Abstract

In this paper, we propose a new classification system for image databases, particularly valid for noisy and geometrically distorted images. This system consists of three steps. In the first step, we apply a new image denoising technique based on the resolution of the Perona and Malik model using the finite element method (FEM). In the second step, we use the orthogonal invariant moments, applied to the obtained denoised images, to extract the feature vectors of images. In this step, we use a new set of orthogonal polynomials derived from the orthogonal Legendre polynomials, we call them orthogonal adapted-Legendre polynomials. These polynomials are used to define a series of orthogonal moments, which are invariant to translation, rotation, and scale. In the third steps, we use the radial basis function neural network (RBF), where the calculated feature vectors are the inputs of the input layer. To show the effectiveness of the proposed approach, we perform experimental tests and a comparative study with other well-known classification systems. The results obtained show the superiority and efficiency of our system.

中文翻译：

---

混合有限元和正交勒让德矩的图像分类

摘要

在本文中，我们提出了一种新的图像数据库分类系统，特别适用于嘈杂和几何失真的图像。该系统包括三个步骤。第一步，我们使用有限元方法（FEM），基于Perona和Malik模型的分辨率，应用一种新的图像去噪技术。在第二步中，我们使用正交不变矩，将其应用于获得的去噪图像，以提取图像的特征向量。在这一步中，我们使用从正交勒让德多项式派生的一组新的正交多项式，我们称它们为正交自适应勒让德式多项式。这些多项式用于定义一系列正交矩，这些矩对于平移，旋转和比例不变。在第三步中，我们使用径向基函数神经网络（RBF），其中计算出的特征向量是输入层的输入。为了显示该方法的有效性，我们进行了实验测试以及与其他知名分类系统的比较研究。获得的结果表明了我们系统的优越性和效率。