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基于TCS230颜色传感器的色彩识别器的设计 外文翻译


Sensing color with the TAOS TCS230
The TAOS TCS230 is a small, highly integrated color sensing device packaged in a clear plastic 8-pin SOIC. It reports, as analog frequency, the amount of shortwave (blue), mediumwave (green), longwave (red), and wideband (white) optical power incident onto the device. It can be used in a variety of color sensing applications. Details of the device can be found in its datasheet. This white paper details the concepts and calculations involved in color sensing using the TCS230. We will use the ColorChecker chart as an optical stimulus to work through a numerical example of color sensing. The chart, depicted in Figure 1, is manufactured and distributed by GretagMacbeth. The chart measures approximately 13 inches by 9 inches (330 mm by 230 mm); it contains 24 colored patches arranged in a 6 by 4 array. Figures 2 through 5 overleaf show the spectral reflectance of the patches in each of the four rows of the chart – that is, the fraction of incident light that is reflected (with respect to an ideal diffuse reflector), as a function of wavelength from 350 nm to 750 nm.

Figure 1 The ColorChecker contains 18 colored patches and a 6-step gray series.

Figure 2 ColorChecker spectra, top row.

Figure 3 ColorChecker spectra, second row.

Figure 4 ColorChecker spectra, third row.

Figure 5 ColorChecker spectra, bottom row (neutral series)

Figure

6

Cone

sensitivities

of

cone

photoreceptors

are

shown.

Theshortwave-sensitivephotoreceptors are much less sensitive than the other two types. The responses of the mediumwave and longwave photoreceptors have a great deal of overlap. Vision is not sensitive to the precise wavelength of the stimulus: Whatatters is optical power integrated under each response curve.

Introduction to color vision
Photoreceptor cells called cones in the retina are responsible for human color vision. There are three types of cone cells, sensitive to longwave, mediumwave, and shortwave radiation within the electro-magnetic spectrum between about 400 nm and 700 nm. Because the cone sensitivities are very roughly in the parts of the spectrum that appear red, green, and blue, color scientists denote the cell types as ρ,γ , and , the Greek letters for r, g, and b. (To denote the sensors R, G, and B would wrongly suggest a closer correspondence.) Estimates of the spectral response of the cone types are graphed in Figure 6 above. Light in the physical world can be characterized by spectral power distributions (SPDs). Colored objects can be characterized by spectral reflectance curves, such as those of the ColorChecker. However, vision is insensitive to the exact wavelength of a stimulus: According to the modern theory of color science, all that matters is the integral of optical power underneath each response curve. That there are exactly three types of cone cells leads to the property of trichromaticity: Three components are necessary and sufficient to characterize color. Some people might use the phrase “color as sensed by the eye,” but I con-sider that qualifier to be redundant at best, and misleading at worst: Color is defined by vision, so there is no need to use the qualifying phrase “as sensed by the eye,” or to use the adjective visible when

referring to color.

Overview of CIE Colorimetry
The spectral responses of the cone cells that I graphed in Figure 6 were unavailable to researchers in the 1920s. Researchers at the time used psychophysical experiments, such as the famous color matching experiment, to tease out the data. The CIE is the international body responsible for color standards.In1931, that organization adopted the color matching functions denoted x (λ ), y (λ ), and z (λ ), graphed in Figure 7.

Figure 7 CIE 1931, 2°color-matching functions. A camera with 3 sensors must have these spectral response curves, or linear combinations of them, in order to capture all colors. However, practical considerations make this difficult. These analysis functions are not comparable to spectral power distributions!

Weighting a physical SPD under each of these three curves (that is, forming the wavelength-by-wavelength product), and summing the results, forms a triple of three numbers, denoted X, Y, and Z. In continuous mathematics, three integrals need to be computed; in discrete math, a matrix product is sufficient. The X, Y, and Z tristim-ulus values characterize color. They are linear-light quantities, propor-tional to optical power, that incorporate the wavelength sensitivity of human vision. The Y value is luminance, which is ordinarily expressed in units of candela per meter squared (cd· m-2). If you are measuring reflectance, the reflected tristimulus values depend upon the spectral characteristics of the illuminant, and their amplitudes scale with the power of the illumination. Relative luminance is the ratio of reflected

luminance to the luminance of the illumination; it is also known as the luminance factor.

