Respuesta :

The arbitrary rotations and positions are known as transformations.

Objects in space have arbitrary rotation and position which do not deform the objects.

The arbitrary rotations and positions are known as transformations.

By computing a fingerprint we can recognize the object's transformations.

A fingerprint can be computed using tensor fields of arbitrary order and dimension.

since this resembles the moment of inertia it is called the moment of the field.

There are two types of invariances:

  1. Rotational invariance
  2. Scale invariance

There are various properties of the above invariances;

Properties of rotational invariance:

  1. In value : M(f(x))= M(R(f(x)))
  2. In domain : M(f(x))= M(f(R^-1x))
  3. M(f(x))= M(Rf(R^-1x))
  4. M(f(x))= M(Rf([tex]R_{0}[/tex]^-1x))
  5. M(f(x))= M(f(x - t))

Properties of scale invariance:

  1. In value : M(f(x))= M(s f(x))
  2. In domain: M(f(x))= M(s f(x))
  3. M(f(x))= M([tex]s^{p}[/tex] f(x / s))
  4. M(f(x))= M (t f(x / s))

For more information on moments invariants click on the link below:

https://brainly.com/question/6278006

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