MITRE Implementation of ISO 12233 Spatial Frequency Response (SFR)

MITRE实现ISO 12233空间频率响应（SFR）

译者注：The MITRE Corporation是一个向美国*提供系统工程、研究开发和信息技术支持的非营利性组织。本SPR算法由C语言开发且开源，代码下载链接 MITRE - Image Quality Evaluation。

作者：
Margaret A. Lepley     mlepley@mitre.org
MITRE MTF and IQS Assessment     mtf@mitre.org
The MITRE Corporation

The ISO International Standard 12233 [1] describes a method for computing the spatial frequency response (SFR1) of an imaging system from the image of an edge target that is slightly slanted with respect to the vertical or horizontal axis. Our goal was to implement code to perform this computation as specified in the standard.

ISO国际标准12233[1]描述了一种用于从相对于垂直或水平轴略微倾斜的边缘目标的图像计算成像系统的空间频率响应（SFR1）的方法。我们的目标是实现代码来执行标准中指定的计算。

This report includes a discussion of the SFR computation, implementation details for our code, and verification examples.

此报告包括对SFR计算的讨论、代码的实现细节和验证示例。

How should SFR be computed? 应如何计算SFR？

The SFR computation has 3 slightly different descriptions within ISO 122332:
a. Section 6.3.2: text, flow chart, and figures
b. Annex A: informative source code in ‘C’
c. Annex C: normative mathematical specification

在ISO 122332中，SFR计算有3个稍有不同的描述：
a. 第6.3.2节：文本、流程图和图表
b. 附录A：C源代码信息
c. 附录C：规范性数学规范

Unfortunately these three do not always agree on the small details, and even Annex C is at times unclear and at times potentially contradictory. As further information we also downloaded the ISO 12233 Slant Edge Analysis Tool matlab code, sfrmat 2.0, from the International Imaging Industry Association (I3A) website [2], to help judge intent in places where the standard was less than clear.

不幸的是，这三个部分并不总是在小细节上达成一致，甚至附录C有时也不明确，有时可能相互矛盾。作为进一步的信息，我们还从国际成像工业协会（I3A）网站[2]下载了iso12233斜边分析工具matlab代码sfrmat2.0，以帮助判断标准不明确的地方的意图。

This report documents the basic sections of a SFR measurement of this type, and lists how a, b, c, and sfrmat approach each of them. Finally the choice made for the MITRE_SFR code, which is trying to strictly adhere to the standard, is given.

本报告记录了这类SFR测量的基本部分，并列出了a、b、c和sfrmat如何处理它们。最后给出了严格遵守标准的MITRE_SFR码的选择。

[1] In this document, as in ISO 12233, the term SFR refers to the spatial frequency response obtained from the edge image output of an imaging system. It would be equivalent to the imaging system’s Modulation Transfer Function (MTF) if the SFR computed from the image is divided by the SFR of the target edge, or if the target edge is a ‘knife edge’ with respect to the given imaging system, and if the imaging system does not exhibit any substantial frequency-independent contrast reduction (such as veiling glare). In other contexts the term SFR has a more general meaning, i.e., it is not tied to a specific target type.

注1：在本文中，与ISO 12233一样，术语SFR是指从成像系统的边缘图像输出获得的空间频率响应。其等效于成像系统的调制传递函数（MTF），如果SFR从图像中的边缘目标计算所得，或者如果目标边缘是相对于给定成像系统的“刀口”，或者成像系统没有表现出任何实质性的与频率无关的对比度降低（如遮掩眩光）。在其他上下文中，术语SFR具有更一般的含义，即它与特定的目标类型无关。

[2] ISO 12233 is currently being revised to add a sine wave-based SFR measurement. The differences noted in the 12233:2000 edge-based SFR description may be corrected in this future edition. It is anticipated that the new version will not be approved and published until late 2007.

注2：ISO 12233目前正在修订，已经添加基于正弦波的SFR测量。12233:2000基于边缘的SFR描述中指出的差异可在未来版本中更正。预计新版本要到2007年底才能获得批准和出版。

The math behind all the concepts mentioned here is not provided, but a brief list of the key algorithm sections that are stable and those that vary is provided to enable the discussion that follows. The algorithmic segments that will be discussed are:

这里没有提供所有提到的概念背后的数学，但是提供了稳定的关键算法部分和变化的关键算法部分的简短列表，以便进行下面的讨论。将要讨论的算法部分包括：