A New Vectorial Order Approach Based on the Classification of Tuples Attribute and Relative Absolute Adaptive Referent: Applications to Multicomponent Images

In this paper, we are presenting a new vector order, a solution to the open problem of the generalization of mathematical morphology to multicomponent images and multidimensional data. This approach uses the paradigm of P–order. Its primary principle consists, first in partitioning the multi-component image in the attribute space by a classification method in different numbers of classes, and then the vector attributes are ordered within each class (intra-order-class). And finally the classes themselves are ordered in turn from their barycenter (inter-class order). Thus, two attribute vectors (or colors) whatever, belonging to the vector image can be compared. Provided with this relation of order, vectors attributes of a multivariate image define a complete lattice ingredient necessary for the definition of the various morphological operators. In fact, this method creates a strong close similarity between vectors in order to move towards an order of the same principle as defined in the set of real numbers. The more the number of classes increases, the more the colors of the same class are similar and therefore the absolute adaptive referent tends to be optimal. On the other hand, the more the class number decreases or equals two, the more our approach tends towards the hybrid order developed previously. The proposed order has been implemented on different morphological operators through different multicomponent images. The fundamental robustness of our approach and that relating to noise have been tested. The results on the gradient, Laplacian and Median filter operators show the performance of our new order.

Application of the Dempster-Shafer Theory to the Classification of Pixels from Aster Satellite Images and Spectral Indices

In this paper, it is proposed to apply the Dempster-Shafer Theory (DST) or the theory of evidence to map vegetation, aquatic and mineral surfaces with a view to detecting potential areas of observation of outcrops of geological formations (rocks, breastplates, regolith, etc.). The proposed approach consists in aggregating information by using the DST. From pretreated Aster satellite images (geo-referencing, geometric correction and resampling at 15 m), new channels were produced by determining the spectral indices NDVI, MNDWI and NDBaI. Then, the DST formalism was modeled and generated under the MATLAB software, an image segmented into six classes including three absolute classes (E,V,M) and three classes of confusion ({E,V}, {M,V}, {E,M}). The control on the land, based on geographic coordinates of pixels of different classes on said image, has made it possible to make a concordant interpretation thereof. Our contribution lies in taking into account imperfections (inaccuracies and uncertainties) related to source information by using mass functions based on a simple support model (two focal elements: the discernment framework and the potential set of belonging of the pixel to be classified) with a normal law for the good management of these.

Modeling and Characterization of Vegetation, Aquatic and Mineral Surfaces Using the Theory of Plausible and Paradoxical Reasoning from Satellite Images: Case of the Toumodi-Yamoussoukro-Tiébissou Zone in V Baoulé(Côte d’Ivoire)

In this paper, the theory of plausible and paradoxical reasoning of Dezert- Smarandache (DSmT) is used to take into account the paradoxical charac-ter through the intersections of vegetation, aquatic and mineral surfaces. In order to do this, we developed a classification model of pixels by aggregating information using the DSmT theory based on the PCR5 rule using the ∩NDVI, ∩MNDWI and ∩NDBaI spectral indices obtained from the ASTER satellite images. On the qualitative level, the model produced three simple classes for certain knowledge (E, V, M) and eight composite classes including two union classes characterizing partial ignorance ({E,V}, {M,V}) and six classes of intersection of which three classes of simple intersection (E∩V, M∩V, E∩M) and three classes of composite intersection (E∩{M,V}, M∩{E,V}, V∩{E,M}), which represent paradoxes. This model was validated with an average rate of 93.34% for the well-classified pixels and a compliance rate of the entities in the field of 96.37%. Thus, the model 1 retained provides 84.98% for the simple classes against 15.02% for the composite classes.

A Semi-Vectorial Hybrid Morphological Segmentation of Multicomponent Images Based on Multithreshold Analysis of Multidimensional Compact Histogram

In this work, we propose an original approach of semi-vectorial hybrid morphological segmentation for multicomponent images or multidimensional data by analyzing compact multidimensional histograms based on different orders. Its principle consists first of segment marginally each component of the multicomponent image into different numbers of classes fixed at K. The segmentation of each component of the image uses a scalar segmentation strategy by histogram analysis;we mainly count the methods by searching for peaks or modes of the histogram and those based on a multi-thresholding of the histogram. It is the latter that we have used in this paper, it relies particularly on the multi-thresholding method of OTSU. Then, in the case where i) each component of the image admits exactly K classes, K vector thresholds are constructed by an optimal pairing of which each component of the vector thresholds are those resulting from the marginal segmentations. In addition, the multidimensional compact histogram of the multicomponent image is computed and the attribute tuples or ‘colors’ of the histogram are ordered relative to the threshold vectors to produce (K + 1) intervals in the partial order giving rise to a segmentation of the multidimensional histogram into K classes. The remaining colors of the histogram are assigned to the closest class relative to their center of gravity. ii) In the contrary case, a vectorial spatial matching between the classes of the scalar components of the image is produced to obtain an over-segmentation, then an interclass fusion is performed to obtain a maximum of K classes. Indeed, the relevance of our segmentation method has been highlighted in relation to other methods, such as K-means, using unsupervised and supervised quantitative segmentation evaluation criteria. So the robustness of our method relatively to noise has been tested.

Method of Estimation of Chemical Compounds of a Solution by Analysis of Video Images of Titration from a Semi-Automatic Approach

To titrate or measure a chemical species in a solution is to estimate its quantity of matter or its molar concentration in a given solution. Several methods of estimating molar concentrations of chemical species exist, the main ones being Colorimetric titration, Conductimetric titration, pH metric titration. In practice, all these methods present approximative results because the operator repeats the experiment to ensure the reliability of the results. As a consequence, we have a prolonged time of the experiment which involves a cost in reagents. Given the repetitions of the same experiment, the final result is the average of the results of each experiment. The aim of this paper is to correct this subjectivity by implementing a semi-automatic approach based on colorimetric titration. At the end of the implementation of our approach, we compared our results to those of existing techniques. These results show the reliability of the calculation by the semi-automatic method. This method of estimating the volume at equivalence is fast because it is not manual and does not involve the use of geometric measuring instruments to find the volume at equivalence. This method improves the manual calculation of the volume at equivalence used in the laboratories in school and student environment.

A New Hybrid Order Approach to Morphological Color Image Processing Based on Reduced Order with Adaptive Absolute Reference

Mathematical morphology can process the binary and grayscale image successfully. This theory cannot be extended to the color image directly. In color space, a vector represents a pixel, so in order to compare vectors, vectoriel orderings must be defined first. This paper addresses the question of the extension of morphological operator to the case of color images. The proposed method used the order by bit mixing to replace the conditional order. Our order is based on a combination of reduced and bit mixing ordering of the underlying data. Additionally it is a total ordering. Since it not only solves the problems of false color generated by the marginal order but also those of multiple extrema generated by reduced order. The performance of the introduced operators is illustrated by means of different applications: color gradients for segmenting, image smoothing (noise suppression) by median filter operator and Laplacian operators. Examples of natural color images and synthetic color images are given. Experimental results show the improvement brought by this new method.