In Sections 5.6 and 8.2.1 we discussed display encoding, the process of converting linear radiance values to nonlinear code values for the display hardware. The function applied by display encoding is the inverse of the display’s electrical optical transfer function (EOTF), which ensures that the input linear values match the linear radiance emitted by the display. Our earlier discussion glossed over an important step that occurs between rendering and display encoding, one that we are now ready to explore.
在第5.6节和第8.2.在第一节中，我们讨论了将线性辐射值转换为显示硬件的非线性代码值的过程。显示编码应用的函数是显示器的电光传输函数(EOTF)逆函数确保输入线性值与显示器发射的线性辐射相匹配。我们之前的讨论忽略了显示和显示代码之间的一个重要步骤，我们现在准备探索它。
Tone mapping or tone reproduction is the process of converting scene radiance values to display radiance values. The transform applied during this step is called the end-to-end transfer function, or the scene-to-screen transform. The concept of image state is key to understanding tone mapping [1602]. There are two fundamental image states. Scene-referred images are defined in reference to scene radiance values,and display-referred images are defined in reference to display radiance values. Image state is unrelated to encoding. Images in either state may be encoded linearly or nonlinearly. Figure 8.13 shows how image state, tone mapping, and display encoding fit together in the imaging pipeline, which handles color values from initial rendering to final display.
色调映射或色调再现是将场景辐射值转化为显示辐射值的过程。应用于此步骤的变换称为端到端传输函数，或场景到屏幕的变换。图像状态的概念是理解色调映射的关键[1602]。图像状态有两种基本状态。参照场景辐射值定义参照场景图像，参照显示辐射值定义参照显示图像。图像状态与编码无关。任何状态下的图像都可以线性或非线性编码。图8.13显示了图像状态、色调映射和显示代码如何在成像管中配合，从初始渲染到最终显示的颜色值。
Figure 8.13. The imaging pipeline for synthetic (rendered) images. We render linear scene referred radiance values, which tone mapping converts to linear display-referred values. Display encoding applies the inverse EOTF to convert the linear display values to nonlinearly encoded values(codes),which are passed to the display. Finally, the display hardware applies the EOTF to convert the nonlinear display values to linear radiance emitted from the screen to the eye.
图8.13.合成(渲染)图像的成像管。我们渲染线性场景参考辐射值，将色调映射转换为线性显示参考值。显示编码应用程序反向EOTF将线性显示值转换为非线性编码值(代码)并传输给显示器。最后，显示硬件应用程序EOTF将非线性显示值转换为从屏幕发射到眼睛的线性辐射。
There are several common misconceptions regarding the goal of tone mapping. It is not to ensure that the scene-to-screen transform is an identity transform, perfectly reproducing scene radiance values at the display. It is also not to “squeeze” every bit of information from the high dynamic range of the scene into the lower dynamic range of the display, though accounting for differences between scene and display dynamic range does play an important part.
色调映射的目标有几个常见的误解。它并不能保证从场景到屏幕的转换是一致的，并在显示器上完美地再现场景亮度值。虽然考虑到场景和显示器动态范围之间的差异，但并不是每个来自场景的高动态范围的信息都会挤压到显示器的低动态范围。
To understand the goal of tone mapping, it is best to think of it as an instance of image reproduction [757]. The goal of image reproduction is to create a displayreferred image that reproduces—as closely as possible, given the display properties and viewing conditions—the perceptual impression that the viewer would have if they were observing the original scene. See Figure 8.14.
为了理解色调映射的目标，最好将其视为图像复制的例子[757]。图像再现的目标是创建显示参考图像，在给定的显示属性和观看条件下，尽可能接近观众在观看原始场景时的感知印象。.14。
Figure 8.14. The goal of image reproduction is to ensure that the perceptual impression evoked by the reproduction (right) is as close as possible to that of the original scene (left).
图8.14.图像再现的目标是确保再现(右)引起的感知印象尽可能接近原始场景(左)。
There is a type of image reproduction that has a slightly different goal. Preferred image reproduction aims at creating a display-referred image that looks better, in some sense, than the original scene. Preferred image reproduction will be discussed later, in Section 8.2.3.
