dark boundary between adjacent bright colors.

有一圈奇怪的暗色邊緣。噁！在真實世界，

Yuk!

失焦的顏色會平順地從紅→黃→綠混合─ 不是紅→棕→綠！

In the real world, out of focus colors blend smoothly, going from red to yellow to green

這種混色問題也不限於相片模糊功能─幾乎任何時候

– not red to brown to green!

電腦模糊照片或軟體使用透明邊緣時，

This color blending problem isn’t limited to digital photo blurring, either – pretty

就會看到這類恐怖的渣渣。

much any time a computer blurs an image or tries to use transparent edges, you’ll see

這醜東西有個很簡單的解釋，和很簡單的解法。

the same hideous sludge.

一切始於我們如何感受亮度。

There’s a very simple explanation for this ugliness – and a simple way to fix it.

人類視覺一如聽覺，大致以對數級的相對尺度感測，

It all starts with how we perceive brightness.

也就是它對一個燈泡變成兩個燈泡的亮度差， 感受遠比101個燈泡

Human vision, like our hearing, works on a relative, roughly logarithmic scale: this

變成102個燈泡還強烈，儘管物理亮度的增長相同。

means that flipping from one light to two changes the percieved brightness a TON more

我們的眼睛和大腦對背景全黑時的亮度小差異

than going from a hundred and one to a hundred and two, despite adding the same physical

遠比對背景全亮時的同等差異敏銳。

amount of light.

遠比對背景全亮時的同等差異敏銳。

Our eyes and brains are simply better at detecting small differences in the absolute brightness

反觀電腦與數位感測器，完全基於擊中光感測器的

of dark scenes, and bad at detecting the same differences in bright scenes.

光子數量顯示亮度，因此光線增加多少就感測到多少，

Computers and digital image sensors, on the other hand, detect brightness purely based

無關背景亮度。

on the number of photons hitting a photodetector – so additional photons register the same

儲存數位照片時， 電腦會記錄每個像素裡每種單色的亮度值─

increase in brightness regardless of the surrounding scene.

紅、綠、藍，通常0就代表亮度為零

When a digital image is stored, the computer records a brightness value for each colors

而1就代表100%亮度。 因此0.5看起來是1的一半亮，是否？

– red, green and blue – at each point of the image.

非也。這個顏色看似半白半黑，但這是由於

Typically, zero represents zero brightness and one represents 100 percent brightness.

我們的對數視覺，以物理上的絕對亮度而言，它僅有

So 0.5 is half as bright as 1, right?

純白的五分之一多光子。 更瘋狂的是，亮度值0.25的圖像僅包含純白光子數的

NOPE.

二十分之一！

This color might LOOK like it’s halfway between black and white, but that’s because

數位圖像設計成比物理真實更暗有個好理由：

of our logarithmic vision – in terms of absolute physical brightness, it’s only

記住，人類視覺更容易察覺黑暗背景中的微小亮度變化

one fifth as many photons as white.

數位圖像時代早期的軟體工程師， 會以此作為節省硬碟空間的招數之一。

Even more crazy, an image value of 0.25 has just one twentieth the photons of white!

數位圖像時代早期的軟體工程師， 會以此作為節省硬碟空間的招數之一。

Digital imaging has a good reason for being designed in this darker-than-the-numbers-suggest

這把戲很容易：當數位相機拍了張照，與其儲存

way: remember, human vision is better at detecting small differences in the brightness of dark

原先的亮度，不如存其正平方根─導致暗色擁有較多

scenes, which software engineers took advantage of as a way of saving disk space in the early

儲存點，亮色有較少儲存點，大致模仿了

days of digital imaging.

人類視覺的感受方式。當你需要在螢幕播放影像，

The trick is simple: when a digital camera captures an image, instead of storing the

只要平方回去就能還原色彩。

brightness values it gives, store their square roots – this samples the gradations of dark

一切安好─直到你打算修圖。例如模糊效果，

colors with more data points and bright colors with fewer data points, roughly imitating

是將像素色彩混成周遭像素顏色的平均。太簡單啦。

the characteristics of human vision.

但你在平方前和平方後做此步驟

When you need to display the image on a monitor, just square the brightness back to present

會得到不同結果！很不幸，多數電腦軟體都會弄錯。

the colors properly.

會得到不同結果！很不幸，多數電腦軟體都會弄錯。

This is all well and good – until you decide to modify the image file.

例如你想模糊紅色和綠色的邊界，你會期待中間是

Blurring, for example, is achieved by replacing each pixel with an average of the colors of

半紅半綠的顏色，而懶惰的多數電腦只會把圖像檔中的

nearby pixels.

亮度相加除以二，忘了真正的亮度已經被相機平方根

Simple enough.

以便儲存！因此平均值會太暗，正是因為

But depending on whether you take the average before or after the square-rooting gives different

兩個正平方根的平均，必不大於兩數平均的正平方根。

results!!

為了正確混合紅色和綠色並避免噁爛污漬，電腦理當

And unfortunately, the vast majority of computer software does this incorrectly.

先平方兩者的亮度以還原被平方根的影像，再來平均，

Like, if you want to blur a red and green boundary, you’d expect the middle to be

再平方根回去，你看這好棒棒啊，真正的黃色！

half red and half green.

不幸的是，大多數軟體，從iOS到instagram到photoshop

And most computers attempt that by lazily averaging the brightness values of the image

的預設，都用了懶惰又愚蠢的錯誤平均步驟。

FILE, forgetting that the actual brightness values were square-rooted by the camera for

雖然photoshop和其他專業軟體有進階設定可以調整，

better data storage!

讓你能用數學和物理正確的方式混合，

So the average ends up being too dark, precisely because an average of two square roots is

然而美麗不該作為預設值嗎？ (這就是精確數學的威力！)

always less than the square root of an average.

To correctly blend the red and green and avoid the ugly dark sludge, the computer SHOULD

have first squared each of the brightnesses to undo the camera’s square rooting, then

averaged them, and then squared-rooted it back – look how much nicer it is!!

Unfortunately, the vast majority of software, ranging from iOS to instagram to the standard

settings in Adobe Photoshop, takes the lazy, ugly, and wrong approach to image brightness.

And while there are advanced settings in photoshop and other professional graphics software that

let you use the mathematically and physically correct blending, shouldn’t beauty just

be

the default?