Model-Based Design of Optimal Nonlinear Filters for Binary Images

所有平移不变的二值图像滤波器都具有形态表示。因此，寻找最优过滤器涉及到寻找产生具有最小误差(在我们的例子中为平均绝对误差(MAE))的过滤器的结构元素。当将观察到的(被破坏的)和理想的图像都视为随机集过程时，这种观察导致用于恢复和增强滤光片的自动化设计过程。设计的一个关键方面是假设理想的和观察到的过程的图像模型。这项研究关注与建模假设相关的过滤器稳健性：相对于偏离设计假设，过滤器性能下降到什么程度？我们的方法是假设理想和观测的图像过程是参数化的，并考虑对对应于不同参数向量的图像应用给定参数向量的最优滤波的效果。增强算法的设计是电子办公设备制造中不可或缺的一部分。这很耗时(长达一年)，而且性能受到人类仅考虑相对较少数量的可能算法的能力的限制。最近，增强算法已经由使用统计学并结合图像和成像系统的数学模型的更高级算法自动设计，从而显著缩短设计时间，同时产生更好的增强。本研究从不同的形象模型来研究设计。它还解决了“稳健性”问题：由于所设计的增强算法是基于建模假设的，因此实际应用要求我们对与设计时所基于的数据不同程度不同的图像数据如何执行有一个合理的想法。

All translation-invariant binary image filters possess morphological representations. Hence, finding an optimal filter involves finding the structuring elements that yield a filter having minimum error - in our case, mean-absolute error (MAE). This observation leads to automated design procedures for restoration and enhancement filters when treating both the observed (corrupted) and ideal images as random set processes. A key design aspect is postulation of image models for the ideal and observed processes. This research concerns filter robustness relative to modeling assumptions: to what degree is filter performance degraded relative to deviations from the design assumptions? Our approach is to assume parameterized ideal and observed image processes and to consider the effects of applying an optimal filter for a given parameter vector to images corresponding to different parameter vectors. The design of enhancement algorithms is an integral part of the manufacture of electronic office equipment. This time-consuming (up to a year), and performance is limited by the ability of a human being to consider only a relatively small number of possible algorithms. Recently, enhancement algorithms have been automatically designed by higher-level algorithms that use statistics in conjunction with mathematical models of images and imaging systems, thereby significantly cutting design time while at the same time producing better enhancement. The present research investigates design from various image models. It also addresses the "robustness" question: since a designed enhancement algorithm is based on modeling assumptions, practical application requires that we have a reasonable idea of how it will perform on image data that differs to varying degrees from the data on which it has been designed.