图像复制的目标略有不同。图像再现的首选是创建一个显示参考图像，在某种意义上看起来比原始场景更好。图像再现的首选将是8.2.3节中讨论。
The goal of reproducing a similar perceptual impression as the original scene is a challenging one, considering that the range of luminance in a typical scene exceedsdisplay capabilities by several orders of magnitude. The saturation (purity) of at least some of the colors in the scene are also likely to far outstrip display capabilities.Nevertheless, photography, television, and cinema do manage to produce convincing perceptual likenesses of original scenes, as did Renaissance painters. This achievement is possible by leveraging certain properties of the human visual system.
考虑到典型场景中的亮度范围超过了显示能力的几个数量级，再现与原始场景相似的感知印象的目标是具有挑战性的。场景中至少有一些颜色的饱和度（纯度）可能远远超过显示能力。然而，就像文艺复兴时期的画家一样，摄影、电视和电影确实是法产生了令人信服的原始场景的感性相似性。通过利用人类视觉系统的某些特性，这一成就是可能的。
The visual system compensates for differences in absolute luminance, an ability called adaptation. Due to this ability, a reproduction of an outdoor scene shown on a screen in a dim room can produce a similar perception as the original scene,although the luminance of the reproduction is less than 1% of the original. However,the compensation provided by adaptation is imperfect. At lower luminance levels the perceived contrast is decreased (the Stevens effect), as is the perceived “colorfulness”(the Hunt effect).
视觉系统补偿绝对亮度的差异，这种能力叫做适应。由于这种能力，在昏暗房间的屏幕上显示的室外场景的再现可以产生与原始场景相似的感觉，尽管再现的亮度小于原始的1%。然而，适应所提供的补偿是不完善的。在较低的亮度水平下，感觉到的对比度降低(史蒂文斯效应)，感觉到的“色彩丰富”(亨特效应)也是如此。
Other factors affect actual or perceived contrast of the reproduction. The surround of the display (the luminance level outside the display rectangle, e.g., the brightness of the room lighting) may increase or decrease perceived contrast (the BartlesonBreneman effect). Display flare, which is unwanted light added to the displayed image via display imperfections or screen reflections, reduces the actual contrast of the image,often to a considerable degree. These effects mean that if we want to preserve a similar perceptual effect as the original scene, we must boost the contrast and saturation of the display-referred image values [1418].
他因素影响再现的实际或感知对比度。显示器的周围环境(显示矩形外的亮度水平，例如室内照明的亮度)可能会增加或减少感知的对比度(BartlesonBreneman效应)。显示器眩光是通过显示器缺陷或屏幕反射添加到显示图像中的不需要的光，通常会在相当大的程度上降低图像的实际对比度。这些效应意味着，如果我们想要保持与原始场景相似的感知效果，我们必须提高显示参考图像值的对比度和饱和度[1418]。
However, this increase in contrast exacerbates an existing problem. Since the dynamic range of the scene is typically much larger than that of the display, we have to choose a narrow window of luminance values to reproduce, with values above and below that window being clipped to black or white. Boosting the contrast further narrows this window. To partially counteract the clipping of dark and bright values,a soft roll-off is used to bring some shadow and highlight detail back.
然而，这种对比度的增加加剧了现有的问题。由于场景的动态范围通常比显示器的动态范围大得多，我们必须选择一个窄的亮度值窗口来再现，该窗口上下的值被剪切为黑色或白色。提高对比度进一步缩小了这个窗口。为了部分抵消暗值和亮值的剪切，使用柔和的衰减来恢复一些阴影和高光细节。
All this results in a sigmoid (s-shaped) tone-reproduction curve, similar to the one provided by photochemical film [1418]. This is no accident. The properties of photochemical film emulsion were carefully adjusted by researchers at Kodak and other companies to produce effective and pleasing image reproduction. For these reasons, the adjective “filmic” often comes up in discussions of tone mapping.
所有这些导致了s形色调再现曲线，类似于光化学胶片提供的曲线[1418]。这不是偶然的。柯达和其他公司的研究人员仔细调整了光化学胶片感光乳剂的特性，以产生有效和令人满意的图像复制。由于这些原因，形容词“电影的”经常出现在色调映射的讨论中。
The concept of exposure is critical for tone mapping. In photography, exposure refers to controlling the amount of light that falls on the film or sensor. However,in rendering, exposure is a linear scaling operation performed on the scene-referred image before the tone reproduction transform is applied. The tricky aspect of exposure is to determine what scaling factor to apply. The tone reproduction transform and exposure are closely tied together. Tone transforms are typically designed with the expectation that they will be applied to scene-referred images that have been exposed a certain way.
