Model-Based Design of Optimal Nonlinear Filters for Binary Images

所有的消隐不变二值图像滤波器都具有形态学表示。 因此，找到最佳滤波器涉及找到产生具有最小误差（在我们的情况下，平均绝对误差（MAE））的滤波器的结构元素。 这种观察导致自动化的恢复和增强过滤器的设计程序时，同时观察（损坏）和理想的图像作为随机集过程。 一个关键的设计方面是假设的理想和观察过程的图像模型。 本研究关注滤波器的鲁棒性相对于建模假设：在多大程度上是滤波器的性能相对于设计假设的偏差下降？ 我们的方法是假设参数化的理想和观察到的图像过程，并考虑应用一个最佳滤波器为一个给定的参数向量对应于不同的参数向量的图像的影响。 增强算法的设计是电子办公设备制造的一个组成部分。 这种耗时（长达一年）和性能受到人类仅考虑相对少量的可能算法的能力的限制。 最近，增强算法已经由高级算法自动设计，高级算法结合图像和成像系统的数学模型使用统计数据，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探讨设计。 它还解决了“鲁棒性”的问题：由于设计的增强算法是基于建模假设，实际应用需要我们有一个合理的想法，它将如何执行图像数据，不同程度的数据，它已经被设计。

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.