消除像素怪兽：融合理论篇——Jim Blinn's Corner

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在Jim Blinn的"Jim Blinn's Corner"系列文章中，我们关注的是"Compositing, Part I: Theory"这一篇。这是一篇经典的关于计算机图形学的文章，由James F. Blinn撰写，他在加利福尼亚理工学院分享了他的见解。文章的核心内容是关于像素颜色与透明度的关联，即所谓的"alpha compositing"或"透明混合"技术。这项技术不仅因为其视觉效果优美（即"anti-aliening"，意指消除屏幕锯齿的效果，这里可能是指减少3D几何体和像素显示产生的视觉不平滑）而被重视，它在计算机图形处理中的实用性也得到了广泛认可。 Blinn提到，许多人在不同的领域独立地发现了这种存储像素并考虑其透明度的重要性，因此这个概念有了多个名称：如matting（图像剪辑）、image compositing（图像合成）、alpha blending（透明混合）、overlaying（叠加）以及lerping（插值）。其中，Porter和Duff的一篇论文对这种操作进行了完整的编码，他们将其称为"over"运算符。在这篇文章中，Blinn将介绍一种新的方法来处理和优化这个过程，这可能是对传统alpha compositing算法的一种创新或是对不同场景下的优化策略。他可能会探讨如何通过更高效的方式来实现像素的透明度计算，减少边缘锯齿，提高图像质量，或者如何在实时渲染、图形编辑软件甚至游戏开发中应用这一理论。 "Compositing, Part I: Theory"是关于计算机图形基础中的一个重要概念，它涉及像素处理的深入理论和实践技巧，对于理解现代图形渲染技术的发展具有重要意义。阅读这篇文章，读者可以了解到如何在数字艺术与技术中巧妙地结合透明度与颜色，以创建出流畅、无瑕疵的视觉体验。

JIM BLINN’S CORNER

Cornpositing, Part I: Theory

lames F. Blinn, California Institute of Technology

Associating a pixel’s color with its opacity is the basis for a

cornpositing function that is simple, elegant, and general. But there

are more reasons than mere prettiness to store pixels this way

My currently favorite journalistic quote comes from a mag-

azine called

Morph’s Outpost on the Digital Frontier.

They

refer to the operation of avoiding jaggies as “anti-aliening.”

Either this was a typo or they thought of the jaggies as aliens.

This got

thinking about ways to get rid of these creatures

-the offspring of 3D geometry and raster displays.

B,,, = Bo,d + a(F - Bad

One of the most important anti-aliening tools in computer

graphics comes from a generalization of the simple act of

storing a pixel into a frame buffer. Several people simultane-

ously discovered the usefulness of this operation, so it goes by

several names: matting, image compositing, alpha blending,

overlaying, or lerping. It was most completely codified in a

paper by Porter and Duff,’ where they call it the “over” oper-

ator. In this column I’m going to show a new way to derive

Porter and Duff’s “over” operator and describe some imple-

mentation details that I’ve found useful. In a later column 1’11

go into some of the subtleties of how this operator works with

integer pixel arithmetic.

You can actually use the value of a for a variety of things. In

addition to its anti-aliening function, it can represent transpar-

ent objects or establish a global fade amount. For this reason,

the a value also goes by various names: coverage amount,

opacity, or simply alpha. You can also think of it as 1 minus

the transparency of the pixel. I’m going to call it opacity for

now. If it’s 0, the new pixel is transparent and does not affect

the frame buffer. If it’s 1, the new pixel is opaque and com-

pletely replaces the current frame buffer color.

Next, suppose that we want to layer another object on top

of our image. We just blend in the new object’s color, which

1’11 call G, on top of our current background image using its

opacity p,

The basic idea

The simplest form of compositing goes as follows. Say we

want to overlay a foreground image on some background

image. The foreground image only covers a part of the back-

ground; pixels inside the foreground shape will completely

replace the corresponding background pixels, and pixels

outside the shape leave the background pixels intact.

We can keep on plastering stuff on top of our image until we

are happy. This is the essence of 2-1/2D rendering, also known

as the painter’s algorithm or temporal priority.

For most rendering purposes I’ve been able to provide this

as the only necessary accessing operation into the frame

buffer. But it’s not quite general enough.

Associativity

If we want anti-aliened edges, though, things are a bit more

There is another intriguing generalization here. Both F and

complicated. Pixels on the edge of the shape only partially cover G have an opacity, but B doesn’t. Does it even mean anything

the background pixels. If the shape is to be properly anti- to composite into a pixel that already has an opacity? Yes.

aliened, we must blend the foreground color, F, and background

Consider the following scenario. Suppose we have the images

color, B, according to the fraction CX. This value represents the

F and G, but haven’t yet decided what to use for a back-

percentage of the pixel covered by color F. The standard way to ground. Let’s see if we can merge F and G into one image, H,

calculate this is to find the geometric area covered by F. This that we can store away and later overlay on B to get the same

implements a simple box filter for anti-aliening. More accurate result. If we denote the compositing operation with the sym-

filters

can

be used, but 1’11 stick to the box for now. bol &, what we want is

Now let’s get down to algebra. F and B are each three-

element vectors representing the red, green, and blue compo-

nents of a pixel. Ordinary vector algebra applies. The new

color in the frame buffer is

(B&F)&G=B&(F&G)

In other words we want to make compositing

associative.

B,,, = (1 - a) Bold + aF

which can be more efficiently calculated as

How can we define H = F & G to make this work out? We

want to calculate a new pixel color H and opacity yin terms of

colors F and G and their own opacities a and 0. Plug in the

definitions:

September 1994

0272.17.16/94/$04.00 0 1994 IEEE

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