schema, the validation procedures as well as support for semiautomatic procedures regarding quality assurance.

Neural network segmentation of images from stained cucurbits leaves with colour symptoms of biotic and abiotic stresses

Jarosław Gocławski, Joanna Sekulska-Nalewajko, Elżbieta Kuźniak (2012)

International Journal of Applied Mathematics and Computer Science

The increased production of Reactive Oxygen Species (ROS) in plant leaf tissues is a hallmark of a plant's reaction to various environmental stresses. This paper describes an automatic segmentation method for scanned images of cucurbits leaves stained to visualise ROS accumulation sites featured by specific colour hues and intensities. The leaves placed separately in the scanner view field on a colour background are extracted by thresholding in the RGB colour space, then cleaned from petioles to...

Nonlinear Tensor Diffusion in Image Processing

Stašová, Olga, Mikula, Karol, Handlovičová, Angela, Peyriéras, Nadine (2017)

Proceedings of Equadiff 14

This paper presents and summarize our results concerning the nonlinear tensor diffusion which enhances image structure coherence. The core of the paper comes from [3, 2, 4, 5]. First we briefly describe the diffusion model and provide its basic properties. Further we build a semi-implicit finite volume scheme for the above mentioned model with the help of a co-volume mesh. This strategy is well-known as diamond-cell method owing to the choice of co-volume as a diamondshaped polygon, see [1]. We...

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