# Pixel density - can the playing field be leveled???

Started Jun 6, 2009 | Discussions thread

Graystar wrote:

bushi wrote:

Graystar wrote:

When you downsample an image you’re not reducing the noise. You’re just making the noise smaller, along with everything else in the image.

It is not true. When downsampling, you are reducing noise. Why? The answer is, statistics. Noise by definition is random. Image details by definitions are NOT random. When you have four ideally red pixels forming a square, each of them with some random noise added to the ideal red value (bare in mind, noise can be positive or negative), and you resize this four pixels to 50% of its original size (meaning that they'll produce one pixel after downsampling), you will (in great simplification) end up with the mean value of the original four pixels - well, depending on actual algorithm, but there will be mean value of some sort involved, always.

And because noise is random, the noise values will (statistically, to some degree) cancel out , thus resulting in less-noisy pixel after scaling down.

I think you mean 25% of the original size (1 is 25% of 4.)

What you’re not realizing is that you are averaging out signal as well as noise, and so the signal to noise ratio stays the same. That’s why noise isn’t reduced.

In your example, with "4 ideally red" pixels, you've stepped into the same trap that DPReview's Phil Askey stepped into in his blog "Downsampling to reduce noise..." You've created a dimensionless image. If all the pixels in your image are just a single color then your image remains exactly the same no matter how you scale it. It will contain the same exact detail (none) whether you reduced it by 90% or expand it by 10,000%. Since the image contains no detail, or put another way, no signal, it cannot possibly be useful in evaluating shifts in the signal to noise ratio caused by image manipulations.

In a real image, manipulations will affect noise and detail in the same exact way, and the signal to noise ratio will stay the same.

There is signal (the brightness of the red patch), I think your point more precisely is that there is no high frequency signal. Noise has a spectrum that spans all spatial frequencies. When an image is downsampled, one removes high frequency signal (detail) as well as the high frequency noise. The remaining low frequency signal and noise are the very much the same (assuming the downsampling was done properly) as they were before downsampling, so the image at any given scale relative to frame size remains the same.

The problem with bushi's argument is that it compares the image noise at two different scales -- the pixel scale before downsampling, and the pixel scale after downsampling. The fact that noise at the latter scale is smaller is simply a statement that the magnitude of lower frequency noise is smaller, due to simple scaling properties of the random fluctuations of noise.

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