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A well-posed multiscale regularization scheme for digital image denoising

V.B. Surya Prasath (2011)

International Journal of Applied Mathematics and Computer Science

We propose an edge adaptive digital image denoising and restoration scheme based on space dependent regularization. Traditional gradient based schemes use an edge map computed from gradients alone to drive the regularization. This may lead to the oversmoothing of the input image, and noise along edges can be amplified. To avoid these drawbacks, we make use of a multiscale descriptor given by a contextual edge detector obtained from local variances. Using a smooth transition from the computed edges,...

An analytical iterative statistical algorithm for image reconstruction from projections

Robert Cierniak (2014)

International Journal of Applied Mathematics and Computer Science

The main purpose of the paper is to present a statistical model-based iterative approach to the problem of image reconstruction from projections. This originally formulated reconstruction algorithm is based on a maximum likelihood method with an objective adjusted to the probability distribution of measured signals obtained from an x-ray computed tomograph with parallel beam geometry. Various forms of objectives are tested. Experimental results show that an objective that is exactly tailored statistically...

An automatic segmentation method for scanned images of wheat root systems with dark discolourations

Jarosław Gocławski, Joanna Sekulska-Nalewajko, Ewa Gajewska, Marzena Wielanek (2009)

International Journal of Applied Mathematics and Computer Science

The analysis of plant root system images plays an important role in the diagnosis of plant health state, the detection of possible diseases and growth distortions. This paper describes an initial stage of automatic analysis-the segmentation method for scanned images of Ni-treated wheat roots from hydroponic culture. The main roots of a wheat fibrous system are placed separately in the scanner view area on a high chroma background (blue or red). The first stage of the method includes the transformation...

An efficient algorithm for adaptive total variation based image decomposition and restoration

Xinwu Liu, Lihong Huang (2014)

International Journal of Applied Mathematics and Computer Science

With the aim to better preserve sharp edges and important structure features in the recovered image, this article researches an improved adaptive total variation regularization and H −1 norm fidelity based strategy for image decomposition and restoration. Computationally, for minimizing the proposed energy functional, we investigate an efficient numerical algorithm-the split Bregman method, and briefly prove its convergence. In addition, comparisons are also made with the classical OSV (Osher-Sole-Vese)...

An Update on bdim the Italian Digital Mathematical Library

Zelati, Vittorio Coti (2011)

Towards a Digital Mathematics Library. Bertinoro, Italy, July 20-21st, 2011

bdim has been in operation since the fall of 2010 and has been slowly growing in the last year. I will report here: 1) on what is new in bdim with respect to the first presentation in DML 2010; 2) on some of the technical aspects of our implementation; 3) on the projects for the near future; 4) on some of the issues related to possible integration of bdim with EuDML.

Analysis of gradient flow of a regularized Mumford-Shah functional for image segmentation and image inpainting

Xiaobing Feng, Andreas Prohl (2004)

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

This paper studies the gradient flow of a regularized Mumford-Shah functional proposed by Ambrosio and Tortorelli (1990, 1992) for image segmentation, and adopted by Esedoglu and Shen (2002) for image inpainting. It is shown that the gradient flow with L 2 × L ∞ initial data possesses a global weak solution, and it has a unique global in time strong solution, which has at most finite number of point singularities in the space-time, when the initial data are in H 1 × H 1 ∩ L ∞ . A family of fully discrete approximation...

Analysis of gradient flow of a regularized Mumford-Shah functional for image segmentation and image inpainting

Xiaobing Feng, Andreas Prohl (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper studies the gradient flow of a regularized Mumford-Shah functional proposed by Ambrosio and Tortorelli (1990, 1992) for image segmentation, and adopted by Esedoglu and Shen (2002) for image inpainting. It is shown that the gradient flow with L2 x L∞ initial data possesses a global weak solution, and it has a unique global in time strong solution, which has at most finite number of point singularities in the space-time, when the initial data are in H1 x H1 ∩ L∞. A family of fully...

Another look at a model for evaluating interface aesthetics

David Ngo, John Byrne (2001)

International Journal of Applied Mathematics and Computer Science

Gestalt psychologists promulgated the principles of visual organisation in the early twentieth century. These principles have been discussed and re-emphasised, and their importance and relevance to user interface design is understood. However, a limited number of systems represent and make adequate use of this knowledge in the form of a design tool that supports certain aspects of the user interface design process. The graphic design rules that these systems use are extremely rudimentary and often...

Application of the adaptive center-weighted vector median framework for the enhancement of cDNA microarray images

Rastislav Lukac, Bogdan Smołka (2003)

International Journal of Applied Mathematics and Computer Science

In this paper a novel method of noise reduction in color images is presented. The new technique is capable of attenuating both impulsive and Gaussian noise, while preserving and even enhancing the sharpness of the image edges. Extensive simulations reveal that the new method outperforms significantly the standard techniques widely used in multivariate signal processing. In this work we apply the new noise reduction method for the enhancement of the images of the so called gene chips. We demonstrate...

Applying fuzzy logic in video surveillance systems.

José Manuel Molina, Jesús García, Oscar Pérez, Javier Carbó, Antonio Berlanga, José Ignacio Portillo (2005)

Mathware and Soft Computing

In this work, the application of fuzzy logic in surveillance systems based on cameras is analyzed. Three different fuzzy systems have been tested and compared with a crisp decision system. The first one has been developed using an expert knowledge, the second one was learned from recorded videos, and a third one is developed as a refinement taking into account evaluation with ground truth. In all cases, the core of the system is the association function, in which the developed fuzzy system takes...

bdim: the Italian Digital Mathematical Library

Coti Zelati, Vittorio (2010)

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

We present bdim (Bibliteca Digitale Italiana di Matematica) the Italian project of math digitization. The project has been started by SIMAI (Società Italiana di Matematica Applicata e Industriale) and UMI (Unione Matematica Italiana) with initial support from the Biblioteca Digitale Italiana and the Italian Ministry of Beni and Attività Culturali and with the help of Numdam. At the moment bdim consists of approximately 1,300 articles, 11,000 pages (articles from Bollettino Unione Matematica Italiana,...

Binary operations on automatic functions

Juhani Karhumäki, Jarkko Kari, Joachim Kupke (2008)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Real functions on the domain [ 0 , 1 ) n – often used to describe digital images – allow for different well-known types of binary operations. In this note, we recapitulate how weighted finite automata can be used in order to represent those functions and how certain binary operations are reflected in the theory of these automata. Different types of products of automata are employed, including the seldomly-used full cartesian product. We show, however, the infeasibility of functional composition; simple examples...

Binary operations on automatic functions

Juhani Karhumäki, Jarkko Kari, Joachim Kupke (2007)

RAIRO - Theoretical Informatics and Applications

Real functions on the domain [0,1)n – often used to describe digital images – allow for different well-known types of binary operations. In this note, we recapitulate how weighted finite automata can be used in order to represent those functions and how certain binary operations are reflected in the theory of these automata. Different types of products of automata are employed, including the seldomly-used full Cartesian product. We show, however, the infeasibility of functional composition; simple...

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