Morphology for Image Processing. Part I

In this article we defined mathematical morphology image processing with set operations. First, we defined Minkowski set operations and proved their properties. Next, we defined basic image processing, dilation and erosion proving basic fact about them [5], [8].Yamazaki Hiroshi - Shinshu University, Nagano, JapanByliński Czesław - University of Białystok, PolandWasaki Katsumi - Shinshu University, Nagano, JapanCzesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.Yuzhong Ding and Xiquan Liang. Preliminaries to mathematical morphology and its properties. Formalized Mathematics, 13(2):221-225, 2005.Noboru Endou, Takashi Mitsuishi, and Yasunari Shidama. Dimension of real unitary space. Formalized Mathematics, 11(1):23-28, 2003.H. J. A. M. Heijimans. Morphological Image Operators. Academic Press, 1994.Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990.P. Soille. Morphological Image Analysis: Principles and Applications. Springer, 2003.Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990

General Adaptive Neighborhood Image Processing. Part II: Practical Applications Issues

23 pagesInternational audienceThe so-called General Adaptive Neighborhood Image Processing (GANIP) approach is presented in a two parts paper dealing respectively with its theoretical and practical aspects. The General Adaptive Neighborhood (GAN) paradigm, theoretically introduced in Part I [20], allows the building of new image processing transformations using context-dependent analysis. With the help of a specified analyzing criterion, such transformations perform a more significant spatial analysis, taking intrinsically into account the local radiometric, morphological or geometrical characteristics of the image. Moreover they are consistent with the physical and/or physiological settings of the image to be processed, using general linear image processing frameworks. In this paper, the GANIP approach is more particularly studied in the context of Mathematical Morphology (MM). The structuring elements, required for MM, are substituted by GAN-based structuring elements, fitting to the local contextual details of the studied image. The resulting morphological operators perform a really spatiallyadaptive image processing and notably, in several important and practical cases, are connected, which is a great advantage compared to the usual ones that fail to this property. Several GANIP-based results are here exposed and discussed in image filtering, image segmentation, and image enhancement. In order to evaluate the proposed approach, a comparative study is as far as possible proposed between the adaptive and usual morphological operators. Moreover, the interests to work with the Logarithmic Image Processing framework and with the 'contrast' criterion are shown through practical application examples

A graph-based mathematical morphology reader

This survey paper aims at providing a "literary" anthology of mathematical morphology on graphs. It describes in the English language many ideas stemming from a large number of different papers, hence providing a unified view of an active and diverse field of research

Multiscale Astronomical Image Processing Based on Nonlinear Partial Differential Equations

Astronomical applications of recent advances in the field of nonastronomical image processing are presented. These innovative methods, applied to multiscale astronomical images, increase signal-to-noise ratio, do not smear point sources or extended diffuse structures, and are thus a highly useful preliminary step for detection of different features including point sources, smoothing of clumpy data, and removal of contaminants from background maps. We show how the new methods, combined with other algorithms of image processing, unveil fine diffuse structures while at the same time enhance detection of localized objects, thus facilitating interactive morphology studies and paving the way for the automated recognition and classification of different features. We have also developed a new application framework for astronomical image processing that implements some recent advances made in computer vision and modern image processing, along with original algorithms based on nonlinear partial differential equations. The framework enables the user to easily set up and customize an image-processing pipeline interactively; it has various common and new visualization features and provides access to many astronomy data archives. Altogether, the results presented here demonstrate the first implementation of a novel synergistic approach based on integration of image processing, image visualization, and image quality assessment

Logarithmic mathematical morphology: a new framework adaptive to illumination changes

A new set of mathematical morphology (MM) operators adaptive to illumination changes caused by variation of exposure time or light intensity is defined thanks to the Logarithmic Image Processing (LIP) model. This model based on the physics of acquisition is consistent with human vision. The fundamental operators, the logarithmic-dilation and the logarithmic-erosion, are defined with the LIP-addition of a structuring function. The combination of these two adjunct operators gives morphological filters, namely the logarithmic-opening and closing, useful for pattern recognition. The mathematical relation existing between ``classical'' dilation and erosion and their logarithmic-versions is established facilitating their implementation. Results on simulated and real images show that logarithmic-MM is more efficient on low-contrasted information than ``classical'' MM