Figure 8 SPDs of various illuminants are graphed here. Illuminant A, shown in orange, is representative of tungsten light sources; it is deficient in shortwave power, and may cause errors in sensing blue colors. The blue line graphs the SPD of a Nichia white LED. There is a peak in the blue portion of the spectrum: Uncorrected, the sensor would report excessive blue values. The other four lines represent CIE standard illuminants C, D50, D55, and D65.

In many applications, tristimulus signals (including luminance) scale with the illumination, and are otherwise uninteresting in themselves. What is more interesting is the ratios among them, which characterize color disregarding luminance. The CIE has standardized the projective transformation of Equation 1, in the margin, to transform [X, Y, Z] values into a pair of [x, y] chromaticity coordinates that represent color disregarding luminance. These coordinates are suitable for plotting in two dimensions on a chromaticity diagram. x = /( + + ) y = /( + + ) Eq 1 Chromaticity coordinates

Illumination
A nonemissive object must be illuminated in order to be visible. The SPD reflected from an illuminated object is the wavelength-by-wave-length product of the illuminant’s SPD and the spectral reflectance of the object. Before light reaches the eye, the interaction among light sources and materials takes place in the spectral domain, not in the domain of trichromaticity. To accurately model these interactions

requires spectral computations. When applying the TCS230, attention must be paid to the spectral content of the illumination and to poten-tial interaction between the illumination and the samples to be sensed. Generally, the less spiky the spectra, the better. Figure 8 graphs several illuminants. Your application may involve sensing color, in which case the preceding description applies. However, some applications of the TCS230 involve not so much estimating color as seen by the eye but rather sensing physical parameters associated with optical power in the visible range. In such applications, to approximate the visual response may not be the best approach: It may be more effective to take a more direct approach to estimating the parameters of the underlying physical process.

The Color Checker
Equipped with knowledge of how spectra are related to colors, the plotting of chromaticity coordinates, and the dependence of colors upon illumination, we can return to the ColorChecker. GretagMac-beth doesn’t publish or guarantee the spectral composition of the patches of the ColorChecker. However, nominal CIE [X, Y, Z] values are published. The patches in the bottom row of the ColorChecker contain neutral colors; the numeric notations in the legends of Figure 5 reflect one tenth of the lightness (L*) values of those patches. Thespectra graphed on pages 2 and 3 represent the physical wave-length-by-wavelength reflectance of the patches. These spectral reflec-tances have been measured by color measurement instrument called a spectrophotometer. If you had access to a light source having perfectly even distribution of power across the visible spectrum, then the reflectance curves graphed here could simply be scaled to repre-sent the reflectance in your application. Practical light sources do not have perfectly even spectral distributions, so compensation is neces-sary: You must compute the wavelength-by-wavelength product of the illuminant’s SPD with the spectral reflectance of the chart. We will first calculate the CIE [X, Y, Z] values from the chart. (These values should agree with the figures provided by Gretag.) Then we will calculate the [R, G, B] values that will be detected by a TCS230. To calculate CIE [X, Y, Z], we take the 31× matrix representing the color 3 matching functions (CMFs) of the CIE Standard Observer, and perform a matrix product with 31 spectral response values as corrected for illumination. This produces the [X, Y, Z] tristimulus values. When chromaticity coordinates [x, y] are computed

from [X, Y, Z] through the projective transform in Equation 1, then plotted, the chromaticity diagram in Figure 9 results. The horseshoe-shaped figure, closed at the bottom, contains all colors: Every non-negative spectral distribution produces an [x, y] pair that plots within this region. The lightly-shaded triangle shows the region containing all colors that can be produced by an additive RGB system using sRGB (Rec. 709) primary colors. This region typifies video and desktop computing (sRGB). The points plotted in Figure 9 are the colors of the ColorChecker. White and gray values are clustered near the center of the chart.

Figure 9 Coordinates of ColorChecker patches are graphed on the CIE [x, y] chromaticity diagram. The horseshoe encloses all colors; the triangle encloses the colors that can be represented in video (Rec. 709) and in desktop computing (sRGB).

