如何计算200×200像素图像的无损压缩比？

Let’s walk through this step by step to make it crystal clear:

1. Calculate the original uncompressed data size #

First, we need to find how much space the image takes without any compression:

• Total pixels in the image: 200 × 200 = 40,000 pixels
• Each pixel uses 10 bits to represent its color
• Original size = 40,000 pixels × 10 bits/pixel = 400,000 bits

2. Determine the compressed data size #

Since we’re using the shortest possible equal-length codes for up to 4 unique colors:

• To represent 4 distinct values, we only need 2 bits (because 2² = 4—think of 00, 01, 10, 11 as unique codes for each color)
• Compressed size = 40,000 pixels × 2 bits/pixel = 80,000 bits

3. Compute the compression ratio #

The compression ratio here is the percentage of the original size that the compressed file occupies. The formula is:

Compression Ratio % = (Compressed Size / Original Size) × 100

Plugging in our numbers:

(80,000 / 400,000) × 100 = 20%

That’s exactly where the 20% comes from—each pixel’s data is reduced from 10 bits to 2 bits, which is 1/5 of the original size, or 20%.

内容的提问来源于stack exchange，提问作者Drago