Quiz

Model fitting is always the first step in analysing a shape and is thus crucial for any application of shape modelling. Here are some questions that let you check your understanding.

Question 1

In order to analyse a shape using the model, we need to find a deformation field. What are the requirements for this deformation field? Multiple answers are possible.

It should represent the deformations from the reference shape to the target shape.

It should represent the deformations from the mean shape to the target shape.

It should establish correspondence, i.e. the deformation field should map corresponding points to each other.

It should map exactly to the contour or surface of the target shape.

Question 2

Can we expect the Iterative Closest Point (ICP) algorithm to find a global optimum?

Yes, it will always find the globally best solution.

No, it will only find the next local optimum.

Question 3

The ICP procedure can be stopped at two instances: after the search for closest points, (which will lead to a discrete deformation field that matches the target contour exactly) or after applying Gaussian Process regression, where we do not necessarily match the contour. Are there cases where it is better to stop the procedure after the regression step?

No, this does not make sense, as we won’t have correspondence in this case.

Yes, for example in cases where the given target contour is noisy.

Question 4

Assume have a model where the deformations at every point are independent (think of a model whose covariance function is a Gaussian kernel with smoothness parameter close to 0). What can we say about the result of the ICP procedure?

We find a good solution quickly, because the model is very flexible.

We cannot expect to find a good solution, because the model is too flexible and will not be able to correct the deformation found in the closest point step.

Question 5

What is the advantage of using the shape model as prior knowledge for finding the deformation field that relates the reference to the target shape? Multiple answers are possible.

The shape model allows us to recognize and discard noise in a target shape.

The shape model restricts the space of possible solutions, which allows us to search more efficiently.

The shape model restricts the space of possible solutions, and hence we are more likely to find the global optimum.

Because it enlarges the space of possible solutions and hence allows us to find a better solution.