The TCS230
Figure 10 shows the responses of the four channels of the TCS230. The black curve shows the response of the unfiltered sensor elements. The red, green, and blue curves show the responses of the longwave-sensitive, mediumwave-sensitive, and shortwave-sensitive elements respectively. As I mentioned on page 5, the CIE model of color vision involves inte-grating an SPD under the X(λ), Y(λ), and Z(λ) color matching func-tions (graphed in Figure 7), producing X, Y, and Z values. To use the TCS230 to estimate color we perform an analogous calculation, but using the TCS230 sensitivity functions instead of the CIE CMFs: We integrate the SPD under the TCS230’s sensitivity curves, and produce R,

G, and B values. The device R, G, and B values will depend upon several factors: the spectral content of the illuminant, the spectral reflectance of the sample, the spectral attenuation of any intervening optical components (such as the lens), and finally, the spectral response functions of the TCS230. The various spectral phenomena are modelled by computing wavelength-by-wavelength products.

Figure 10 TCS230 spectral sensitivities are graphed here. The red, green, and blue channels are graphed in the corresponding colors; the gray line reflects the sensitivity of the clear (unfiltered) channel. Because these responses are different from the CIE standard observer, the values reported by the TCS230 are not colorimetric. However, suitable signal processing yields color information that is sufficiently accurate for many industrial applications.

Owing to the fact that the TCS230 is sensitive to infrared light (having wavelengths above 700 nm), and the fact that most light sourcesproduce power in the infrared region, typical applications include an IR cut filter in front of the TCS230. Figure 11 overleaf shows the response of a typical IR cut filter. To form a more accurate estimate of color requires processing the raw TCS230 R, G, and B values through a linear 3× matrix whose coeffi-cients are optimized with 3 respect to the spectrum of the illuminant, the spectral response of intervening optical components, and theresponse curves of the TCS230. The data processing operation can be represented in matrix form as follows: x=M?tEq2 The symbol t represents a three-element vector containing the device values captured from a color patch. M represents the 3× color correction matrix that we will 3 apply to these values through matrix multiplication, denoted by the ? symbol. The

symbol x represents the resulting vector of estimated [X, Y, Z] values. We can use matrix notation to symbolize processing a set of three color patches at once, by arranging the three sets of device values into successive columns of a 3× 3 matrix T. Successive rows of T contain red, green, and blue data respectively. Upon matrix multiplication by M, the columns of the resulting matrix X contain XYZ values of the successive samples; the rows of X contain X, Y, and Z values respec-tively. One equation expresses the mapping of three patches at once: X=M?TEq3 Given a matrix T whose columns contain three sets of device samples, and a matrix X containing the corresponding set of three ideal XYZ triples, there is a unique matrix M that maps from T to X. It is foundby computing the matrix inverse of T, then computing the matrix product (by premultiplication) with X: M=X ? T ?1 Eq 4 The resulting 3× color correction matrix M exactly maps the each of the chosen 3 three sets of device values to the corresponding set of tris-timulus values. It is not necessary to invert matrices at the time of sensing! The matrix M can be computed in advance, based upon the samples that are expected to be presented to the sensor in the intended application. To process three device values upon sensing a sample, all that is necessary is computation of the matrix product of Equation 3. A color correction matrix that produces good results across more than three samples can be computed through a numerical optimization procedure. When this is done, no particular sample is likely to map exactly to its ideal tristimulus set, but a linear matrix can be constructed that minimizes the error across a range of samples (where the error is measured in a least-squares sense). The color correction operation is still accomplished exactly as in Equation 2.

