Jean-Charles Pinoli

Image dynamic range enhancement and stabilization in the context of the logarithmic image processing model

Abstract Images of a scene observed under a variable illumination or with a variable optical aperture are not identical. Does a privileged representant exist? In which physical setting? In which mathematical context? With which meaning and criterion? How to obtain it? The authors answer to such questions in the physical setting of logarithmic imaging processes. For such a purpose, they use the logarithmic image processing (LIP) model, known to be a compatible mathematical framework. After short recalls on this model, the paper presents two image transforms: one performs an optimal enhancement and stabilization of the overall dynamic range, and the other does of the mean dynamic range. The results obtained on X-ray images, as well as for some natural scenes, are shown. Also the implementation of the transforms is addressed.

Differentiation-Based Edge DetectionUsing the Logarithmic Image Processing Model

The logarithmic image processing (LIP) model is a mathematical framework which provides a specific set of algebraic and functional operations for the processing and analysis of intensity images valued in a bounded range. The LIP model has been proved to be physically justified by that it is consistent with the multiplicative transmittance and reflectance image formation models, and with some important laws and characteristics of human brightness perception. This article addresses the edge detection problem using the LIP-model based differentiation. First, the LIP model is introduced, in particular, for the gray tones and gray tone functions, which represent intensity values and intensity images, respectively. Then, an extension of these LIP model notions, respectively called gray tone vectors and gray tone vector functions, is studied. Third, the LIP-model based differential operators are presented, focusing on their distinctive properties for image processing. Emphasis is also placed on highlighting the main characteristics of the LIP-model based differentiation. Next, the LIP-Sobel based edge detection technique is studied and applied to edge detection, showing its robustness in locally small changes in scene illumination conditions and its performance in the presence of noise. Its theoretical and practical advantages over several well-known edge detection techniques, such as the techniques of Sobel, Canny, Johnson and Wallis, are shown through a general discussion and illustrated by simulation results on different real images. Finally, a discussion on the role of the LIP-model based differentiation in the current context of edge detection is presented.

A general comparative study of the multiplicative homomorphic log-ratio and logarithmic image processing approaches

Abstract This article presents a comparative study of the multiplicative homomorphic image processing (MHIP), the log-ratio image processing (LRIP) and the logarithmic image processing (LIP). These three image processing approaches are based on abstract linear mathematics and provide specific operations and structures that have opened up new pathways to the development of image processing techniques. The MHIP approach was designed for the processing of multiplied images, the LRIP approach was introduced to overcome the out-of-range problem associated with many image processing techniques, while the LIP approach was developed for the processing of images valued in a bounded intensity range. First, it is claimed that an image processing framework must be physically relevant, mathematically consistent, computationally tractable and practically fruitful. It is also pointed out that the classical linear image processing (CLIP) is not adapted to non-linear and/or bounded range images or imaging systems, such as transmitted light images, practical digital images or the human brightness perception system. Then, the importance and usefulness of several mathematical fields, such as abstract linear algebra and abstract analysis, for image representation and processing within such image settings are discussed. Third, the MHIP, LRIP and LIP approaches are presented, focusing on their distinctive ideas, structures and properties for image representation and processing, rather than an in-depth review. Next, a study of the relationships and differences between their image representations and basic algebraic operations is detailed. Finally, a general comparative discussion is developed, showing the main physical, mathematical, computational and practical characteristics of these three abstract-linear-mathematics-based image processing approaches, and summarizing their respective advantages and disadvantages. It is concluded and highlighted through real application examples in both image enhancement and edge detection areas that the LIP approach surpasses the two other approaches, although, from a strictly practical point of view, a detailed quantitative comparative study on real applications is now necessary.

General Adaptive Neighborhood Image Processing. Part I: Introduction and Theoretical Aspects

The 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 Adaptive Neighborhood (AN) paradigm allows the building of new image processing transformations using context-dependent analysis. Such operators are no longer spatially invariant, but vary over the whole image with ANs as adaptive operational windows, taking intrinsically into account the local image features. This AN concept is here largely extended, using well-defined mathematical concepts, to that General Adaptive Neighborhood (GAN) in two main ways. Firstly, an analyzing criterion is added within the definition of the ANs in order to consider the radiometric, morphological or geometrical characteristics of the image, allowing a more significant spatial analysis to be addressed. Secondly, general linear image processing frameworks are introduced in the GAN approach, using concepts of abstract linear algebra, so as to develop operators that are consistent with the physical and/or physiological settings of the image to be processed.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 transforms perform a relevant spatially-adaptive image processing, in an intrinsic manner, that is to say without a priori knowledge needed about the image structures. Moreover, in several important and practical cases, the adaptive morphological operators are connected, which is an overwhelming advantage compared to the usual ones that fail to this property.

