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Wrapping up: Week 6

In this week we have seen how we can fit a model to a target surface. To this end we have introduced a variant of the classical Iterative Closest Points …

Wrapping up: Week 5

This week we have made a big leap into practical applications of shape modelling. We have discussed Gaussian Process (GP) regression, which lets us incorporate knowledge about deformations that we …

Positive Semi-Definite Kernels

A covariance function needs to be positive semi-definite (p.s.d) to define a valid Gaussian Process model. While this property is not easy to check, once we know that a kernel …

Wrapping up: Week 4

This week we have seen how we can generalize the classical point distribution models, by allowing the covariance function to be defined by any positive semi-definite kernel function. We experimented …

Wrapping up: Week 3

With this week’s topic, we have now covered all the concepts that we need for understanding how shape families can be modelled. After having discussed last week how shape families …

Covariance functions

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 …

Introduction

So far in the course we have learned how to define a Gaussian Process (GP(mu, k)) by estimating its mean (mu) and covariance function (k) from example data. Estimating the …

Scalismo Lab: building a shape model from data

In this hands-on step, we will learn how to build a statistical shape model from a given dataset of meshes in correspondence, using Principal Component Analysis (PCA) in Scalismo. Doing …

Wrapping up: Week 2

In this week we have set the mathematical foundations for the rest of the course. Most importantly, we have seen that we can think of any shape in the shape …

Wrapping up: Week 1

In this week we have taken a look at the main concepts and basic notions of shape modelling. We have discussed what we mean by the term shape and how …

What is Principal Component Analysis (PCA)?

A very popular method in shape modelling is Principal Component Analysis (PCA). PCA is closely related to the Karhunen-Loève (KL) expansion. It can be seen as the special case where …

Finite rank representations of a Gaussian Process

In this video we will discuss an alternative representation of Gaussian Processes using the the Karhunen-Loève expansion (KL). We will provide a visual explanation of this expansion and discuss how …

Gaussian Process sampling and marginalisation

Get acquainted with discrete and continuous Gaussian Processes in Scalismo. Here we apply the concept of marginalisation of continuous Gaussian Processes in Scalismo and learn how to sample discrete deformation …