『物理』量測『輻射』之『通量』︰

Radiometry

Radiometry is a set of techniques for measuring electromagnetic radiation, including visible light. Radiometric techniques in optics characterize the distribution of the radiation’s power in space, as opposed to photometric techniques, which characterize the light’s interaction with the human eye. Radiometry is distinct from quantum techniques such as photon counting.

The use of radiometers to determine the temperature of objects and gasses by measuring radiation flux is called pyrometry. Handheld pyrometer devices are often marketed as infrared thermometers.

Radiometry is important in astronomy, especially radio astronomy, and plays a significant role in Earth remote sensing. The measurement techniques categorized as radiometry in optics are called photometry in some astronomical applications, contrary to the optics usage of the term.

Spectroradiometry is the measurement of absolute radiometric quantities in narrow bands of wavelength.^[1]

 

不同於『人眼』所見『光度』的『明暗』︰

Photometry (optics)

Photometry is the science of the measurement of light, in terms of its perceived brightness to the human eye.^[1] It is distinct from radiometry, which is the science of measurement of radiant energy (including light) in terms of absolute power. In modern photometry, the radiant power at each wavelength is weighted by a luminosity function that models human brightness sensitivity. Typically, this weighting function is the photopic sensitivity function, although the scotopic function or other functions may also be applied in the same way.

Photopic (daytime-adapted, black curve) and scotopic [1] (darkness-adapted, green curve) luminosity functions. The photopic includes the CIE 1931 standard [2] (solid), the Judd-Vos 1978 modified data [3] (dashed), and the Sharpe, Stockman, Jagla & Jägle 2005 data [4] (dotted). The horizontal axis is wavelength in nm.

 

因此『物理量』非與『感知度』成比例，故而『客觀』逢『主觀』耶？所以『色彩』不得不依賴『比色法』

色度學

色度學（Colorimetry），又名比色法，是量化和物理上描述人們顏色知覺的科學和技術。 色度學同光譜學（spectrophotometry）相近 ，但是色度學更關心的是於人們顏色知覺物理相關的光譜。最常用的是CIE1931色彩空間和相關的數值。

乎！如果說『無色彩』之『灰階』︰

Grayscale

In photography and computing, a grayscale or greyscale digital image is an image in which the value of each pixel is a single sample, that is, it carries only intensity information. Images of this sort, also known as black-and-white, are composed exclusively of shades of gray, varying from black at the weakest intensity to white at the strongest.^[1]

Grayscale images are distinct from one-bit bi-tonal black-and-white images, which in the context of computer imaging are images with only two colors, black and white (also called bilevel or binary images). Grayscale images have many shades of gray in between.

Grayscale images are often the result of measuring the intensity of light at each pixel in a single band of the electromagnetic spectrum (e.g. infrared, visible light, ultraviolet, etc.), and in such cases they are monochromatic proper when only a given frequency is captured. But also they can be synthesized from a full color image; see the section about converting to grayscale.

Numerical representations

The intensity of a pixel is expressed within a given range between a minimum and a maximum, inclusive. This range is represented in an abstract way as a range from 0 (total absence, black) and 1 (total presence, white), with any fractional values in between. This notation is used in academic papers, but this does not define what “black” or “white” is in terms of colorimetry.

Another convention is to employ percentages, so the scale is then from 0% to 100%. This is used for a more intuitive approach, but if only integer values are used, the range encompasses a total of only 101 intensities, which are insufficient to represent a broad gradient of grays. Also, the percentile notation is used in printing to denote how much ink is employed in halftoning, but then the scale is reversed, being 0% the paper white (no ink) and 100% a solid black (full ink).

In computing, although the grayscale can be computed through rational numbers, image pixels are stored in binary, quantized form. Some early grayscale monitors can only show up to sixteen (4-bit) different shades, but today grayscale images (as photographs) intended for visual display (both on screen and printed) are commonly stored with 8 bits per sampled pixel, which allows 256 different intensities (i.e., shades of gray) to be recorded, typically on a non-linear scale. The precision provided by this format is barely sufficient to avoid visible banding artifacts, but very convenient for programming because a single pixel then occupies a single byte.

Technical uses (e.g. in medical imaging or remote sensing applications) often require more levels, to make full use of the sensor accuracy (typically 10 or 12 bits per sample) and to guard against roundoff errors in computations. Sixteen bits per sample (65,536 levels) is a convenient choice for such uses, as computers manage 16-bit words efficiently. The TIFF and the PNG (among other) image file formats support 16-bit grayscale natively, although browsers and many imaging programs tend to ignore the low order 8 bits of each pixel.

No matter what pixel depth is used, the binary representations assume that 0 is black and the maximum value (255 at 8 bpp, 65,535 at 16 bpp, etc.) is white, if not otherwise noted.

 

也得和『採色、顯色裝置』相干︰

Converting color to grayscale

Conversion of a color image to grayscale is not unique; different weighting of the color channels effectively represent the effect of shooting black-and-white film with different-colored photographic filters on the cameras.

Colorimetric (luminance-preserving) conversion to grayscale

A common strategy is to use the principles of photometry or, more broadly, colorimetry to match the luminance of the grayscale image to the luminance of the original color image.^[2][3] This also ensures that both images will have the same absolute luminance, as can be measured in its SI units of candelas per square meter, in any given area of the image, given equal whitepoints. In addition, matching luminance provides matching perceptual lightness measures, such as L^* (as in the 1976 CIE Lab color space) which is determined by the linear luminance Y (as in the CIE 1931 XYZ color space) which we will refer to here as Y_linear to avoid any ambiguity.

