论文标题
线性扩张 - 探索使用凸孔程序训练的训练
Linear Dilation-Erosion Perceptron Trained Using a Convex-Concave Procedure
论文作者
论文摘要
数学形态（MM）是用于图像处理和分析的非线性操作员的理论。形态神经网络（MNN）是神经元计算形态算子的神经网络。扩张和侵蚀是MM的基本操作员。从代数的角度来看，扩张和侵蚀分别与超级和幼稚操作分别通勤。在本文中，我们介绍\ textIt {线性扩张 - 验知perceptron}（$ \ ell $ -dep），该{$ \ ell $ -DEP）是通过在计算扩张和侵蚀之前应用线性转换给出的。 $ \ ell $ -DEP模型的决策功能是通过添加扩张和侵蚀来定义的。此外，培训$ \ ell $ -DEP可以作为凸 - 凸优化问题配方。我们将$ \ ell $ -DEP模型的性能与使用多个分类问题的其他机器学习技术进行了比较。计算实验支持所提出的$ \ ell $ -DEP模型在二进制分类任务中的潜在应用。
Mathematical morphology (MM) is a theory of non-linear operators used for the processing and analysis of images. Morphological neural networks (MNNs) are neural networks whose neurons compute morphological operators. Dilations and erosions are the elementary operators of MM. From an algebraic point of view, a dilation and an erosion are operators that commute respectively with the supremum and infimum operations. In this paper, we present the \textit{linear dilation-erosion perceptron} ($\ell$-DEP), which is given by applying linear transformations before computing a dilation and an erosion. The decision function of the $\ell$-DEP model is defined by adding a dilation and an erosion. Furthermore, training a $\ell$-DEP can be formulated as a convex-concave optimization problem. We compare the performance of the $\ell$-DEP model with other machine learning techniques using several classification problems. The computational experiments support the potential application of the proposed $\ell$-DEP model for binary classification tasks.
