Noël Richard

Probabilistic pseudo-morphology for grayscale and color images

Mathematical morphology offers popular image processing tools, successfully used for binary and grayscale images. Recently, its extension to color images has become of interest and several approaches were proposed. Due to various issues arising from the vectorial nature of the data, none of them imposed as a generally valid solution. We propose a probabilistic pseudo-morphological approach, by estimating two pseudo-extrema based on Chebyshev inequality. The framework embeds a parameter which allows controlling the linear versus non-linear behavior of the probabilistic pseudo-morphological operators. We compare our approach for grayscale images with the classical morphology and we emphasize the impact of this parameter on the results. Then, we extend the approach to color images, using principal component analysis. As validation criteria, we use the estimation of the color fractal dimension, color textured image segmentation and color texture classification. Furthermore, we compare our proposed method against two widely used approaches, one morphological and one pseudo-morphological. We propose a pseudo-morphology based on probabilistic tools.We use Chebyshev inequality and PCA for estimating pseudo-extrema of a set.Our operators are linear or non-linear depending on the choice of a parameter.We extend the approach to multivariate images, particularly for the color domain.Validation is performed through texture feature extraction.

A Comprehensive Evaluation of Spectral Distance Functions and Metrics for Hyperspectral Image Processing

Distance functions are at the core of important data analysis and processing tools, e.g., PCA, classification, vector median filter, and mathematical morphology. Despite its key role, a distance function is often used without careful consideration of its underlying assumptions and mathematical construction. With the objective of identifying a suitable distance function for hyperspectral images so as to maintain the accuracy of hyperspectral image processing results, we compare existing distance functions and define a suitable set of selection criteria. Bearing in mind that the selection of distance functions is highly related to the actual definition of the spectrum, we also classify the existing distance functions based on how they inherently define a spectrum. Theoretical constraints and behavior, as well as numerical tests are proposed for the evaluation of distance functions. With regards to the evaluation criteria, Euclidean distance of cumulative spectrum (ECS) was found to be the most suitable distance function.

The lacunarity of colour fractal images

Lacunarity is a very useful metric for the multi-scale analysis of the images that exhibit fractal properties. For its computation there exist several approaches, the probabilistic algorithm being accepted as the most elegant approach. However, all the existing methods are defined for one dimensional signals or binary images with extension to grey-scale images. We propose a colour expression of the lacunarity based on the probabilistic algorithm for the computation of the fractal dimension. To validate this new approach, we used both synthetic colour fractal images and natural fractal images. We comment our results and spot several issues regarding the interpretation of lacunarity curves, then we conclude.

A fast color quantization using a matrix of local pallets

We present a robust color quantization method based on the matrix of local pallets. The method proposed extracts a set of one-dimensional colors resulting from image partitioning. Image windowing depends upon the image variance which gives information on color dispersion. The color sets are then used to form the rows of the local pallet matrix that will be used as a smaller image. The selection of the principal pallet used to quantize the color image is accomplished on the local pallet matrix by computing the histogram, dividing the color interval adoptively and choosing the most frequent color with respect to interval total frequency. The experimental results give a good visual appearance and show that the method is very fast.

Spatio temporal characteristics of the human color perception for digital quality assessment

Understanding the contrast sensitivity function (CSF) of the Human Visual System (HVS) has been in the focus of human psychophysics for more than 3 decades. This effort, despite certain successes, is far from closure. In this paper we present a study on the spatio-temporal characteristics of the HVS. We propose a new method of integration of both spatial and temporal effects in the CSF curve that is to be used in color image quality evaluation. The obtained results are very encouraging and show that the new CSF allows some improvements of the classical quality evaluation scheme.

Perceptual color hit-or-miss transform: application to dermatological image processing

The hit-or-miss transform is a mathematical morphological processing designed to find objects in image. Its extension to grayscale domain is not unique, but Barat’s method is the most appropriate to find specific objects with bandwidth in space and color evolutions. This tolerance is possible with the use of non-flat structuring elements. In this paper, a color extension of the Barat’s method is presented. For this purpose, a new mathematical morphology method, based on the concept of convergence in the CIELAB space and where the definition of non-flat structuring elements is possible, is used. A comparison with the existing approaches in the literature is done. Results are given and commented on synthetic and real images.

Color Image Segmentation

Splitting an input image into connected sets of pixels is the purpose of image segmentation. The resulting sets, called regions, are defined based on visual properties extracted by local features. To reduce the gap between the computed segmentation and the one expected by the user, these properties tend to embed the perceived complexity of the regions and sometimes their spatial relationship as well. Therefore, we developed different segmentation approaches, sweeping from classical color texture to recent color fractal features, in order to express this visual complexity and show how it can be used to express homogeneity, distances, and similarity measures. We present several segmentation algorithms, like JSEG and color structure code (CSC), and provide examples for different parameter settings of features and algorithms. The now classical segmentation approaches, like pyramidal segmentation and watershed, are also presented and discussed, as well as the graph-based approaches. For the active contour approach, a diffusion model for color images is proposed. Before drawing the conclusions, we talk about segmentation performance evaluation, including the concepts of closed-loop segmentation, supervised segmentation and quality metrics, i.e., the criteria for assessing the quality of an image segmentation approach. An extensive list of references that covers most of the relevant related literature is provided.

Spectral Ordering Assessment Using Spectral Median Filters

Distance-based mathematical morphology offers a promising opportunity to develop a metrological spectral image processing framework. Within this objective, a suitable spectral ordering relation is required and it must be validated by metrological means, e.g. accuracy, bias, uncertainty, etc. In this work we address the questions of suitable ordering relation and its uncertainty for the specific case of hyperspectral images. Median filter is shown to be a suitable tool for the assessment of spectral ordering uncertainty. Several spectral ordering relations are provided and the performances of spectral median filters based on the aforementioned ordering relations are compared.

Toward a full-band texture features for spectral images

Facing the increasing number of multi and hyperspectral image acquisitions, in particular for medical and industrial applications, we need accurate features to analyse and assess the content complexity in a metrological way. In this paper, we explore an original way to compute texture features for spectral images in a full-band and vector process. To do it, we developed a dedicated approach for Mathematical Morphology using distance function. Thanks to this, we extend the classical mathematical morphology to spectral images. We show in this paper the scientific construction and preliminary results.

A fuzzy hierarchical attributed graph approach for handwritten hieroglyphs description

For a complex writting as egyptian hieroglyphs, combining the works done in hierarchical modelizations and fuzzy grammar definitions seems natural. This paper introduce the hierarchical-fuzzy-attributed graph (FHAG), extended from fuzzy-attributed graph, which modelize attributes by fuzzy-tree grammar. We give a formal definition of FHAGs and explain the building process. Some results are given with a recognition system based on single models comparisons.