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Covariance functions

In this video Marcel Lüthi explains the basic mathematical properties a covariance function needs to fulfil.

Using a Gaussian Process model to model the shape variations within a shape family, we have two parameters to characterise what constitutes a likely shape: the mean function and the covariance function.

In this video we discuss the mathematical properties of a valid covariance function and show how we can define interesting covariance functions for modelling shapes, even when we have no example shapes available to learn the covariance function from data. This knowledge will greatly enhance our modelling ability and allows us to overcome limitations of classical shape models.

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Statistical Shape Modelling: Computing the Human Anatomy

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