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I'm reading an article about multi-scale representation of image, and it is said that, convolving the image with a Gaussian kernel at different $\sigma$, then different scale representation is created.

This really confuses me, because I think the image is just blurred by Gaussian with different $\sigma$, each blurred version still has the same image size, so I don't think they're scaled, unless each blurred is downsampled to a smaller image size, which means I think different size representation is truely the

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The larger the σ of the blur kernel, beyond an amount intrinsic to the image, the more the image is low-pass filtered and thus suitable for downsampling with little additional loss of information due to aliasing. This use of the term "scale" seems to relate to the remaining information content or to the size to which an image is suitable for downsampling without significant additional filtering. Here, scale is not just the current number of pixels, which may be larger (but carry little additional information).

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Multi Scale means different scale of details of the image.
It comes from the intuition that blurring image with Gaussian Blur with $ \sigma $ vanishes data which is smaller then $ \frac{\sigma}{3} $.

In practice it is similar to Multi Rate Analysis of Filters in Signal Processing.
You look at the image in frequency domain and divide its data into octaves.
This partition can be done with any LPF Filter (Yet for perfect reconstruction there is some analysis).
In Image Processing the most widely used LPF is the Gaussian Blur.

By the way this is the idea behind Wavelets as well (Intuitively, in Wavelets they create special family of filters with certain set of properties).

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