Object recognition and classification by mixed finite element method and invariants of orthogonal adapted-Legendre momen
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ORIGINAL PAPER
Object recognition and classification by mixed finite element method and invariants of orthogonal adapted-Legendre moments Amal Hjouji1 · Jaoua EL-Mekkaoui2 · Mostafa Jourhmane1 Received: 13 October 2019 / Accepted: 27 July 2020 © Springer-Verlag France SAS, part of Springer Nature 2020
Abstract In this paper, we present a new technique of extraction of descriptor vectors of the images and a new 2D image classification system especially valid for the image databases which contain noisy or geometrically distorted objects. This system consists of three steps. In the first steps, we use an image denoising technique by solving the Perona–Malik equations using the mixed finite element method based on Taylor–Hood finite element. In the second, we extract the descriptor vectors from the images by using the orthogonal moments applied to the obtained denoised images. In this context we present a new set of orthogonal polynomials based on orthogonal Legendre polynomials, we call them orthogonal adapted-Legendre polynomials. This set of orthogonal polynomials is used to define a new type of orthogonal moments. This helps to build a set of orthogonal moments that are invariant to translation, rotation and scale. These invariant moments are derived algebraically from the invariant geometric moments. In the third steps, we use the multi layer perceptron neural network where the calculated descriptor vectors are the inputs of the input layer. To show the effectiveness of our approach we perform experimental tests on two databases and we present a comparative study with other well-known classification systems. The experimental results obtained show the superiority of our system. Keywords Mixed finite element method · Image filtering · Adapted-Legendre orthogonal invariant moments · 2D image classification · Multi layer perceptron neural network (MLP)
1 Introduction Over the years, many methods have been developed for classification patterns. Each method can have its own technique as partitioning or hierarchical method [1], k-means [2], fuzzy k-means clustering [3,4], artificial neural networks [5–9] etc. Given their lack of efficiency for the image databases which contain noisy or geometrically distorted objects, several researchers have been working to improve them, or to invent new methods to satisfy current demand. For a good 2D image classification, it is necessary to extract descriptor-vectors of images which are invariant
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Jaoua EL-Mekkaoui [email protected] Amal Hjouji [email protected]
1
TIAD Laboratory, Sultan Moulay Slimane University, Beni Mellal, Morocco
2
Transmission and Information Processing Laboratory, EST, Sidi Mohamed Ben Abdellah University, Fez, Morocco
under the three types of transformations: scaling, rotation and translation. In the last several years, an increasing number of research groups have proposed the orthogonal invariant moments [10–19]. The descriptors extracted from the invariant moments first introduced by Hu [20], to guarantee relatively the previous properti
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