JPEG 压缩

JPEG is a clever image compression algorithm that exploits a human perceptual bias and the structure of natural images. It makes a change of basis before encoding so that the rewritten image representation concentrates the signal that humans are most perceptive to, and thus, the remaining details can be discarded without horribly degrading visual fidelity.

JPEG 是一种巧妙的图像压缩算法，它利用了人类的感知偏差和自然图像的结构。在编码之前进行基变换，使得重写的图像表示集中了人类最敏感的信号，因此，其余细节可以被丢弃而不会严重降低视觉保真度。

A digital image is a mapping from two-dimensional spatial coordinates to pixel values:
I:D⊂Z2→C.I: D \subset \mathbb{Z}^2 \to \mathcal{C}.I:D⊂Z2→C. Here DDD is a finite grid of pixel locations and C\mathcal{C}C is the set of possible values. In the RGBRGBRGB model, C={0,…,255}3\mathcal{C}=\{0,\dots,255\}^3C={0,…,255}3, representing three 8-bit color channels.

一张 数字图像 是从二维空间坐标到像素值的映射：
I:D⊂Z2→C.I: D \subset \mathbb{Z}^2 \to \mathcal{C}.I:D⊂Z2→C. 这里 DDD 是像素位置的有限网格，C\mathcal{C}C 是可能值的集合。在 RGBRGBRGB 模型中，C={0,…,255}3\mathcal{C}=\{0,\dots,255\}^3C={0,…,255}3，表示三个 8 位颜色通道.

A property of human vision is that we are more sensitive to luminance (brightness) than to chrominance (color differences). Edges and fine detail in brightness are noticeable, while small variations in color are much harder to perceive. JPEG exploits this by separating brightness from color, meaning that instead of working directly in RGBRGBRGB, each pixel is converted to the Y′CbCrY'CbCrY′CbCr color space:

人类视觉的一个特性是我们对luminance（亮度）比对chrominance（颜色差异）更敏感。亮度中的边缘和精细细节很明显，而颜色的小变化则更难察觉。JPEG 通过将亮度与颜色分离来利用这一点，这意味着不是直接在RGBRGBRGB中工作，而是将每个像素转换为Y′CbCrY'CbCrY′CbCrcolor space：

(R,G,B)→(Y′,Cb,Cr).(R,G,B) \rightarrow (Y', C_b, C_r).(R,G,B)→(Y′,Cb,Cr).

Original RGB image

960px × 720px•Raw RGB: 1.98 MB

960px × 720px•原始 RGB: 1.98 MB

RGB R channel

Equivalently, the chroma channels encode how color deviates from the luminance signal: CbC_bCb is proportional to B−Y′B - Y'B−Y′ and CrC_rCr to R−Y′R - Y'R−Y′.

等价地，色度通道编码颜色如何偏离亮度信号：CbC_bCb 与 B−Y′B - Y'B−Y′ 成比例，CrC_rCr 与 R−Y′R - Y'R...