To convert a color from a colorspace based on an RGB color model to a grayscale representation of its luminance, weighted sums must be calculated in a linear RGB space, that is, after the gamma compression function has been removed first via gamma expansion.^[4]

For the sRGB color space, gamma expansion is defined as

where C_srgb represents any of the three gamma-compressed sRGB primaries (R_srgb, G_srgb, and B_srgb, each in range [0,1]) and C_linear is the corresponding linear-intensity value (R_linear, G_linear, and B_linear, also in range [0,1]). Then, linear luminance is calculated as a weighted sum of the three linear-intensity values. The sRGB color space is defined in terms of the CIE 1931 linear luminance Y_linear, which is given by

.^[5]

The coefficients represent the measured intensity perception of typical trichromat humans, depending on the primaries being used; in particular, human vision is most sensitive to green and least sensitive to blue. To encode grayscale intensity in linear RGB, each of the three primaries can be set to equal the calculated linear luminance Y (replacing R,G,B by Y,Y,Y to get this linear grayscale). Linear luminance typically needs to be gamma compressed to get back to a conventional non-linear representation. For sRGB, each of its three primaries is then set to the same gamma-compressed Y_srgb given by the inverse of the gamma expansion above as

In practice, because the three sRGB components are then equal, it is only necessary to store these values once in sRGB-compatible image formats that support a single-channel representation. Web browsers and other software that recognizes sRGB images will typically produce the same rendering for such a grayscale image as it would for an sRGB image having the same values in all three color channels.

 

能不叫人頭疼嗎？？若講現代『顯示器』基本符合『sRGB』標準，不知『ColorPy』程式庫之『色彩空間』以及『裝置假設』人

《ColorPy/colorpy/colormodels.py》

colormodels.py – Conversions between color models
Description:
Defines several color models, and conversions between them.
The models are:

xyz – CIE XYZ color space, based on the 1931 matching functions for a 2 degree field of view.

Spectra are converted to xyz color values by integrating with the matching functions in ciexyz.py.

xyz colors are often handled as absolute values, conventionally written with uppercase letters XYZ, or as scaled values (so that X+Y+Z = 1.0), conventionally written with lowercase letters xyz.
This is the fundamental color model around which all others are based.

rgb – Colors expressed as red, green and blue values, in the nominal range 0.0 – 1.0. These are linear color values, meaning that doubling the number implies a doubling of the light intensity. rgb color values may be out of range (greater than 1.0, or negative), and do not account for gamma correction. They should not be drawn directly.

irgb – Displayable color values expressed as red, green and blue values, in the range 0 – 255. These have been adjusted for gamma correction, and have been clipped into the displayable range 0 – 255.
These color values can be drawn directly.

Luv – A nearly perceptually uniform color space.

Lab – Another nearly perceptually uniform color space.

As far as I know, the Luv and Lab spaces are of similar quality.
Neither is perfect, so perhaps try each, and see what works best for your application.

The models store color values as 3-element NumPy vectors.
The values are stored as floats, except for irgb, which are stored as integers.

 

將要如何『解讀』程式『輸出』呢？？

pi@raspberrypi:~  ipython3 --pylab
Python 3.4.2 (default, Oct 19 2014, 13:31:11) 
Type "copyright", "credits" or "license" for more information.

IPython 2.3.0 -- An enhanced Interactive Python.
?         -> Introduction and overview of IPython's features.
%quickref -> Quick reference.
help      -> Python's own help system.
object?   -> Details about 'object', use 'object??' for extra details.
Using matplotlib backend: TkAgg

In [1]: import colorpy.misc

In [2]: 線性編碼灰階 = ['#000000', '#1A1A1A', '#333333', '#4D4D4D', '#666666', '#808080', '#999999', '#B3B3B3', '#CCCCCC', '#E6E6E6', '#FFFFFF']

In [3]: 線性編碼灰階級 = ['0.0', '0.1', '0.2', '0.3', '0.4', '0.5', '0.6', '0.7', '0.8', '0.9', '1.0']

In [4]: colorpy.misc.colorstring_patch_plot (線性編碼灰階, 線性編碼灰階級, 'Grayscale', 'grayscale', num_across=8)
Saving plot grayscale

In [5]: 線性強度灰階 = ['#000000', '#5A5A5A', '#7B7B7B', '#949494', '#A9A9A9', '#BBBBBB', '#CBCBCB', '#D9D9D9', '#E7E7E7', '#F4F4F4', '#FFFFFF']

In [6]: 線性強度灰階級 = 線性編碼灰階級

In [7]: colorpy.misc.colorstring_patch_plot (線性強度灰階, 線性強度灰階級, 'Grayscale', 'grayscale', num_across=8)
Saving plot grayscale

In [8]: 

 

【 Linear encoding 】

 

【 Linear intensity  】

 

On most displays (those with gamma of about 2.2), one can observe that the linear-intensity scale has a large jump in perceived brightness between the intensity values 0.0 and 0.1, while the steps at the higher end of the scale are hardly perceptible. The gamma-encoded scale, which has a nonlinearly-increasing intensity, will show much more even steps in perceived brightness.