The Logarithmic Image Processing Model: Connections with Human Brightness Perception and Contrast Estimators

The logarithmic image processing (LIP) model is amathematical framework based on abstract linear mathematicswhich provides a set of specific algebraic and functionaloperations that can be applied to the processing of intensityimages valued in a bounded range. The LIP model has been provedto be physically justified in the setting of transmitted lightand to be consistent with several laws and characteristics ofthe human visual system. Successful application examples havealso been reported in several image processing areas, e.g.,image enhancement, image restoration, three-dimensional imagereconstruction, edge detection and image segmentation.The aim of this article is to show that the LIP model is atractable mathematical framework for image processing which isconsistent with several laws and characteristics of humanbrightness perception. This is a survey article in the sensethat it presents (almost) previously published results in arevised, refined and self-contained form. First, an introductionto the LIP model is exposed. Emphasis will be especially placedon the initial motivation and goal, and on the scope of themodel. Then, an introductory summary of mathematicalfundamentals of the LIP model is detailed. Next, the articleaims at surveying the connections of the LIP model with severallaws and characteristics of human brightness perception, namelythe brightness scale inversion, saturation characteristic, Webersand Fechners laws, and the psychophysical contrast notion. Finally,it is shown that the LIP model is a powerful and tractable framework for handling the contrast notion. This is done througha survey of several LIP-model-based contrast estimators associated with special subparts (point, pair of points,boundary, region) of intensity images, that are justified bothfrom a physical and mathematical point of view.

General Adaptive Neighborhood Image Processing

The 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 spatially-adaptive 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.

Logarithmic adaptive neighborhood image processing (LANIP): introduction, connections to human brightness perception, and application issues

A new framework for image representation, processing, and analysis is introduced and exposed through practical applications. The proposed approach is called logarithmic adaptive neighborhood image processing (LANIP) since it is based on the logarithmic image processing (LIP) and on the general adaptive neighborhood image processing (GANIP) approaches, that allow several intensity and spatial properties of the human brightness perception to be mathematically modeled and operationalized, and computationally implemented. The LANIP approach is mathematically, computationally, and practically relevant and is particularly connected to several human visual laws and characteristics such as: intensity range inversion, saturation characteristic, Webers and Fechners laws, psychophysical contrast, spatial adaptivity, multiscale adaptivity, morphological symmetry property. The LANIP approach is finally exposed in several areas: image multiscale decomposition, image restoration, image segmentation, and image enhancement, through biomedical materials and visual imaging applications.

Color Adaptive Neighborhood Mathematical Morphology and its application to pixel-level classification

In this paper spatially adaptive Mathematical Morphology (MM) is studied for color images. More precisely, the General Adaptive Neighborhood Image Processing (GANIP) approach is generalized to color images. The basic principle is to define a set of locally Color Adaptive Neighborhoods (CAN), one for each point of the image, and to use them as adaptive structuring elements (ASE) for morphological operations. These operators have been applied to images in different color spaces and compared with other kinds of ASEs extended to color images. Results show that the proposed method is more respectful with the borders of the objects, as well as with the color transitions within the image. Finally, the proposed adaptive morphological operators are applied to the classification of color texture images.

General Adaptive Neighborhood Mathematical Morphology

This paper aims to present a novel framework, entitled General Adaptive Neighborhood Image Processing (GANIP), focusing on the area of adaptive morphology. The usual fixed-shape structuring elements required in Mathematical Morphology (MM) are substituted by adaptive (GAN-based) spatial structuring elements. GANIP and MM results to the so-called General Adaptive Neighborhood Mathematical Morphology (GANMM). Several GANMM-based image filters are defined. They satisfy strong morphological and topological properties such as connectedness. The practical results in the fields of image restoration and image enhancement confirm and highlight the theoretical advantages of the GANMM approach.

General Adaptive Neighborhood Choquet Image Filtering

A novel framework entitled General Adaptive Neighborhood Image Processing (GANIP) has been recently introduced in order to propose an original image representation and mathematical structure for adaptive image processing and analysis. The central idea is based on the key notion of adaptivity which is simultaneously associated with the analyzing scales, the spatial structures and the intensity values of the image to be addressed. In this paper, the GANIP framework is briefly exposed and particularly studied in the context of Choquet filtering (using fuzzy measures), which generalizes a large class of image filters. The resulting spatially-adaptive operators are studied with respect to the general GANIP framework and illustrated in both the biomedical and materials application areas. In addition, the proposed GAN-based filters are practically applied and compared to several other denoising methods through experiments on image restoration, showing a high performance of the GAN-based Choquet filters.