通道均值（Channel-wise Mean）与像素均值（Pixel-wise Mean）的计算及二者差异解析求助

Hey there! Let's break down the difference between channel-wise mean and pixel-wise mean clearly—this is a super common point of confusion when working with image data, so you’re not alone.

First, Let's Lock in Definitions & Outputs #

Let’s start with the basics to avoid mix-ups:

Pixel-wise Mean (Global Image Mean) #

• This is the overall average of every single value in the entire image, regardless of which channel it’s in.
• You sum up every numerical value across all pixels and all channels, then divide by the total number of values (that’s width × height × number of channels).
• The output is a single scalar number.
• Quick example: For a 2x2 RGB image (3 channels), there are 12 total values. Add all 12 together, divide by 12—that’s your pixel-wise mean.

Channel-wise Mean (Per-Pixel Channel Average) #

• As you noted, this returns an MxN matrix (same dimensions as your original image’s width/height). Here’s why:
• For every individual pixel location, you calculate the average of all the channel values at that spot. If you’re working with RGB, that means averaging the R, G, B values for each pixel, then compiling those averages into a single-channel MxN matrix.

Step-by-Step Math for Channel-wise Mean #

Let’s use a tiny concrete example to make this stick:

Suppose we have a 2x2 RGB image with these pixel values:

# Pixel (0,0): R=10, G=20, B=30
# Pixel (0,1): R=40, G=50, B=60
# Pixel (1,0): R=70, G=80, B=90
# Pixel (1,1): R=100, G=110, B=120

Calculate the channel mean for each pixel:

• (0,0): (10 + 20 + 30) / 3 = 20
• (0,1): (40 + 50 + 60) / 3 = 50
• (1,0): (70 + 80 + 90) / 3 = 80
• (1,1): (100 + 110 + 120) / 3 = 110

The final MxN matrix looks like this:

[[20, 50],
 [80, 110]]

Quick Clarification: Don’t Mix Up with "Per-Channel Global Mean" #

A quick heads-up: Sometimes people use "channel-wise mean" to refer to a different calculation—the global average of each individual channel (e.g., for RGB, you’d get 3 numbers: average of all R pixels, average of all G pixels, average of all B pixels). That outputs an array equal to the number of channels, not an MxN matrix. But based on your description, you’re referring to the per-pixel channel average, so we focused on that.

Easy Way to Remember #

• Pixel-wise mean: Everything in the image, averaged into one number. Think of dumping all the image’s values into a bucket and taking the average.
• Channel-wise mean (MxN output): Each pixel’s own channel values, averaged into one value per pixel. Think of compressing each multi-channel pixel down to a single number, keeping the image’s original shape.

内容的提问来源于stack exchange，提问作者Olutomilayo Dolapo