A cathode ray tube (CRT), for example, converts a video signal to light in a nonlinear way, because the electron gun’s intensity (brightness) as a function of applied video voltage is nonlinear. The light intensity I is related to the source voltage V_s according to

where γ is the Greek letter gamma. For a CRT, the gamma that relates brightness to voltage is usually in the range 2.35 to 2.55; video look-up tables in computers usually adjust the system gamma to the range 1.8 to 2.2,^[1] which is in the region that makes a uniform encoding difference give approximately uniform perceptual brightness difference, as illustrated in the diagram at the top of this section.

For simplicity, consider the example of a monochrome CRT. In this case, when a video signal of 0.5 (representing mid-gray) is fed to the display, the intensity or brightness is about 0.22 (resulting in a dark gray). Pure black (0.0) and pure white (1.0) are the only shades that are unaffected by gamma.

To compensate for this effect, the inverse transfer function (gamma correction) is sometimes applied to the video signal so that the end-to-end response is linear. In other words, the transmitted signal is deliberately distorted so that, after it has been distorted again by the display device, the viewer sees the correct brightness. The inverse of the function above is:

 

where V_c is the corrected voltage and V_s is the source voltage, for example from an image sensor that converts photocharge linearly to a voltage. In our CRT example 1/γ is 1/2.2 or 0.45.

A color CRT receives three video signals (red, green and blue) and in general each color has its own value of gamma, denoted γ_R, γ_G or γ_B. However, in simple display systems, a single value of γ is used for all three colors.

Other display devices have different values of gamma: for example, a Game Boy Advance display has a gamma between 3 and 4 depending on lighting conditions. In LCDs such as those on laptop computers, the relation between the signal voltage V_s and the intensity I is very nonlinear and cannot be described with gamma value. However, such displays apply a correction onto the signal voltage in order to approximately get a standard γ = 2.5 behavior. In NTSC television recording, γ = 2.2.

The power-law function, or its inverse, has a slope of infinity at zero. This leads to problems in converting from and to a gamma colorspace. For this reason most formally defined colorspaces such as sRGB will define a straight-line segment near zero and add raising x + K (where K is a constant) to a power so the curve has continuous slope. This straight line does not represent what the CRT does, but does make the rest of the curve more closely match the effect of ambient light on the CRT. In such expressions the exponent is not the gamma; for instance, the sRGB function uses a power of 2.4 in it, but more closely resembles a power-law function with an exponent of 2.2, without a linear portion.

 

誠所見或不同，知之者明矣☆

Simple monitor tests

To see whether one’s computer monitor is properly hardware adjusted and can display shadow detail in sRGB images properly, they should see the left half of the circle in the large black square very faintly but the right half should be clearly visible. If not, one can adjust their monitor’s contrast and/or brightness setting. This alters the monitor’s perceived gamma. The image is best viewed against a black background.

This procedure is not suitable for calibrating or print-proofing a monitor. It can be useful for making a monitor display sRGB images approximately correctly, on systems in which profiles are not used (for example, the Firefox browser prior to version 3.0 and many others) or in systems that assume untagged source images are in the sRGB colorspace.

On some operating systems running the X Window System, one can set the gamma correction factor (applied to the existing gamma value) by issuing the command xgamma -gamma 0.9 for setting gamma correction factor to 0.9, and xgamma for querying current value of that factor (the default is 1.0). In OS X systems, the gamma and other related screen calibrations are made through the System Preferences. Microsoft Windows versions before Windows Vista lack a first-party developed calibration tool.

In the test pattern to the right, the linear intensity of each solid bar is the average of the linear intensities in the surrounding striped dither; therefore, ideally, the solid squares and the dithers should appear equally bright in a properly adjusted sRGB system.

顏色列表

此列表僅列出常見的色彩，色彩的多樣性使得在實際上難以全部列舉或命名。另外由於各種顯示器在未經校正前有色差存在，因此以下的色彩呈現僅供參考。

 

 

 

 

 

 

 

 

 

 

所有的故事都有一個開始，『知覺量化』的故事也是一樣︰

一六一四年 John Napier 約翰‧納皮爾在一本名為《 Mirifici Logarithmorum Canonis Descriptio  》── 奇妙的對數規律的描述 ── 的書中，用了三十七頁解釋『對數』 log ，以及給了長達九十頁的對數表。這有什麼重要的嗎？想一想即使在今天用『鉛筆』和『紙』做大位數的加減乘除，尚且困難也很容易算錯，就可以知道對數的發明，對計算一事貢獻之大的了。如果用一對一對應的觀點來看，對數把『乘除』運算『變換』成『加減』運算︰

，更不要說還可以算『平方』、『立方』種種和開『平方根』、『立方根』等等的計算了。

傳聞納皮爾還發明了的『骨頭計算器』，他的書對於之後的天文學、力學、物理學、占星學的發展都有很大的影響。他的運算變換 Transform 的想法，開啟了『換個空間』解決『數學問題』的大門，比方『常微分方程式的  Laplace Transform』與『頻譜分析的傅立葉變換』等等。

這個對數畫起來是這個樣子︰

不只如此這個對數關係竟然還跟人類之『五官』── 眼耳鼻舌身 ── 受到『刺激』── 色聲香味觸 ── 的『感覺』強弱大小有關。一七九五年出生的 Ernst Heinrich Weber 韋伯，一位德國物理學家，是一位心理物理學的先驅，他提出感覺之『方可分辨』JND just-noticeable difference 的特性。比方說你提了五公斤的水，再加上半公斤，可能感覺差不了多少，要是你沒提水，說不定會覺的突然拿著半公斤的水很重。也就是說在『既定的刺激』下， 感覺的方可分辨性大小並不相同。韋伯實驗後歸結成一個關係式︰