曝光的概念对于色调映射至关重要。在摄影中，曝光是指控制落在胶片或传感器上的光量。然而，在渲染中，曝光是在应用色调再现变换之前对场景参考图像执行的线性缩放操作。暴露的棘手之处在于确定应用什么比例因子。色调再现转换和曝光是紧密联系在一起的。色调变换通常被设计为期望它们将被应用于以某种方式曝光的场景引用图像。
The process of scaling by exposure and then applying a tone reproduction transform is a type of global tone mapping, in which the same mapping is applied to all pixels. In contrast, a local tone mapping process uses different mappings pixel to pixel,based on surrounding pixels and other factors. Real-time applications have almost exclusively used global tone mapping (with a few exceptions [1921]), so we will focus on this type, discussing first tone-reproduction transforms and then exposure.
通过曝光进行缩放然后应用色调再现变换的过程是一种全局色调映射，其中相同的映射应用于所有像素。相反，局部色调映射过程基于周围的像素和其他因素，使用不同的像素到像素的映射。实时应用程序几乎只使用全局色调映射(除了少数例外[1921])，所以我们将集中讨论这种类型，首先讨论色调再现转换，然后讨论曝光。
It is important to remember that scene-referred images and display-referred images are fundamentally different. Physical operations are only valid when performed on scene-referred data. Due to display limitations and the various perceptual effects we have discussed, a nonlinear transform is always needed between the two image states.
重要的是要记住以场景为参考的图像和以显示器为参考的图像是根本不同的。物理操作仅在对场景引用的数据执行时有效。由于显示器的限制和我们已经讨论过的各种感知效果，在两种图像状态之间总是需要非线性变换。
色调再现变换
Tone reproduction transforms are often expressed as one-dimensional curves mapping scene-referred input values to display-referred output values. These curves can be applied either independently to R, G, and B values or to luminance. In the former case, the result will automatically be in the display gamut, since each of the displayreferred RGB channel values will be between 0 and 1. However, performing nonlinear operations (especially clipping) on RGB channels may cause shifts in saturation and hue, besides the desired shift in luminance. Giorgianni and Madden [537] point out that the shift in saturation can be perceptually beneficial. The contrast boost that most reproduction transforms use to counteract the Stevens effect (as well as surround and viewing flare effects) will cause a corresponding boost in saturation, which will counteract the Hunt effect as well. However, hue shifts are generally regarded as undesirable,and modern tone transforms attempt to reduce them by applying additional RGB adjustments after the tone curve.
色调再现变换通常被表示为将场景参考输入值映射到显示器参考输出值的一维曲线。这些曲线可以独立应用于R、G和B值，也可以应用于亮度。在前一种情况下，结果将自动在显示色域中，因为每个显示参考的RGB通道值将在0和1之间。但是，在RGB通道上执行非线性操作(尤其是裁剪)可能会导致饱和度和色调的偏移，以及所需的亮度偏移。Giorgianni和Madden [537]指出，饱和度的变化在感觉上是有益的。大多数再现变换用来抵消史蒂文斯效应(以及环绕和观看眩光效应)对比度增强将导致饱和度的相应增强，这也将抵消亨特效应。然而，色调偏移通常被认为是不期望的，并且现代色调转换试图通过在色调曲线之后应用额外的RGB调整来减少它们。
By applying the tone curve to luminance, hue and saturation shifts can be avoided(or at least reduced). However, the resulting display-referred color may be out of the display’s RGB gamut, in which case it will need to be mapped back in.
通过将色调曲线应用于亮度，可以避免(或至少减少)色调和饱和度偏移。但是，产生的显示器参考颜色可能超出显示器的RGB色域，在这种情况下，需要将其映射回显示器。
One potential issue with tone mapping is that applying a nonlinear function to scene-referred pixel colors can cause problems with some antialiasing techniques. The issue (and methods to address it) are discussed in Section 5.4.2.
