用机器学习逼近投票式排序，提升彩色图像形态学处理效果
Approximating Condorcet Ordering for Vector-valued Mathematical Morphology
- 基于投票机制构建向量排序的近似方法
- 学习得到的简化排序在彩色图像上有效提升形态学运算性能
- 适合图像处理与空间数据分析的研究者参考
数学形态学为图像和空间数据处理提供了非线性框架。尽管已有大量成功应用将数学形态学扩展至彩色和高光谱图像等向量值图像，但针对构建形态学算子的最佳向量排序仍无共识。本文通过研究一种基于多组向量排序生成的康多塞排序（Condorcet ranking）的简化排序近似方法来解决该问题。受投票问题启发，康多塞排序依据各元素被不同排序方式投票次数从高到低排列。本文提出一种机器学习方法，学习一个能逼近康多塞排序的简化排序映射。初步计算实验验证了该方法在彩色图像上定义向量值形态学算子的有效性。
原文摘要 · Abstract (English)
Mathematical morphology provides a nonlinear framework for image and spatial data processing and analysis. Although there have been many successful applications of mathematical morphology to vector-valued images, such as color and hyperspectral images, there is still no consensus on the most suitable vector ordering for constructing morphological operators. This paper addresses this issue by examining a reduced ordering approximating the Condorcet ranking derived from a set of vector orderings. Inspired by voting problems, the Condorcet ordering ranks elements from most to least voted, with voters representing different orderings. In this paper, we develop a machine learning approach that learns a reduced ordering that approximates the Condorcet ordering. Preliminary computational experiments confirm the effectiveness of learning the reduced mapping to define vector-valued morphological operators for color images.
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