Quiz

Additionally to estimating the parameters of a Gaussian Process from data, we have learned how define a Gaussian Process ourselves by defining the covariance functions. In this quiz you can check if you have understood how this can be done.

Question 1

Smoothness of a deformation field means that the deformation of two points that are close together is similar. Why do we virtually always make this assumption when modelling shapes?

It implies that points, which are close together on the reference surface, will remain close together in the new shape.

It reflects the fact that the shapes themselves are always smooth.

Assuming smoothness makes the modelling simpler.

Question 2

What happens to the shape variations if we multiply the covariance function with a scalar greater than 1?

The deformations are diminished (the variance of each point becomes smaller).

The deformations are amplified (the variance of each point becomes larger).

There is no change. The multiplication only affects the correlation between the deformations.

Question 3

What is the effect of increasing the parameter σ in the Gaussian kernel?

The deformations are amplified.

The deformations become smoother.

The deformations become less smooth.

Question 4

If we want to limit correlations to only one part of the domain, how could we achieve this effect?

We could multiply a given covariance function with a kernel for which k(x,x’) is zero if either x or x’ is not part of this domain.

We could multiply a given covariance function with a kernel for which k(x,x’) is zero if both x and x’ are not part of this domain.

We could add a given covariance function with a kernel for which k(x,x’) is zero if both x and x’ are not part of this domain.