色调映射的一个潜在问题是，将非线性函数应用于场景参考像素颜色会导致某些抗锯齿技术出现问题。第5.4.2节讨论了该问题(以及解决该问题的方法)。
The Reinhard tone reproduction operator [1478] is one of the earlier tone transforms used in real-time rendering. It leaves darker values mostly unchanged, while brighter values asymptotically go to white. A somewhat-similar tone-mapping operator was proposed by Drago et al. [375] with the ability to adjust for output display luminance, which may make it a better fit for HDR displays. Duiker created an approximation to a Kodak film response curve [391, 392] for use in video games. This curve was later modified by Hable [628] to add more user control, and was used in the game Uncharted 2. Hable’s presentation on this curve was influential, leading to the “Hable filmic curve” being used in several games. Hable [634] later proposed a new curve with a number of advantages over his earlier work.
赖因哈德色调再现运算符[1478]是实时渲染中使用的早期色调变换之一。它使较暗的值基本保持不变，而较亮的值逐渐变为白色。Drago等人[375]提出了一种有点类似的色调映射算子，能够调整输出显示器亮度，这可能使其更适合HDR显示器。杜克创建了一个用于视频游戏的柯达胶片响应曲线的近似值[391，392]。这条曲线后来被Hable [628]修改，增加了更多的用户控制，并在游戏《神秘海域2》中使用。哈布尔对这条曲线的介绍很有影响力，导致“哈布尔电影曲线”在几个游戏中被使用。Hable [634]后来提出了一种新的曲线，与他早期的工作相比，它有许多优点。
Day [330] presents a sigmoid tone curve that was used on titles from Insomniac Games, as well as the game Call of Duty: Advanced Warfare. Gotanda [571, 572] created tone transforms that simulate the response of film as well as digital camera sensors. These were used on the game Star Ocean 4 and others. Lottes [1081] points out that the effect of display flare on the effective dynamic range of the display is significant and highly dependent on room lighting conditions. For this reason, it is important to provide user adjustments to the tone mapping. He proposes a tone reproduction transform with support for such adjustments that can be used with SDR as well as HDR displays.
Day [330]呈现了一种sigmoid色调曲线，这种曲线曾用于失眠游戏以及游戏《使命召唤:高级战争》的标题。Gotanda [571，572]创造了模拟胶片和数码相机传感器响应的色调变换。这些被用在游戏《星际海洋4》和其他游戏上。Lottes [1081]指出，显示器耀斑对显示器有效动态范围的影响是显著的，并且高度依赖于室内照明条件。因此，为用户提供色调映射调整非常重要。他提出了一种支持这种调整的色调再现转换，可以用于SDR以及HDR显示器。
The Academy Color Encoding System (ACES) was created by the Science and Technology Council of the Academy of Motion Picture Arts and Sciences as a proposed standard for managing color for the motion picture and television industries.The ACES system splits the scene-to-screen transform into two parts. The first is the reference rendering transform (RRT), which transforms scene-referred values into display-referred values in a standard, device-neutral output space called the output color encoding specification (OCES). The second part is the output device transform(ODT), which converts color values from OCES to the final display encoding. There are many different ODTs, each one designed for a specific display device and viewing condition. The concatenation of the RRT and the appropriate ODT creates the overall transform. This modular structure is convenient for addressing a variety of display types and viewing conditions. Hart [672] recommends the ACES tone mapping transforms for applications that need to support both SDR and HDR displays.
学院色彩编码系统(ACES)是由美国电影艺术与科学学院的科学技术委员会创建的，作为管理电影和电视行业色彩的建议标准。ACES系统将场景到屏幕的转换分成两部分。第一个是参考渲染转换(RRT)，它将场景参考值转换为标准的、设备中立的输出空间(称为输出颜色编码规范(OCES))中的显示参考值。第二部分是输出设备转换(ODT)，它将颜色值从OCES转换为最终的显示编码。有许多不同的ODT，每一种都是为特定的显示设备和观看条件而设计的。RRT和适当的ODT的连接创建了整体变换。这种模块化结构便于处理各种显示器类型和观看条件。Hart [672]为需要支持SDR和HDR显示的应用推荐了ACES色调映射转换。
Although ACES was designed for use in film and television, its transforms are seeing growing use in real-time applications. ACES tone mapping is enabled by default in the Unreal Engine [1802], and it is supported by the Unity engine as well [1801].Narkowicz gives inexpensive curves fitted to the ACES RRT with SDR and HDR ODTs [1260, 1261], as does Patry [1359]. Hart [672] presents a parameterized version of the ACES ODTs to support a range of devices.
