What exactly is meant by translation invariant dictionaries/wavelets?

1. What is invariant in translation?
2. What is translation invariant in CNN?
3. What does the term translational invariance imply?
4. What is CWT and DWT?

What is invariant in translation?

Translation invariance means that the system produces exactly the same response, regardless of how its input is shifted.

What is translation invariant in CNN?

Translational Invariance makes the CNN invariant to translation. Invariance to translation means that if we translate the inputs the CNN will still be able to detect the class to which the input belongs. Translational Invariance is a result of the pooling operation.

What does the term translational invariance imply?

Translational invariance implies that, at least in one direction, the object is infinite: for any given point p, the set of points with the same properties due to the translational symmetry form the infinite discrete set p + na | n ∈ Z = p + Z a.

What is CWT and DWT?

This topic describes the major differences between the continuous wavelet transform (CWT) and the discrete wavelet transform (DWT) – both decimated and nondecimated versions. cwt is a discretized version of the CWT so that it can be implemented in a computational environment.