ΔR/R = K

R:  既有刺激之物理量數值
ΔR:  方可分辨 JND 所需增加的刺激之物理量數值
K: 特定感官之常數，不同的感官不同

。之後  Gustav Theodor Fechner  費希納，一位韋伯派的學者，提出『知覺』perception 『連續性』假設，將韋伯關係式改寫為︰

，求解微分方程式得到︰

假如刺激之物理量數值小於 時，人感覺不到 ，就可將上式寫成︰

這就是知名的韋伯-費希納定律，它講著：在絕對閾限 之上，主觀知覺之強度的變化與刺激之物理量大小的改變呈現自然對數的關係，也可以說，如果刺激大小按著幾何級數倍增，所引起的感覺強度卻只依造算術級數累加。

─── 摘自《千江有水千江月》

 

在故事展開前特此提醒讀者︰

『量』與『數』大不同。『物理量』是有『單位』的。

由於主觀『知覺強度』一般符合『物理量』刺激之『對數關係』。然而『對數』是『非線性』的。所以從『因次分析』的觀點來看，

之『無因次』 『表述』實優於

也。

追求五官之『絕對 □ 感』者，或當知『等距量表』哩︰

這樣就可以將一個有多種『機率』 ，能產生互斥『結果』 的『彩票』 表示成︰

。

如此『期望效用函數理論』之『四條公設』可以表示為︰

【完整性公設】Completeness

，，或

任意的兩張『彩票』都可以比較『喜好度』 ，它的結果只能是上述三種關係之一，『偏好 』，『偏好 』 ，『無差異』 。

【遞移性公設】 Transitivity

如果 ，而且 ，那麼 。

【連續性公設】 Continuity

如果 , 那麼存在一個『機率』 ，使得 。

【獨立性公設】 Independence

如果 , 那麼對任意的『彩票』 與『機率』 ，滿足 。

對於任何一個滿足上述公設的『理性經紀人』 rational agent ，必然可以『建構』一個『效用函數』，使得 ，而且對任意兩張『彩票』，如果 。此處 代表對 『彩票』的『效用期望值』，簡記作 ，符合

。

它在『微觀經濟學』、『博弈論』與『決策論』中，今天稱之為『預期效用假說』 Expected utility hypothesis，指在有『風險』的情況下，任何『個體』所應該作出的『理性選擇』就是追求『效用期望值』的『最大化』。假使人生中的『抉擇』真實能夠如是的『簡化』，也許想得到『快樂』與『幸福』的辦法，就清楚明白的多了。然而有人認為這個『假說』不合邏輯。一九五二年，法國總體經濟學家莫里斯‧菲力‧夏爾‧阿萊斯 Maurice Félix Charles Allais ── 一九八八年，諾貝爾經濟學獎的得主 ── 作了一個著名的實驗，看看實際上人到底是怎麼『做選擇』的，這個『阿萊斯』發明的『彩票選擇實驗』就是大名鼎鼎的『阿萊斯悖論』 Allais paradox 。

針對百人測試所設計的『彩票』：

彩票甲：百分之百的機會得到一百萬元。【期望值 100 萬】

彩票乙：百分之十的機會得到五百萬元，百分之八十九的機會得到一百萬元，百分之一的機會什麼也得不到。【期望值 139 萬】

實驗結果：絕大多數人選擇甲而非乙。

然後改用另一組『彩票』，對同一群人繼續進行測試︰

彩票丙：百分之十一的機會得到一百萬元，百分之八十九的機會什麼也得不到。【期望值 11 萬】

彩票丁：百分之十的機會得到五百萬元，百分之九十的機會什麼也得不到。【期望值 50 萬】

實驗結果：絕大多數人選擇丁而非丙。

這條『S 型曲線』的不對稱性呈現出，當人們面對一個『損失』的『結果』，所產生之『厭惡感』或者說『傷感情』，比『獲益』之『情況』下所生的『滿意度』也許講『感覺好』，更為『強烈』。這使『展望理論』基本上不同於『期望效用函數理論』。有人將此理論的引申結論，整理成︰

確定效應：處於穫益狀態時，多數人是風險厭惡者。
反射效應：處於損失狀態時，多數人是風險喜好者。
損失規避：多數人對損失比對穫益敏感。
參照依賴：多數人對得失的判斷往往由參照點決定。

── 『人的行為』應當用著『純理性』來『定義』嗎？

還是應該要講『有人情』真的就『不合理』的嗎？？──

─── 摘自《物理哲學·下中…》

 

亦可免於誤解所謂『費希納』之個體局部以及『史蒂文斯』的整體大眾『心理學』議論乎︰

Stevens’s power law

Stevens’s power law is a proposed relationship between the magnitude of a physical stimulus and its perceived intensity or strength. It is often considered to supersede the Weber–Fechner law on the basis that it describes a wider range of sensations, although critics argue that the validity of the law is contingent on the virtue of approaches to the measurement of perceived intensity that are employed in relevant experiments. In addition, a distinction has been made between local psychophysics, where stimuli are discriminated only with a certain probability, and global psychophysics, where the stimuli would be discriminated correctly with near certainty (Luce & Krumhansl, 1988). The Weber–Fechner law and methods described by L. L. Thurstone are generally applied in local psychophysics, whereas Stevens’s methods are usually applied in global psychophysics.

