Pareto-dominated Hypervolume Measure: An Alternative Approach to Color Morphology
Pareto-dominated Hypervolume Measure: An Alternative Approach to Color Morphology
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DOI：
10.1109/his.2007.49
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发表时间：
2007-09
期刊：
影响因子：
--
通讯作者：
M. Köppen;K. Franke
中科院分区：
文献类型：
--
作者：
M. Köppen;K. Franke
在本文中，提出了一种基于帕累托主导超体积测量的彩色和多光谱图像数学形态学非线性滤波的替代方法。在此背景下研究了部分集理论，并成功应用于彩色图像的形态过滤。特别是评估多目标优化算法质量的需求提出了几种措施。其中一个度量，超体积，基于由一组点支配的所有点的勒贝斯克度量，并将一组帕累托最优点映射到非负标量。通过考虑彩色图像域中的超体积，可以表明该超体积对应于另一种颜色形态，滤波图像中的每个像素代表原始彩色图像中其邻居集合的超体积。在下文中，将导出用作图像处理滤波器的超体积的一些属性，并且将建议这种方法在颜色形态学方面的一些潜在应用。
In this paper, an alternative approach to the non-linear filtering of mathematical morphology for color and multi-spectral images based on the Pareto-dominated hypervolume measure is presented. Parteo-set theory is studied in this context, and among others, successfully implemented in the morphological filtering of color images. The demand to assess the quality of a multi-objective optimization algorithms, in particular, has put forth several kind of measures. One of these measures, the hypervolume, bases on the Lebesque measure of all points dominated by a set of points and maps a set of Pareto-optimal points to a non-negative scalar. By considering the hypervolume in the color-image domain, it can be shown that this hypervolume corresponds to another kind of color morphology, were each pixel in the filtered image represents the hypervolume of its set of neighbours in the original color image. In the following, some properties of the hypervolume, as used as an image-processing filter will be derived, and some potential applications of this approach to color morphology will be suggested.