What is the difference between single scale and multi scale?

Question

My question is about the difference between single scale and multi scale in scale space theory. But I think I have to write what I understand about scale space theory and what I guess is the difference between single scale and multi scale:

• Kernel is an operator which we put on detected data and save its result as sample points.
• Out put of operation depends on size of kernel and its coefficients.
• If size of kernel and its coefficients only depend to one independent variable, the operator is called single scale, for example for Single Scale Retinex which those only depend on size of Gaussian kernel.
• Multi Scale Retinex is a multi scale operator; because it is defined as the weighted average of n Single Scale Retinex images for different σ values.

Am I understand concepts true? Also what about difference between single scale and multi scale?

Answer 1

In analogy to Discrete Fourier Transform, you may thing the DFT analyze the data using Multi Frequency approach. We check the response of the data to different frequencies where the response is based on correlation with some signal.

In Multi scale the idea is the same, checking the response of the signal to different templates.
Usually it is some kind of a kernel which we can change its scale.
The most common one is the Gaussian kernel and the scale parameter is the variance of the kernel.

The idea is developed under the concept of Wavelets where it is build by a frailly of kernel with some mathematical properties.

In you example, multi scale means we analyze the output of a set of images each is a response to convolution to a Gaussian Kernel with different variance.