虽然ACES是为电影和电视设计的，但它的变形在实时应用中的使用越来越多。ACES色调映射在Unreal引擎中默认启用[1802]，Unity引擎也支持它[1801]。Narkowicz用SDR和HDR ODT[1260，1261]给出了适合ACES RRT的廉价曲线，Patry [1359]也是如此。Hart [672]提出了ACES ODTs的参数化版本，以支持一系列器件。
Tone mapping with HDR displays requires some care, since the displays will also apply some tone mapping of their own. Fry [497] presents a set of tone mapping transforms used in the Frostbite game engine. They apply a relatively aggressive tone reproduction curve for SDR displays, a less-aggressive one for displays using the HDR10 signal path (with some variation based on the peak luminance of the display),and no tone mapping with displays using the Dolby Vision path (in other words,they rely upon the built-in Dolby Vision tone mapping applied by the display). The Frostbite tone reproduction transforms are designed to be neutral, without significant contrast or hue changes. The intent is for any desired contrast or hue modifications to be applied via color grading (Section 8.2.3). To this end, the tone reproduction transform is applied in the ICTCP color space [364], which was designed for perceptual uniformity and orthogonality between the chrominance and luminance axes. The Frostbite transform tone-maps the luminance and increasingly desaturates the chromaticity as the luminance rolls off to display white. This provides a clean transform without hue shifts.
HDR显示器的色调映射需要一些小心，因为显示器也会应用它们自己的一些色调映射。Fry [497]提出了一组在冻伤游戏引擎中使用的色调映射变换。它们对SDR显示器应用相对积极的色调再现曲线，对使用HDR10信号路径的显示器应用较不积极的曲线(根据显示器的峰值亮度有一些变化)，对使用Dolby Vision路径的显示器不应用色调映射(换言之，它们依赖显示器应用的内置Dolby Vision色调映射)。冻伤色调再现转换设计为中性，没有明显的对比度或色调变化。目的是通过颜色分级(第8.2.3节)应用任何所需的对比度或色调修改。为此，在ICTCP色彩空间[364]中应用色调再现变换，这是为了色度和亮度轴之间的感知均匀性和正交性而设计的。冻伤变换对亮度进行色调映射，并随着亮度衰减以显示白色而逐渐降低色度的饱和度。这提供了没有色调偏移的清晰变换。
Ironically, following issues with assets (such as fire effects) that were authored to leverage the hue shifts in their previous transform, the Frostbite team ended up modifying the transform, enabling users to re-introduce some degree of hue shifting to the display-referred colors. Figure 8.15 shows the Frostbite transform compared with several others mentioned in this section.
具有讽刺意味的是，在之前的转换中，资源(如火焰效果)被创作为利用色调偏移，在出现问题后，Frostbite团队最终修改了转换，使用户能够重新引入某种程度的色调偏移到显示器引用的颜色。图8.15显示了冻伤变换与本节提到的其他几种变换的比较。
Figure 8.15. A scene with four different tone transforms applied. Differences are primarily seen in the circled areas, where scene pixel values are especially high. Upper left: clipping (plus sRGB OETF); upper right: Reinhard [1478]; lower left: Duiker [392]; lower right: Frostbite (hue-preserving version) [497]. The Reinhard, Duiker, and Frostbite transforms all preserve highlight information lost by clipping. However, the Reinhard curve tends to desaturate the darker parts of the image [628, 629],while the Duiker transform increases saturation in darker regions, which is sometimes regarded as a desirable trait [630]. By design, the Frostbite transform preserves both saturation and hue, avoiding the label hue shift that can be seen in the lower left circle on the other three images. (Images courtesy of c 2018 Electronic Arts Inc.)
