Nenashev Vadim A, Khanykov Igor G, Kharinov Mikhail V
Laboratory of Intelligent Technologies and Modelling of Complex Systems, Institute of Computing Systems and Programming, Saint Petersburg State University of Aerospace Instrumentation, 67 B. Morskaia St., 190000 Saint Petersburg, Russia.
Laboratory of Big Data Technologies for Sociocyberphysical Systems, St. Petersburg Federal Research Center of the Russian Academy of Sciences, 14 Line V.O. 39, 199178 Saint Petersburg, Russia.
J Imaging. 2022 Oct 6;8(10):274. doi: 10.3390/jimaging8100274.
The paper presents a model of structured objects in a grayscale or color image, described by means of piecewise constant image approximations, which are characterized by the minimum possible approximation errors for a given number of pixel clusters, where the means the total squared error. An ambiguous image is described as a non-hierarchical structure but is represented as an ordered superposition of object hierarchies, each containing at least one optimal approximation in = 1, 2,..., etc., colors. For the selected hierarchy of pixel clusters, the objects-of-interest are detected as the pixel clusters of optimal approximations, or as their parts, or unions. The paper develops the known idea in cluster analysis of the joint application of Ward's and K-means methods. At the same time, it is proposed to modernize each of these methods and supplement them with a third method of splitting/merging pixel clusters. This is useful for cluster analysis of big data described by a convex dependence of the optimal approximation error on the cluster number and also for adjustable object detection in digital image processing, using the optimal hierarchical pixel clustering, which is treated as an alternative to the modern informally defined "semantic" segmentation.
本文提出了一种灰度或彩色图像中结构化对象的模型，该模型通过分段常数图像近似来描述，其特征在于对于给定数量的像素簇具有尽可能小的近似误差，其中 表示总平方误差。模糊图像被描述为非层次结构，但表示为对象层次结构的有序叠加，每个层次结构在 = 1、2 等颜色中至少包含一个最优近似。对于选定的像素簇层次结构，感兴趣的对象被检测为最优近似的像素簇，或其部分，或并集。本文发展了聚类分析中联合应用沃德法和K均值法的已知思想。同时，建议对这些方法中的每一种进行改进，并用第三种分割/合并像素簇的方法对其进行补充。这对于由最优近似误差对簇数的凸依赖性描述的大数据聚类分析以及在数字图像处理中使用最优层次像素聚类进行可调对象检测很有用，最优层次像素聚类被视为现代非正式定义的“语义”分割的替代方法。