The theory is named after psychophysicist Stanley Smith Stevens (1906–1973). Although the idea of a power law had been suggested by 19th-century researchers, Stevens is credited with reviving the law and publishing a body of psychophysical data to support it in 1957.

The general form of the law is

 

where I is the magnitude of the physical stimulus, ψ(I) is the subjective magnitude of the sensation evoked by the stimulus, a is an exponent that depends on the type of stimulation, and k is a proportionality constant that depends on the units used.

The table to the bottom lists the exponents reported by Stevens.

 

Continuum	Exponent	Stimulus condition
Loudness	0.67	Sound pressure of 3000 Hz tone
Vibration	0.95	Amplitude of 60 Hz on finger
Vibration	0.6	Amplitude of 250 Hz on finger
Brightness	0.33	5° target in dark
Brightness	0.5	Point source
Brightness	0.5	Brief flash
Brightness	1	Point source briefly flashed
Lightness	1.2	Reflectance of gray papers
Visual length	1	Projected line
Visual area	0.7	Projected square
Redness (saturation)	1.7	Red–gray mixture
Taste	1.3	Sucrose
Taste	1.4	Salt
Taste	0.8	Saccharin
Smell	0.6	Heptane
Cold	1	Metal contact on arm
Warmth	1.6	Metal contact on arm
Warmth	1.3	Irradiation of skin, small area
Warmth	0.7	Irradiation of skin, large area
Discomfort, cold	1.7	Whole-body irradiation
Discomfort, warm	0.7	Whole-body irradiation
Thermal pain	1	Radiant heat on skin
Tactual roughness	1.5	Rubbing emery cloths
Tactual hardness	0.8	Squeezing rubber
Finger span	1.3	Thickness of blocks
Pressure on palm	1.1	Static force on skin
Muscle force	1.7	Static contractions
Heaviness	1.45	Lifted weights
Viscosity	0.42	Stirring silicone fluids
Electric shock	3.5	Current through fingers
Vocal effort	1.1	Vocal sound pressure
Angular acceleration	1.4	5 s rotation
Duration	1.1	White-noise stimuli

 

只要『批評』

Criticisms

Stevens generally collected magnitude estimation data from multiple observers, averaged the data across subjects, and then fitted a power function to the data. Because the fit was generally reasonable, he concluded the power law was correct. This approach ignores any individual differences that may obtain and indeed it has been reported that the power relationship does not always hold as well when data are considered separately for individual respondents (Green & Luce 1974).

Another issue is that the approach provides neither a direct test of the power law itself nor the underlying assumptions of the magnitude estimation/production method.

Stevens’s main assertion was that using magnitude estimations/productions respondents were able to make judgements on a ratio scale (i.e., if x and y are values on a given ratio scale, then there exists a constant k such that x = ky). In the context of axiomatic psychophysics, (Narens 1996) formulated a testable property capturing the implicit underlying assumption this assertion entailed. Specifically, for two proportions p and q, and three stimuli, x, y, z, if y is judged p times x, z is judged q times y, then t = pq times x should be equal to z. This amounts to assuming that respondents interpret numbers in a veridical way. This property was unambiguously rejected (Ellermeier & Faulhammer 2000, Zimmer 2005). Without assuming veridical interpretation of numbers, (Narens 1996) formulated another property that, if sustained, meant that respondents could make ratio scaled judgments, namely, if y is judged p times x, z is judged q times y, and if y‘ is judged q times x, z‘ is judged p times y‘, then z should equal z‘. This property has been sustained in a variety of situations (Ellermeier & Faulhammer 2000, Zimmer 2005).

Because Stevens fit power functions to data, his method did not provide a direct test of the power law itself. (Luce 2002), under the condition that respondents’ numerical distortion function and the psychophysical functions could be separated, formulated a behavioral condition equivalent to the psychophysical function being a power function. This condition was confirmed for just over half the respondents, and the power form was found to be a reasonable approximation for the rest (Steingrimsson & Luce 2006).

It has also been questioned, particularly in terms of signal detection theory, whether any given stimulus is actually associated with a particular and absolute perceived intensity; i.e. one that is independent of contextual factors and conditions. Consistent with this, Luce (1990, p. 73) observed that “by introducing contexts such as background noise in loudness judgements, the shape of the magnitude estimation functions certainly deviates sharply from a power function”.

 

仍在，『理論』尚未『 ○ 滿』耶？？

 

 

 

 

 

 

 

 

 

曾經聽得前人說︰作文心法有四字『起承轉合』。既已顏色『起』 ，『承』 □ 當講？

sRGB

sRGB (standard Red Green Blue) is an RGB color space created cooperatively by HP and Microsoft in 1996 for use on monitors, printers and the Internet, and subsequently standardized by the IEC as IEC 61966-2-1:1999.^[1] It is often used as the “default” color space for images that do not contain any color space information, especially if the images are stored as 8-bit integers.

sRGB uses the ITU-R BT.709 primaries, the same as are used in studio monitors and HDTV,^[2] a transfer function (gamma curve) typical of CRTs, and a viewing environment designed to match typical home and office viewing conditions. This specification allowed sRGB to be directly displayed on typical CRT monitors of the time, a factor which greatly aided its acceptance.