基于 TAOS 公司的 TCS230 的颜色感应
TAOS 公司的 TCS230 是一个小的、高度集成、8 引脚、SOIC 封装的色彩传 感装置。它以模拟频率的方式输出短波(蓝色)、中波(绿色)、长波(红色)、 宽带(白)光功率的事件数量。它可用于各种色彩感应应用领域。该设备的详细 资料中可以找到它的数据表。本白皮书详细介绍了色彩感应的概念和使用 TCS230 参与计算。 我们将使用一个光学刺激方案的 ColorChecker 图表工作,通过检测的色彩 数值例子。下图,在图 1 所示,是由 GretagMacbeth 生产和分配。图表长约 13 英寸,9 英寸(330 毫米×230 毫米),它包含了 64 阵列安排 24 色斑。到 5 背 面图 2 显示了在图表的每一行四个补丁的光谱反射-即入射光被反射的那部分 (相 对于一个理想的漫反射)作为波长从 350 功能,纳米到 750 纳米。

图 1 ColorChecker 色补丁包含 18 个和 6 步灰色系列

图 2 ColorChecker 谱,第一行

图 3 ColorChecker 谱,第二排

图 4 ColorChecker 光谱,第三行

图 5 ColorChecker 谱,底排(中性系列)

图 6 锥锥光感受器敏感性所示。 短波敏感的感光细胞远远低于其他两种类型的敏感。 中 波和长波的感光细胞的反应有很大的重叠。视觉是不敏感,准确的刺激波长:什么是光功率 下 atters 每个响应曲线综合。

色觉简介
所谓感光细胞在视网膜视锥细胞是人类色彩视觉负责。 内有电磁频谱三种类 型的视锥细胞,敏感的长波,中波,短波辐射及约 400 纳米之间和 700 纳米。由 于锥敏感性在频谱的部分出现红色,绿色和蓝色的很粗糙,色彩科学家记为ρ , γ ,以及希腊字母为 R,G 细胞的类型,和 b (为了表示对传感器的 R,G,和 B 将错误建议更密切的对应关系。的圆锥体的谱反应的估计是在上面绘制图 6。 ) 在物理世界的光,其特征是光谱功率分布(结构化产品说明)。彩色对象, 其特征是反射光谱曲线,如在的 ColorChecker 的。然而,视觉不敏感,对刺激 精确波长: 根据现代色彩科学理论, 最重要的事情是在每个响应曲线光功率积分。 这恰有三种视锥细胞类型导致 trichromaticity 财产:三个组成部分是必要的和足 够的特征颜色。有些人可能会用“感觉到的颜色的眼睛,“但我了 CON - Sider 的限定词是多余的,充其量,误导在最坏的情况:色彩是由视觉定义,所以没有 必要使用合格的短语“因为感觉到的眼睛,“或使用的形容词时可见指颜色。

概述 Cie 的比色法
锥细胞, 我在图 6 绘制光谱反应无法在 20 世纪 20 年代的研究人员。当时的 研究人员使用,如著名的配色实验心理实验,以梳理出的数据。在 CIE 是国际 机构,颜色标准。 In1931,该组织通过了颜色匹配函数记×(λ )和 Y(λ ) 和 z(λ ),在图 7 绘制。

图 7 Cie 公司 1931 年 2 °色彩匹配功能。一个 3 传感器的相机必须具备以下的光谱响 应曲线,或它们的线性组合,以捕捉所有的颜色。然而,实际的考虑作出这一困难。这些分 析功能比不上光谱功率分布!

加权根据这三个曲线每个物理社民党(即,形成了波长的波长产品) ,总结 的结果,形成了三个数字三倍,记在连续数学的 X,Y 和 Z,三积分需要计算, 在离散数学,矩阵产品就足够了。在 X,Y 和 Z tristim-汗国值特征的颜色。它们 是线性光量,正比于光学力量,即纳入人类视觉波长的敏感性。Y 值是亮度,这 是通常在每平方米坎德拉(光碟?米- 2)为单位表示。如果你是测量反射率,反 射的三刺激值取决于对光源的光谱特性,其幅度与规模的照明电源。相对亮度的 反射亮度的照明亮度的比值,它也被称为亮度因素。

图 8 是绘制各种光源结构化产品说明这里。 A 光源,以橙色显示,钨光源是代表,它 是在短波力量不足,可能会导致感应蓝色的错误。蓝线图的社民党的日亚白光 LED。有一 个光谱的蓝色部分高峰: 裸时, 传感器会举报过度蓝色值。 另外四线代表 Cie 的 ? D50 的, , D55 和 D65 的标准光源。

