专业英语
英文出处：PROCEEDINGS OF THE IEEE, VOL.60, NO.7, JULY 1972
译文
可视化环境中的图像处理
1 简介
图像的质量在整个图像处理领域正在受到越来越多的关注。在某种程度上不断增长的认识是基于复杂的数学方法，这种方法往往是为了突出精度的需要。在图像的读入和输出数字形式的标准的缺乏方面，这里也有一个在不断进步的认识，可以偏向的理解为处理的表面效率以及在不同的设施中对获得的结果进行不确定的比较。更大的认识和要求是部分的受挫做出的响应，因为解决主观失真的措施很难找到。这个困难的一部分是源于物理和主观的结果的必然不同。这个观点在这里的提出是源于我们对图像结构之间关系的重新评估1）数量的表示法的问题2)图像处理的预期效果和不想要的失真3）基于观察者的图像处理的相互作用。
他们提供了一个框架，让我们用来考虑和执行我们的任务。通过加进我们自己对处理图像的理解，以及在物理上和视觉上图像处理时问题方面的理解，这些关于图像质量观点的阐明，加强了我们对它的理解能力。我们提供了这些是希望他们可以被应用在其他领域。
在讨论的过程中，人们注意到图像处理服从乘法叠加性而不是加法叠加性，在操作上和结构上都有令人关注的相同之处，用来实现一部分人类早期的视觉。基于这些相似观点的提出，我们假设了一个视觉模型，这个实验的结果在理论上能够为其增加一些支持，并且提供了模型描述的基准。这个实验性的视觉模型提供了特殊的作用，能够大概的预测视觉处理的特性。
在近几年，大量定量的工作被不同领域的工程师和科学家们所完成，以此来支持人类的视觉模型，这项工作中的很多部分在这里并没有被明确的指出。我们尝试引用参考文献和教材，这样可以更好的收集到这些文献中少数引用到它们的地方，并且能够提供一个统一的解释。
2图像的表示
在传播，存储和处理这些信息上的一个关键问题是如何表示。选择如何表示重要的因素是传输，存储和处理的问题，它们可以被它大大的影响。
如果一个理想的物理图像是作为一个信息载体来考虑，那么它自身的性质就已经选择了一种表示方法，在这里它选择了光能的形式。此外，如果从字面上理解一个光学图像，我们将继续通过创建一个与之相对的信号来加强光能的代表性。这种表示确实是一种非常自然的表示方法，事实上它已经被证明了，它经常被应用于电视和图像处理方面。
说来也奇怪，用光强度来分析在图像技术上是一个相对较新的方法。摄影方面的处理，现在已经过去了一个世纪，但是并没有应用到它。随着有关电的图像处理方法的出现，它才受到重视。为了阐明这一点，想象一个黑白透明度的影像来描绘光学的图像。为了看到这个模型，我们必须用一些强度io来一致的阐述透明度。以某种方法观察光强度ix,y的传输模式。光能的传输取决于在胶状乳剂中非晶体的体积浓度。因此，这些浓度代表着图像的存储形式，这些浓度被表示成cx,y,z。物理的情况在图1中被描述.为了推导出重现图像的ix,y和cx,y,z之间
的关系，我们必须考虑光在介质中的透射性。该物理情况在公式（9）中被给出。
dikCx,y,zi（9）在这里i是光在任意一点传输介质中的强dz
度，k是一个常数，代表非晶体锈银在单位浓度上的衰减能力。整合公式（9）便得到标准的公式（10）。iIx,ydizktCx,y,zdz（10） 0i0
这里Zt代表溶剂的厚度。由于公式（10）积分在可靠性上代表着透明度独立的每个单元锈银的总流量，以及他在Z平面上是如何分布的。公式（10）也可以写成公式（11）.ln(Ix,y0)kdx,y（11）公式（11）的解决方法得出了
公式（12）Ix,yi0ekd（12）由公式（11）可以看出，在透x,y
明度的摄影情况下，图像的物理表示法实际就是dx,y，这个表示法与重现的图像
的强度的对数成比例关系。转而，公式（12）揭示了物理表示法dx,y在它转换成
光强度时取幂。此外，如果ix,y是一个原始图像强度准确可靠的复制值，这些锈
银被用来形成的dx,y一定通过处理被储存在乳剂中，通过对数转换成光能。这种
情况在图2中对对数和指数的转换进行了总结，用来机械化的形成摄影图像，并且得到了证明。出现在公式（11）和公式（12）中的变量i0和 k为了计算方便
被省略了，它们只是质量常数。
在摄影技术上公式（12）的关系是容易理解的，但是经常被表达成公式（13）的形式log(i0Ix,y)Dx,y（13）这里Dx,y叫做强度，与成dx,y比例，直接
叙述这个常用对数，在某种意义上与分贝的定义相似。由于dx,y和Dx,y都与一
般的强度概念有关，所以叫这个对数表示为强度是合理的。如上所述，除了两个可选择的参量所有的表示式是相同的。通过理解公式（11）和公式（12）得出公式(14)和（15）:
I
x,ylog(Ix,y)（14）Ix,yexp()（15） Ix,y
在这里带点的变量代表密度，不带点的变量代表强度。除了一个比例因素和一个附加的变量，这里所有的密度值代表的意思相同。
Image Proceing in the Context of a Visual Model.