 

『承』 ○ 應道！

孟塞爾顏色系統

孟塞爾顏色系統（Munsell Color System）是色度學（或比色法）裡透過明度（value）、色相（hue）及色度（chroma）三個維度來描述顏色的方法。這個顏色描述系統是由美國藝術家阿爾伯特·孟塞爾（Albert H. Munsell，1858－1918）在1898年創製的，在1930年代為USDA採納為泥土研究的官方顏色描述系統。至今仍是比較色法的標準。

早期的幾個色彩體系將顏色放在各種不同的三維顏色固體，但孟塞爾是第一個把色調、明度和色度分離成為感知均勻和獨立的尺度，並且是第一個系統地在三維空間中表達顏色的關係^[1]。孟塞爾的系統，尤其是其後的再標記法，是基於嚴格的人類受試者測量的視覺反應，使之具有堅實的實驗科學依據。基於人類的視覺感知，孟塞爾的系統熬過了其他現代色彩模式的挑戰，儘管在某些領域其地位已被某些特殊用途的模型取代了，如CIELAB（L*a*b*）和CIECAM02。孟塞爾的系統目前仍然是最廣泛使用的系統^[2]。

圖示孟塞爾顏色系統之中中等明度（5）而中等略偏高色度（6）的色相環、明度由全暗（0）到全亮（10）的黑白漸變色柱、中等明度（5）的紫藍色（5PB）色度漸進帶。

 

☆ 繫『ABC』足不足？？又是『品物咸章』之際！！

派︰來知德講︰

杞，枸杞也，杞與瓜皆五月所有之物。乾為果，瓜之象也。因前爻有包魚之包，故此爻亦以包言之。含章者，含藏其章美也。此爻變離，有文明章美之意。又居中，有包含之意，故曰含章。含即杞之包，章即瓜之美。以杞包瓜，即含章之象也。

初六：系于金柅，貞吉，有攸往，見凶，羸豕踟躅。
象曰：系于金柅，柔道牽也。

九二：包有魚，無咎，不利賓。
象曰：包有魚，義不及賓也。

九三：臀無膚，其行次且，厲，無大咎。
象曰：其行次且，行未牽也。

九四：包無魚，起凶。
象曰：無魚之凶，遠民也。

九五：以杞包瓜，含章，有隕自天。
象曰：九五含章，中正也。 有隕自天，志不舍命也。

上九：姤 其角，吝，無咎。
象曰：姤 其角，上窮吝也。

有情天地千絲萬縷，姤且遇也，但求其偶而已，奈何強冠之以柔道之『牽』？恐亦非所願耶！

天地相遇，如果引發『天雷』『地火』，也是乾坤本有之理。宇宙萬象『出』，或知或未知其所『入』，求之於天地相遇之『際』，為得其氣『機』，深入『組元』之道的吧。

………

 

☿ 行︰  文件總長四十七，真真是『杞』小『瓜』大，什麼也沒說，就要人家『以杞包瓜』。還會心『根號一七九』的哩！不知要不要四捨五入，小數點下有幾位，分明是罵人！！☿☹☹

訊︰☿ 后，上古之女王也。何時起加了個 女，就成了姤，祇知求『遇偶』，真不曉『後起者』造字是何肚腸？？

─── 摘自《M♪o 之學習筆記本《辰》組元︰【䷫】以杞包瓜》

 

隨順星語夢言事，轉道『色彩空間』之『系統化』吧☆

 

 

 

 

 

 

 

 

 

 

晨起見藍天，漫步之林野，喜逢

 

雙鶴展翼翱翔而飛。隨口吟著鮑照之

  舞鶴賦

散 幽經以驗物，偉胎化之仙禽。鍾浮曠之藻質，抱清迥之明心。指蓬壺而翻翰，望昆閬而揚音。澘日域以回騖，窮天步而高尋。踐神區其既遠，積靈祀而方多。精含丹 而星曜，頂凝紫而煙華。引員吭之纖婉，頓修趾之洪姱。疊霜毛而弄影，振玉羽而臨霞。朝戲於芝田，夕飲乎瑤池。厭江海而游澤，掩雲羅而見羈。去帝鄉之岑寂， 歸人寰之喧卑。歲崢嶸而愁暮，心惆悵而哀離。

於是窮陰殺節，急景凋年。骫沙振野，箕風動天。嚴嚴苦霧，皎皎悲泉。冰塞長河，雪滿群山。既而氛昏夜歇，景物澄廓。星翻漢回 ，曉月將落。感寒雞之早晨，憐霜雁之違漠。臨驚風之蕭條，對流光之照灼。唳清響於丹墀，舞飛容於金閣。始連軒以鳳蹌，終宛轉而龍躍。躑躅徘徊，振迅騰摧。 驚身蓬集，矯翅雪飛。離綱別赴，合緒相依。將興中止，若往而歸。颯沓矜顧，遷延遲暮。逸翮後塵 ，翱翥先路。指會規翔，臨岐矩步。態有遺妍，貌無停趣。奔機逗節，角睞分形。長揚緩騖，並翼連聲。輕跡凌亂，浮影交橫。眾變繁姿，參差洊密。煙交霧凝，若 無毛質。風去雨還，不可談悉。既散魂而蕩目，迷不知其所之。忽星離而雲罷，整神容而自持。仰天居之崇絕，更惆悵以驚思。

當是時也，燕姬色沮，巴童心恥。巾拂兩停，丸劍雙止。雖邯鄲其敢倫，豈陽阿之能擬。入衛國而乘軒，出吳都而傾市。守馴養於千齡，結長悲於萬里。

信步而走，不覺漸入深林，幾聲鶴鳴，方回過神來。怎到了古澤邊兒了。此間雖然聽聞絕美，四處流沙陷土極度危險。既來之，則安之。何不趁此刻細細瞧瞧，只要小 心謹慎就好。此景只原夢裡有，盎然生趣是仙鄉。一時薄霧轉濃，雖然狐疑，終究不是久待之地。出林後，看那日頭，分明已過了晌午，得敢緊尋路兒歸。