在许多应用中, 三刺激信号 (包括亮度) 与照明规模, 并应在其他无趣自己。 什么是更有趣的是它们之间的比例,所特有的颜色无视亮度。在 CIE 有标准化 的公式 1 中的保证金射影变换,将其转化为一对[的 X,Y 和 Z]值[的 x,y]表示 颜色的色度坐标无视亮度。这些坐标在二维色度图上绘制合适。 x = /( + + ) y = /( + + )
公式 1 色度坐标

照明
一个 nonemissive 对象必须是为了照明可见。社民党从一照物体反射的波长 是按波长的光源产品的社民党和对象的光谱反射率。 光线到达之前光源和材料之 间的眼睛,相互作用发生在谱域的地方,不是在 trichromaticity 域。为了准确地 需要这些相互作用的光谱模型计算。当应用 TCS230,必须注意对光照光谱内容 和电位- TiAl 金属间的照明和样品被觉察的互动。一般来说,越尖的光谱,就越 好。图 8 图数光源。 您的应用程序可能涉及敏感的颜色, 在这种情况下, 前面的说明适用。 然而, 一些应用涉及 TCS230 没有这么多的眼睛所看到的, 而是传感在可见光范围内光 功率相关的物理参数估计的颜色。在这种应用中,近似的视觉反应可能不是最好 的方法:它可能是更有效地采取更直接的方法来估计底层物理过程的参数。

色彩检查
如何光谱与颜色相关的知识装备,绘制色度坐标,对照明色彩的依赖,我们 可以返回的 ColorChecker。GretagMac- Beth 没公布或保证的 ColorChecker 补丁 的光谱成分。然而,标称 Cie 的[的 X,Y 和 Z]值被公布。在底行的 ColorChecker 补丁包含中性色, 在图 5 中的神话传说中的数字符号反映十分之一的亮度 (长*) 值的这些补丁。 光谱绘制 2 和第 3 页上表示物理波长由波长的反射率的补丁。 这些光谱反射 已测色仪测量 tances 称为分光光度计。 如果你有机会访问光源具有完全的权力分 配,甚至在整个可见光谱,反射率曲线则绘制在这里可以简单地扩展到 repre, 发送应用程序中的反射率。实践没有光源的光谱分布十分均匀,因此补偿 neces萨利:你必须计算与图表的光谱反射的光源的波长社民党按波长的产品。 我们将首先从图表计算在 CIE[的 X,Y 和 Z]值。(这些值应同意 Gretag 提 供的数字。)然后我们将计算[的 R,G,B]的,将由一 TCS230 检测值。

为了计算 Cie 公司[的 X,Y 和 Z],我们把 31 ×3 矩阵代表职能的配色在 CIE 标准观察者(CMFs),并执行一个有 31 个光谱响应矩阵产品价值为照明纠 正。这将产生的[x,Y,Z 轴]三刺激值。当色度坐标,通过投影[的 x,y]是来自 [的 X,Y 和 Z]变换计算公式 1,然后绘制,结果如图 9 色度图。马蹄状的人物, 在底部封闭,包含所有的颜色:每个非负的光谱分布产生[的 x,y]对本地区范围 内的阴谋。拥有轻成荫的三角显示包含所有的地区,可以通过一个附加的 RGB 使用的 sRGB 系统(建议 709)原色产生颜色。这个地区 typifies 视频和桌面计 算(的 sRGB)。这些点绘制在图 9 是本的 ColorChecker 的颜色。白色和灰色值 都聚集在附近的图表的中心。

图 9 ColorChecker 补丁坐标上绘制在 CIE 是[的 x, y]色度图。 马蹄形包围了所有的颜色; 包围的三角形代表可以在视频(建议 709)和桌面计算(的 sRGB)的颜色。

