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

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), newchannels 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 character 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 (EÇV, MÇV, EÇM) and three classes of composite intersection (EÇ{M,V}, MÇ{E,V}, VÇ{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 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-com- ponent 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

Fatigue-loading effect on RC beams strengthened with externally bonded FRP

External bonding of fiber-reinforced polymers (FRP) on concrete beams is particularly attractive for the strengthening of civil engineering structures in order to increase their strength and stiffness. Principles for design of such strengthening methods are now established and many guidelines exist. However, fatigue design procedure is still an ongoing research topic.This paper focuses on the damage behavior of FRP-strengthened reinforced concrete (RC) structures subjected to fatigue loading. In order to design bonded reinforcements, an iterative computational method based on section equilibrium and material properties (concrete, steel, adhesive and composite) has been previously developed by authors [1–3]. In the present study, this method is extended to describe the fatigue behavior of RC beams. A specific modeling coupled with an experimental investigation on large-scale beams made it possible to compare the theoretical and experimental fatigue behaviors of RC beams with and without composite reinforcements. The model is developed and calibrated using data of the literature or recorded during experiments specifically carried out for this study. Results showed that the beam deflection and the strain in each material could be calculated with a sufficient accuracy, so that the fatigue behavior of the FRP-strengthened beams was correctly estimated by the model

Rheology of a confined granular material

We study the rheology of a granular material slowly driven in a confined geometry. The motion is characterized by a steady sliding with a resistance force increasing with the driving velocity and the surrounding relative humidity. For lower driving velocities a transition to stick-slip motion occurs, exhibiting a blocking enhancement whith decreasing velocity. We propose a model to explain this behavior pointing out the leading role of friction properties between the grains and the container's boundary.Comment: 9 pages, 3 .eps figures, submitted to PR

Slow dynamics and aging of a confined granular flow

We present experimental results on slow flow properties of a granular assembly confined in a vertical column and driven upwards at a constant velocity V. For monodisperse assemblies this study evidences at low velocities ($1<V<100 \mu m/s$) a stiffening behaviour i.e. the stress necessary to obtain a steady sate velocity increases roughly logarithmically with velocity. On the other hand, at very low driving velocity ($V<1 \mu m/s$), we evidence a discontinuous and hysteretic transition to a stick-slip regime characterized by a strong divergence of the maximal blockage force when the velocity goes to zero. We show that all this phenomenology is strongly influenced by surrounding humidity. We also present a tentative to establish a link between the granular rheology and the solid friction forces between the wall and the grains. We base our discussions on a simple theoretical model and independent grain/wall tribology measurements. We also use finite elements numerical simulations to confront experimental results to isotropic elasticity. A second system made of polydisperse assemblies of glass beads is investigated. We emphasize the onset of a new dynamical behavior, i.e. the large distribution of blockage forces evidenced in the stick-slip regime

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

A new indexation strategy for the recognition of rocks based on the sparse representation of the signals combined with the texture spectrum of Wang

Rock recognition is extremely difficult because of the heterogeneity of rock properties. Today, in the area of petrography, the recognition of rocks is usually done by photo interpretation alongside which other techniques exist such as spectroscopy, microscopy and geochemistry. But with the rise of computer vision, automatic recognition has become possible from digital images of rocks and much research has gone in that direction. Some methods such as image indexation compare the image introduced by the user through a similarity search query in an image database. Other methods such as PCA, SVM, K‑means, neural networks and k-nearest neighbors etc, based on classification strategies have also been studied to identify objects or rocks. In this paper, we have proposed a new method of rocks recognition based on a sparse representation of the signals named K‑SVD combined with the spectra of textures of the rocks. Our approach consists, first to develop through the K-SVD from the initial image, to estimate the dictionary D1 of the parsimonious matrix X1 and the reconstruction error ER1. Then a Wang texture descriptor is applied to the original image to produce a new texture image. Then the K-SVD algorithm is used again on the new image to produce a new D2 dictionary, a new parsimonious X2 matrix and a new ER2 reconstruction error. The selected signature parameter aimed at characterizing a rock in a discriminant manner is the reconstruction error vector  obtained from the two previously calculated errors. The algorithm of the proposed approach has been applied to different direct view images of rock. The experimental results obtained show the relevance of the identification strategy developed. The reconstruction error was chosen here as our discriminating factor