There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

MUCKE aims to mine a large volume of images, to structure them conceptually and to use this conceptual structuring in order to improve large-scale image retrieval. The last decade witnessed important progress concerning low-level image representations. However, there are a number problems which need to be solved in order to unleash the full potential of image mining in applications. The central problem with low-level representations is the mismatch between them and the human interpretation of image content. This problem can be instantiated, for instance, by the incapability of existing descriptors to capture spatial relationships between the concepts represented or by their incapability to convey an explanation of why two images are similar in a content-based image retrieval framework. We start by assessing existing local descriptors for image classification and by proposing to use co-occurrence matrices to better capture spatial relationships in images. The main focus in MUCKE is on cleaning large scale Web image corpora and on proposing image representations which are closer to the human interpretation of images. Consequently, we introduce methods which tackle these two problems and compare results to state of the art methods. Note: some aspects of this deliverable are withheld at this time as they are pending review. Please contact the authors for a preview.

http://ieeexplore.ieee.org/iel2/4524/12820/00592460.pdf

Image Processing

Theory of fuzzy integrals and its applications

Computational geometry

Recent advances in spectral-spatial classification of hyperspectral images are presented in this paper. Several techniques are investigated for combining both spatial and spectral information. Spatial information is extracted at the object (set of pixels) level rather than at the conventional pixel level. Mathematical morphology is first used to derive the morphological profile of the image, which includes characteristics about the size, orientation, and contrast of the spatial structures present in the image. Then, the morphological neighborhood is defined and used to derive additional features for classification. Classification is performed with support vector machines (SVMs) using the available spectral information and the extracted spatial information. Spatial postprocessing is next investigated to build more homogeneous and spatially consistent thematic maps. To that end, three presegmentation techniques are applied to define regions that are used to regularize the preliminary pixel-wise thematic map. Finally, a multiple-classifier (MC) system is defined to produce relevant markers that are exploited to segment the hyperspectral image with the minimum spanning forest algorithm. Experimental results conducted on three real hyperspectral images with different spatial and spectral resolutions and corresponding to various contexts are presented. They highlight the importance of spectral-spatial strategies for the accurate classification of hyperspectral images and validate the proposed methods.

/pdf/advances-in-spectral-spatial-classification-of-hyperspectral-vlt2ik4ef1.pdf

Advances in Spectral-Spatial Classification of Hyperspectral Images

Publisher Summary This chapter presents an account of logarithmic image processing (LIP) theoretical and practical aspects focusing on transmitted image settings. The power of LIP framework is justified by its being not only mathematically well defined, but also physically consistent with the multiplicative transmittance and reflectance image-formation models and with some important laws and characteristics of human brightness perception. In fact, the physical connections are particularly strong with the transmitted image-formation settings. From a physical viewpoint, LIP framework has been shown to be consistent with the transmitted image-formation settings. From a mathematical viewpoint, LIP framework consists in a positive-ordered functional vector-cone structure. From a computational viewpoint, LIP framework provides a set of operations that overcome the out-of-range problem by definition or by using the modulus notion. From a practical viewpoint, LIP allows for introducing image-processing techniques.

Logarithmic image processing: The mathematical and physical framework for the representation and processing of transmitted images

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

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.

/pdf/general-adaptive-neighborhood-image-processing-3havctif4x.pdf

General Adaptive Neighborhood Image Processing

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

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.

Jean-Charles Pinoli

Papers

Logarithmic image processing: The mathematical and physical framework for the representation and processing of transmitted images

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

General Adaptive Neighborhood Image Processing

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

Differentiation-Based Edge DetectionUsing the Logarithmic Image Processing Model