………摘自《M♪o 之學習筆記本《卯》基件︰【䷜】水洊維心》

 

人文覺醒若『柳絮』，『撒鹽』空中胡可擬

謝太傅寒雪日內集，與兒女講論文義。

俄而雪驟,公欣然曰：“白雪紛紛何所似？”兄子胡兒曰：“撒鹽空中差可擬。”兄女曰：“未若柳絮因風起。”公大笑樂。即公大兄無奕女，左將軍王凝之妻也。

 

『美育』或好『柳絮』因風起

秋夕‧杜牧

銀燭秋光冷畫屏，輕羅小扇撲流螢。
天階夜色涼如水，臥看牽牛織女星。

 

，科學格物似『習坎』！！？？

『組元』 tuple 數理如何算？？！！

印刷四分色模式

印刷四分色模式是彩色印刷時採用的一種套色模式，利用色料的三原色混色原理，加上黑色油墨，共計四種顏色混合疊加，形成所謂「全彩印刷」。四種標準顏色是：

• C：Cyan ＝ 青色，常被誤稱為『天藍色』或『湛藍』
• M：Magenta ＝ 洋紅色，又稱為『品紅色』
• Y：Yellow ＝ 黃色
• K：blacK ＝ 黑色，雖然有文獻解釋說這裡的K應該是Key Color（定位套版色）^[1][2][3]，但其實是和製版時所用的定位套版觀念混淆而有此一說。此處縮寫使用最後一個字母K而非開頭的B，是因為在整體色彩學中已經將B給了RGB的Blue藍色。

理想的印刷四分色標準

比較接近實際CMY疊色的示意圖

混色

洋紅色加黃色會形成紅色；洋紅色加青色形成藍色；青色加黃色形成綠色。理論上只用上述三種顏色相加就可以形成包含黑色在內101³共1,030,301色（0～100%模式），但實際印刷時，由於色料本身並非真正純色，三色等量相加之後只能形成一種深灰色或深褐色，而非黑色；實際偏色程度依不同廠牌色料配方而有不同差異。

理想的CMY三原色油墨/墨水/彩色碳粉其印出成品的結果應該完全等同RGB三色光的補色，但目前現實世界裡一般彩色印刷/噴墨/雷射所使用的 CMY三色色料不論何種廠牌實際上均有不同的色偏現象，一般「青色」均略帶洋紅而偏藍，「洋紅」一般同時帶青與黃而偏紫，只有「黃色」僅略帶微量洋紅而略 微偏橙；此外以三層CMY疊印產生黑色不僅不容易立即乾燥、不利於快速印刷，三色疊印也需要非常精確的套印，用於表現有許多細小線條的文字十分不利；直接 以黑色油墨替代不純的CMY三層疊印所產生的不純黑色，也可以大大節省成本。故此「黑色」雖非「原色」，卻成為彩色印刷必備的色彩之一。

以黑色代替其他顏色的量不盡相同，主要考量包括印刷技術形式、紙張和黑色油墨的品質，而採用不同的色彩轉換設定檔進行轉換。

顯示

印刷和電腦螢幕顯示，分屬兩種不同的色彩模式（電腦螢幕為發光體，遵循RGB「三原色光模式原 理」；印刷為CMY+K油墨或墨水疊印、混色，遵循的是CMY「色料的三原色原理」），加上一般油墨印刷各原色網點色階為0～100%，而電腦螢幕各原色 光色階為0～255，兩者產生的色彩數差距甚大：CMYK僅有101³+101共1,030,402色，而RGB卻有256³共16,777,216色； 加上前述印刷油墨並非理想純色，實際形成的色彩空間也小於RGB，使得不管哪一種RGB模式都超出CMYK的色域範圍；故而印刷廠一般都會強調不能以螢幕上所看到的色彩要求輸出成品的色差。

顏色模式的轉換

這種轉換實際並不總是完全一致的，例如從三原色光模式可以轉換成印刷模式，印刷品仍然可以再轉換成三原色光模式顯示。但一件印刷模式的圖片轉換成三原色光模式顯示，再轉換成印刷模式就會造成色彩的畸變，兩件印刷品的顏色會有區別。所以如果商業應用需要顏色非常精確時，不要使用轉換的方法。

印刷四分色模式向三原色光模式轉換時，需要經過一個中間三分色模式的變化，將黑色版的因素去掉。

從四分色向三原光轉換

轉換成三分色

然後再轉換成三原色光

也就是

從三原光向四分色轉換

先轉換成三分色

若 ，則

否則，再轉換成四分色

 

 

大小高低恐疑猜★

朝來夕去見如是，喜得『+』者果愛『-』？

Subtractive color

A subtractive color model explains the mixing of a limited set of dyes, inks, paint pigments or natural colorants to create a wider range of colors, each the result of partially or completely subtracting (that is, absorbing) some wavelengths of light and not others. The color that a surface displays depends on which parts of the visible spectrum are not absorbed and therefore remain visible.

Subtractive color systems start with light, presumably white light. Colored inks, paints, or filters between the watchers and the light source or reflective surface subtract wavelengths from the light, giving it color. If the incident light is other than white, our visual mechanisms are able to compensate well, but not perfectly, often giving a flawed impression of the “true” color of the surface.

