Characterization of image sets: the Galois Lattice approach

This paper presents a new method for supervised image classification. One or several landmarks are attached to each class, with the intention of characterizing it and discriminating it from the other classes. The different features, deduced from image primitives, and their relationships with the sets of images are structured and organized into a hierarchy thanks to an original method relying on a mathematical formalism called Galois (or Concept) Lattices. Such lattices allow us to select features as landmarks of specific classes. This paper details the feature selection process and illustrates this through a robotic example in a structured environment. The class of any image is the room from which the image is shot by the robot camera. In the discussion, we compare this approach with decision trees and we give some issues for future research

Galois lattice theory for probabilistic visual landmarks

This paper presents an original application of the Galois lattice theory, the visual landmark selection for topological localization of an autonomous mobile robot, equipped with a color camera. First, visual landmarks have to be selected in order to characterize a structural environment. Second, such landmarks have to be detected and updated for localization. These landmarks are combinations of attributes, and the selection process is done through a Galois lattice. This paper exposes the landmark selection process and focuses on probabilistic landmarks, which give the robot thorough information on how to locate itself. As a result, landmarks are no longer binary, but probabilistic. The full process of using such landmarks is described in this paper and validated through a robotics experiment

Topological visual localization using decentralized galois lattices

This paper presents a new decentralized method for selecting visual landmarks in a structured environment. Different images, issued from the different places, are analyzed, and primitives are extracted to determine whether or not features are present in the images. Subsequently, landmarks are selected as a combination of these features with a mathematical formalism called Galois - or concept - lattices. The main drawback of the general approach is the exponential complexity of lattice building algorithms. A decentralized approach is therefore defined and detailed here: it leads to smaller lattices, and thus to better performance as well as an improved legibility

Application of response surface methodology to stiffened panel optimization

In a multilevel optimization frame, the use of surrogate models to approximate optimization constraints allows great time saving. Among available metamodelling techniques we chose to use Neural Networks to perform regression of static mechanical criteria, namely buckling and collapse reserve factors of a stiffened panel, which are constraints of our subsystem optimization problem. Due to the highly non linear behaviour of these functions with respect to loading and design variables, we encountered some difficulties to obtain an approximation of sufficient quality on the whole design space. In particular, variations of the approximated function can be very different according to the value of loading variables. We show how a prior knowledge of the influence of the variables allows us to build an efficient Mixture of Expert model, leading to a good approximation of constraints. Optimization benchmark processes are computed to measure time saving, effects on optimum feasibility and objective value due to the use of the surrogate models as constraints. Finally we see that, while efficient, this mixture of expert model could be still improved by some additional learning techniques

Surrogate modeling approximation using a mixture of experts based on EM joint estimation

An automatic method to combine several local surrogate models is presented. This method is intended to build accurate and smooth approximation of discontinuous functions that are to be used in structural optimization problems. It strongly relies on the Expectation-Maximization (EM) algorithm for Gaussian mixture models (GMM). To the end of regression, the inputs are clustered together with their output values by means of parameter estimation of the joint distribution. A local expert is then built (linear, quadratic, artificial neural network, moving least squares) on each cluster. Lastly, the local experts are combined using the Gaussian mixture model parameters found by the EM algorithm to obtain a global model. This method is tested over both mathematical test cases and an engineering optimization problem from aeronautics and is found to improve the accuracy of the approximation

A physics-based approach to flow control using system identification

Control of amplifier flows poses a great challenge, since the influence of environmental noise sources and measurement contamination is a crucial component in the design of models and the subsequent performance of the controller. A modelbased approach that makes a priori assumptions on the noise characteristics often yields unsatisfactory results when the true noise environment is different from the assumed one. An alternative approach is proposed that consists of a data-based systemidentification technique for modelling the flow; it avoids the model-based shortcomings by directly incorporating noise influences into an auto-regressive (ARMAX) design. This technique is applied to flow over a backward-facing step, a typical example of a noise-amplifier flow. Physical insight into the specifics of the flow is used to interpret and tailor the various terms of the auto-regressive model. The designed compensator shows an impressive performance as well as a remarkable robustness to increased noise levels and to off-design operating conditions. Owing to its reliance on only timesequences of observable data, the proposed technique should be attractive in the design of control strategies directly from experimental data and should result in effective compensators that maintain performance in a realistic disturbance environment

Learning-based visual localization using formal concept lattices

We present here a new methodology to perform active visual localization in the context of autnomous mobile robotics. The robot is endowed with a topological map of its environment. During the learning phase, the robot takes a lot of pictures from the environment; each picture is labelled by its origin place in the topological map. After the learning phase, the robot is supposed to locate itself in the learnt environment using the visual sensor. Since the discriminating information is sparse, the usual supervised classification techniques as neural networks are not sufficient to perform efficiently this task. Therefore, we propose to use a symbolic learning approach, the "formal concept analysis". The relevant information is gathered into one concept lattice. A formal classification rule is proposed to achieve localization on the topological map. In order to improve the response rate of the decision process, the original formal landmark set is extended to plausible landmarks for a given confidence level. Experimental results in a structured environment support this approach. Perspectives for implementing active strategy to look for visual information and to improve on-line learning and localization process are presented in the final discussion

Approche décentralisée des treillis de Galois pour la localisation topologique

Ce papier présente une nouvelle technique pour la localisation d'un robot mobile autonome dans un environnement structuré. La localisation est topologique et se base sur les amers visuels. Ces amers sont des combinaisons de caractéristiques visuelles sélectionnées à l'aide d'un formalisme mathématique appelé treillis de Galois, ou treillis de concepts. Pour des très gros contextes, l'approche décentralisée est introduite afin de réduire le nombre de concepts et le temps de construction du treillis. Les algorithmes complets ont été validés expérimentalement et sont exposés dans ce papier

Characterizing image sets using formal concept analysis

This article presents a new method for supervised image classification. Given a finite number of image sets, each set corresponding to a place of an environment, we propose a localization strategy, which relies upon supervised classification. For each place the corresponding landmark is actually a combination of features that have to be detected in the image set. Moreover, these features are extracted using a symbolic knowledge extraction theory, "formal concept analysis". This paper details the full landmark extraction process and its hierarchical organization. A real localization problem in a structured environment is processed as an illustration. This approach is compared with an optimized neural network based classification, and validated with experimental results. Further research to build up hybrid classifier is outlined on discussion