Shift invariance in image processing

1. What is shift invariance in image processing?
2. What means shift invariant?
3. How do you know if shift is invariance?
4. What is shift equivariance?

What is shift invariance in image processing?

A shift-invariant system is one where a shift in the independent variable of the input signal causes a corresponding shift in the output signal. So if the response of a system to an input is , then the response to an input is .

What means shift invariant?

Shift-invariance: this means that if we shift the input in time (or shift the entries in a vector) then the output is shifted by the same amount. Mathematically, we can say that if f(x(t)) = y(t), shift invariance means that f(x(t + ⌧)) = y(t + ⌧).

How do you know if shift is invariance?

If g(x + x0) = H[f(x + x0)] then the system is shift invariant, otherwise it is not.

What is shift equivariance?

So in this case the output of the cat detector should shift exactly in the same way as the cat is shifted So basically shift equivariance means that (click) sfx produces the same result as fsx. In other words f and S commute. F applied to shifted S is the same as S applied to f applied to the output of f.