Conversely, additive color systems start with darkness. Light sources of various wavelengths are added in various proportions to produce a range of colors. Usually, three primary colors are combined to stimulate humans’ trichromatic color vision, sensed by the three types of cone cells in the eye, giving an apparently full range.

Subtractive color mixing

 

RYB

RYB (Red, Yellow, Blue) is the formerly standard set of subtractive primary colors used for mixing pigments. It is used in art and art education, particularly in painting. It predated modern scientific color theory.

Red, yellow, and blue are the primary colors of the standard color “wheel”. The secondary colors, violet (or purple), orange, and green (VOG) make up another triad, formed by mixing equal amounts of red and blue, red and yellow, and blue and yellow, respectively.

The RYB primary colors became the foundation of 18th century theories of color vision as the fundamental sensory qualities blended in the perception of all physical colors and equally in the physical mixture of pigments or dyes. These theories were enhanced by 18th-century investigations of a variety of purely psychological color effects, in particular the contrast between “complementary” or opposing hues produced by color afterimages and in the contrasting shadows in colored light. These ideas and many personal color observations were summarized in two founding documents in color theory: the Theory of Colors (1810) by the German poet and government minister Johann Wolfgang von Goethe, and The Law of Simultaneous Color Contrast (1839) by the French industrial chemist Michel-Eugène Chevreul.

In late 19th and early to mid-20th century commercial printing, use of the traditional RYB terminology persisted even though the more versatile CMY (Cyan, Magenta, Yellow) triad had been adopted, with the cyan sometimes referred to as “process blue” and the magenta as “process red”.

CMY and CMYK printing processes

In color printing, the usual primary colors are cyan, magenta and yellow (CMY). Cyan is the complement of red, meaning that the cyan serves as a filter that absorbs red. The amount of cyan applied to a white sheet of paper controls how much of the red in white light will be reflected back from the paper. Ideally, the cyan is completely transparent to green and blue light and has no effect on those parts of the spectrum. Magenta is the complement of green, and yellow the complement of blue. Combinations of different amounts of the three can produce a wide range of colors with good saturation.

In inkjet color printing and typical mass production photomechanical printing processes, a black ink K (Key) component is included, resulting in the CMYK color model. The black ink serves to cover unwanted tints in dark areas of the printed image, which result from the imperfect transparency of commercially practical CMY inks; to improve image sharpness, which tends to be degraded by imperfect registration of the three color elements; and to reduce or eliminate consumption of the more expensive color inks where only black or gray is required.

Purely photographic color processes almost never include a K component, because in all common processes the CMY dyes used are much more perfectly transparent, there are no registration errors to camouflage, and substituting a black dye for a saturated CMY combination, a trivial prospective cost benefit at best, is technologically impractical in non-electronic analog photography.

 

權衡古今誰人勝！忽爾天地又千年☆

RYB color model

RYB (an abbreviation of red–yellow–blue) is a historical set of colors used in subtractive color mixing and is one commonly used set of primary colors. It is primarily used in art and design education, particularly painting.

RYB predates modern scientific color theory, which has determined that cyan, magenta, and yellow are the best set of three colorants to combine, for the widest range of high-chroma colors.^[1]

Mixture of RYB primary colors

Color wheel

RYB (red–yellow–blue) make up the primary color triad in a standard artist’s color wheel. The secondary colors purple–orange–green (sometimes called violet–orange–green) make up another triad. Triads are formed by three equidistant colors on a particular color wheel. Other common color wheels represent the light model (RGB) and the print model (CMYK).

History

The first known instance of the RYB triad can be found in the work of Franciscus Aguilonius (1567–1617), although he did not arrange the colors in a wheel.^[2]

In his experiments with light, Isaac Newton recognized that colors could be created by mixing color primaries. In his Opticks, Newton published a color wheel to show the geometric relationship between these primaries. This chart was later confused and understood to apply to pigments as well,^[3] though Newton was also unaware of the differences between additive and subtractive color mixing.^[4]

The RYB model was used for printing, by Jacob Christoph Le Blon, as early as 1725.^{[citation needed]}

In the 18th century, the RYB primary colors became the foundation of theories of color vision, as the fundamental sensory qualities that are blended in the perception of all physical colors and equally in the physical mixture of pigments or dyes. These theories were enhanced by 18th-century investigations of a variety of purely psychological color effects, in particular the contrast between “complementary” or opposing hues that are produced by color afterimages and in the contrasting shadows in colored light. These ideas and many personal color observations were summarized in two founding documents in color theory: the Theory of Colors (1810) by the German poet and government minister Johann Wolfgang von Goethe, and The Law of Simultaneous Color Contrast (1839) by the French industrial chemist Michel-Eugène Chevreul.^{[citation needed]}

Painters have long used more than three RYB primary colors in their palettes, and at one point considered red, yellow, blue and green to be the four primaries.^[5] Red, yellow, blue and green are still widely considered the four psychological primary colors,^[6] though red, yellow and blue are sometimes listed as the three psychological primaries,^[7] with black and white occasionally added as a fourth and fifth.^[8]

The cyan, magenta, and yellow primary colors associated with CMYK printing are sometimes known as “process blue”, “process red”^{[citation needed]} and “process yellow”.^{[citation needed]}

 

An RYB color chart from George Field‘s 1841 Chromatography; or, A treatise on colours and pigments: and of their powers in painting showing a red close to magenta and a blue close to cyan, as is typical in printing.