TCS230
图 10 显示了 TCS230 的四个通道的反应。黑色曲线显示了未经过滤的传感 器元件的响应。红色,绿色和蓝色的曲线显示了长波敏感,中波敏感,短波敏感 元素分别响应。 正如我在第 5 页提到,色觉 Cie 的模型,包含集成光栅一个在 X(λ )和 Y (λ )和 z(λ )配色函数行动(图 7 制成图表)社民党,生产 X,Y 和 Z 值。 要使用 TCS230 彩色估计我们执行了一个类似的计算, 但使用而不是在 CIE CMFs TCS230 灵敏度函数:我们整合下 TCS230 的灵敏度曲线社民党,生产的 R,G 和 B 值。该设备的 R,G 和 B 值将取决于几个因素:光源,样品的光谱反射光 谱的内容, 任何干预光学元件的光谱衰减 (如镜头)最后的光谱响应职能 TCS230。 , 各种光谱现象为蓝本,通过计算波长的波长的产品。

图 10 TCS230 光谱灵敏度绘制在这里。红色,绿色和蓝色通道都绘制在相应的颜色;灰 线反映了清除(未过滤)通道的灵敏度。由于这些反应是从 CIE 标准观察者的不同,所报 告的值 TCS230 没有色度。然而,适当的信号处理产生足够的颜色信息,对于许多工业应用 准确。

由于事实 TCS230 是敏感的红外光(波长有 700 纳米以上),而事实上,大 多数光源产生的红外线地区电力, 典型应用包括一个红外截止在 TCS230 前过滤 器。背面图 11 显示了一个典型的红外滤光片的反应。 继续我们的的 ColorChecker 造型,与我们照亮了 CIE D65 光源的的 ColorChecker, 整合下的 TCS230 反射光谱敏感曲线产生, 并最终转化为 Cie 的[的 x,y]坐标。相对亮度值,通过这个过程获得相当准确的,然而,染色体 maticity 坐标不是很准确。图 12 的裸图的 R,G 和 B 值在 CIE 色度。结果从不同的 ColorChecker 坐标图 9 绘制。 对于分歧的原因是 TCS230 的灵敏度函数系统蒸发散不同于匹配功能, 是适 当的 sRGB 色彩了相当大。即使 TCS230 敏感性均符合的 sRGB,在该光源的光 谱功率分布和干预光学康波- nents 会导致一些分歧谱的影响效果接近达成协议。 要形成一个色彩更准确地估计需要处理的原始 TCS230 的 R,G,B 值并通 过线性 3 × 3 矩阵的系数 cients 是相对于该光源,光学元件的干预光谱响应谱 优化,和响应曲线的 TCS230。数据处理操作可以被表示为矩阵形式如下: x=M?t 公式 2 符号 T 表示一个三个元素的载体的设备价值从色块抓获。M 代表 3 ×3 色 校正矩阵,我们将适用于这些价值观通过矩阵乘法,由?符号表示。符号 X 表示 估计[的 X,Y 和 Z]值结果向量。 我们可以利用矩阵符号来象征加工三个色块安排一次设置成一个 3×3 矩阵 吨连续的 T 行连续列值的设备三套,包含红色,绿色和蓝色数据分别。经 M 矩

阵乘法,所产生的矩阵 X 的列包含 XYZ 值的连续采样; X 的行包含 X,Y 和 Z 值分别 tively。一个方程表达了三个补丁一次映射: X=M?T 公式 3 给定一个矩阵 T 的列包含三种器件样品集,并包含一个矩阵 X 某某三元三 组对应的理想, 有一种独特的矩阵 M, T 到 X 的映射是通过计算逆矩阵的 T, 从 然后用 X 矩阵计算产品(由预乘) : M=X ? T ?1 公式 4 由此产生的 3 ×3 色校正矩阵 M 的每一个选择三个值集的设备的 Tristimulus 值对应设置准确的地图。这是没有必要在反矩阵传感时间!矩阵 M 可以 事先计算, 依据的预期将提交拟申请在传感器的样品。要处理三对检测样品元件 值,所有这些都是必要的,是对矩阵乘积的计算公式 3。 一个色彩校正矩阵, 产生在超过三个样本良好的效果,可以通过数值计算优 化过程。当这样做,没有特别的样品可能正好映射到理想三原色集,但一个线性 矩阵可以构造,尽量减少跨样本范围(其中的错误是在最小二乘意义上衡量)的 错误。色彩校正行动仍在完成公式 2 完全一样。


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