INTRODUCTION
Image quality is becoming an increasing concern throughout the field of image proceing.The growing awarene is due in part to the availability of sophisticated digital methods which tend to highlight the need for precision.Also there is a eveloping
realization that the lack of standards for reading images into and writing images out of digital form can bias the apparent effectivenesosf a proce and can make uncertain the comparison of results obtained at different installations.Greater awarene and the desire to respond to it are partially frustrated, because subjective distortion measures which work well are difficult to find.Partof the difficulty stems from the fact that
physical and subjective distortions are necearily different.
The ideas presented here spring from our reevaluation of the relationship between
the structure of images and 1) the problem of quantitative representation, 2) the effect of desired proceing and/or unwanted distortion, and 3) the interaction of images with the human observer.They provide a framework in which we think about and perform our image proceing tasks.By adding to our understanding of what is to be measured when dealing with images and by strengthening the bridge between the objective (physical) and the subjective (visual) aspects of many image proceing iues, these ideas have clarified the meaning of image quality and thus have ‘enhanced our ability to obtain it.[Ye offer them with the hope that they may aid othersw ealsl.
In the course of the discuion it is noted that image proceors which obey
superposition multiplicatively instead of additively, bear an interesting resemblance both operationally and structurally to early portionosf the human visual system.Based on this resemblance a visual model is hypothesized, and the results of an experiment which lends some support to and providesa calibration for the model are described.This tentative visual model is offered only for its special ability to predict approximate visual proceing characteristics.In recent years there has beena large amount of quantitative work done by engineers and scientists from many fields in support of a model for human vision.While many of these works are not referenced explicitly here, we have attempted to reference papers and texts which doa good job of collecting these references in a small number of places while providing a unifying interpretation
.THER EPRESENTATION oF IMAGES
A key question in the transmiion, storage, or proceing of any information is
that of representation.The reason that the choice of representation is important is that the problems of transmiion, storage, and proceing can be substantially effected by it.
If an ideal physical image is considered as a carrier of information, it follows that nature has already chosen a representation..It takes the form of light energy.Furthermore, if one takes nature literally when sensing an optical image, one will continue that representation by creating a ignal proportional to the intensity of that light energy.Indeed this representation seems likea very natural one, and in fact as already indicated, it is commonluys ed in television and digital image proceing.
Strangely enough representation by light intensity analogy is a relatively new practice in image technology.The proce of photography, now over a century old, does not use it.It has only been with the advent of electrical imaging methods that it harse ceived attention.In order to clarify\' this point, imagine a black and white photographic transparency which portrays some optical image.In order to see the reproduction one must illuminate the transparency uniformly with some intensity io and somehow view
the transmitted pattern of light intensity I.The quantities of light which are transmitted are determined by the volume concentrations of amorphous silver suspended in a gelatinous emulsion.Thus it is these concentrations which represent the image in its stored form.Let these concentrations be expreed as .Physically the situation is as depicted in Fig1..In order to derive the relationship between the reproduced image I and C we must consider the transmiion of light through materials.The physics of the situation is given in (9)
dikCx,y,zi(9) dz
where i is the intensity of the light at any point in the transmitting material and K is a constant representing the attenuating ability of a unit concentration of amorphous silver.Integration of (9) according to standard methods yields (10)
iIx,ydizktCx,y,zdz(10) 0i0
where st represents the thickne of the emulsion.Since the integral in the right-hand side of (10) represents the total quantity of silver per unit area of the transparency independent of how that silver is distributed in the z dimension (10) can be rewritten as in (11)ln(Ix,y)kd0
x,yx,y(11) A solution of (11) for I,,, yields (12)Ix,yi0ekd(12)
From (11) it can be seen that in the case of a photographic transparency, the physical representation of the image is actually d which is proportional to the logarithm of the reproduced intensity image.In turn (12) reveals that the physical representation d is exponentiated during its conversion to light intensity.Further, it follows that if Iu is a faithful reproduction of the original intensity image from which the transparency was made, then the quantities of silver used to form the representation d,,, must have beendeposited in the emulsion by a proce which was logarithmically sensitive to light energy.This situation is summarized in Fig.2 where the logarithmic and exponential transformations which mechanize the formation of a photographic image are placed in evidence.The variables io and R which appear in (11) and (12) have been omitted for convenience since they are only scaling constants.\' The relationship of (12) is well known in photography but is usually presented ian somewhat altered form as in(1 3).log(i0Ix,y)Dx,y(13)
Here the quantity Dx,ycalled densitydx,y, is proportional to but related directly
to the common logarithm in a manner similar t o t h a t used in the definition of the decibel.Because Dx,yanddx,y are both related to the popular notion of density it is
reasonable to call any logarithmic representation of an image a density representation.As indicated above, all such representations are the same except for the choice of the
two constant parameters.
Taking this into account(1 1) and (12) may be generalizedto (14) and (15)I
x,ylogI(x,y)(14)Ix,yexp()(15) Ix,y
where the hatted variables represent density and the unhatted variables represent intensity.All density representations arethe same except for a scale factor and an additive constant.