图8.15。应用了四种不同色调变换的场景。差异主要出现在圆圈区域，那里的场景像素值特别高。左上:剪报(加上sRGB OETF)；右上:赖因哈德[1478]；左下:杜克[392]；右下:冻伤(保色版)[497]。“赖因哈德”、“杜克”和“冻伤”变换都保留了因剪裁而丢失的高光信息。然而，赖因哈德曲线往往会降低图像较暗部分的饱和度[628，629]，而杜克变换会增加较暗区域的饱和度，这有时被视为一种理想的特性[630]。通过设计，冻伤变换保留了饱和度和色调，避免了在其他三个图像的左下角圆圈中可以看到的强烈色调偏移。(图片由c 2018电子艺界有限公司提供)
曝光
A commonly used family of techniques for computing exposure relies on analyzing the scene-referred luminance values. To avoid introducing stalls, this analysis is typically done by sampling the previous frame.
一种常用的计算曝光的技术依赖于对场景参考亮度值的分析。为了避免引入停顿，这种分析通常通过对前一帧进行采样来完成。
Following a recommendation by Reinhard et al. [1478], one metric that was used in earlier implementations is the log-average scene luminance. Typically, the exposure was determined by computing the log-average value for the frame [224, 1674]. This log-average is computed by performing a series of down-sampling post-process passes, until a final, single value for the frame is computed.
根据赖因哈德等人[1478]的建议，早期实施中使用的一个度量是对数平均场景亮度。通常，通过计算帧的对数平均值来确定曝光[224，1674]。通过执行一系列下采样后处理过程来计算该对数平均值，直到计算出该帧的最终单个值。
Using an average value tends to be too sensitive to outliers, e.g., a small number of bright pixels could affect the exposure for the entire frame. Subsequent implementations ameliorated this problem by instead using a histogram of luminance values.Instead of the average, a histogram allows computing the median, which is more robust.Additional data points in the histogram can be used for improved results. For example, in The Orange Box by Valve, heuristics based on the 95th percentile and the median were used to determine exposure [1821]. Mittring describes the use of compute shaders to generate the luminance histogram [1229].
使用平均值往往对异常值过于敏感，例如，少量亮像素会影响整个帧的曝光。随后的实现通过使用亮度值的直方图来改善这个问题。直方图允许计算中值，而不是平均值，这更可靠。直方图中的额外数据点可用于改善结果。例如，在阀的橙色框中，基于第95百分位和中位数的试探法用于确定暴露量[1821]。Mittring描述了使用计算着色器来生成亮度直方图[1229]。
The problem with the techniques discussed so far is that pixel luminance is the wrong metric for driving exposure. If we look at photography practices, such as Ansel Adams’ Zone System [10] and how incident light meters are used to set exposure,it becomes clear that it is preferable to use the lighting alone (without the effect of surface albedo) to determine exposure [757]. Doing so works because, to a first approximation, photographic exposure is used to counteract lighting. This results in a print that shows primarily the surface colors of objects, which corresponds to the color constancy property of the human visual system. Handling exposure in this way also ensures that correct values are passed to the tone transform. For example, most tone transforms used in the film or television industry are designed to map the exposed scene-referred value 0.18 to the display-referred value 0.1, with the expectation that 0.18 represents an 18% gray card in the dominant scene lighting [1418, 1602].
到目前为止讨论的技术的问题是像素亮度是驱动曝光的错误度量。如果我们观察摄影实践，如安塞尔·亚当斯的区域系统[10]以及如何使用入射测光表来设置曝光，很明显，最好是单独使用照明(没有表面反照率的影响)来确定曝光[757]。这样做是可行的，因为，在第一个近似值中，照相曝光被用来抵消照明。这产生了主要显示物体表面颜色的印刷品，这对应于人类视觉系统的颜色恒常性。以这种方式处理曝光还可以确保将正确的值传递给色调转换。例如，电影或电视行业中使用的大多数色调转换旨在将曝光场景参考值0.18映射到显示参考值0.1，预期0.18代表主导场景照明中的18%灰色卡[1418，1602]。
Although this approach is not yet common in real-time applications, it is starting to see use. For example, the game Metal Gear Solid V: Ground Zeroes has an exposure system based on lighting intensity [921]. In many games, static exposure levels are manually set for different parts of the environment based on known scene lighting values. Doing so avoids unexpected dynamic shifts in exposure.
尽管这种方法在实时应用程序中还不常见，但它已经开始得到应用。例如，游戏《合金装备V:归零地》有一个基于光照强度的曝光系统[921]。在许多游戏中，静态曝光水平是根据已知的场景照明值为环境的不同部分手动设置的。这样做可以避免意外的曝光动态变化。