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F-AHG-4: Medical image analysis: bending invariant surface registration

This project is motivated by hip fracture, a hugely important health and wealth issue. Hip fracture amongst the elderly causes significant physical and emotional distress, and the cost to health services is considerable, with annual cases forecast to rise to 6.3 million worldwide by 2050. High risk individuals could receive targeted therapy (drugs, exercise), but current screening methods fail to spot the majority of individuals who go on to fracture.

Our recent research demonstrates the potential of cortical thickness maps. These are coloured renderings of the bone surface that show the thickness of the stiff, outer shell (cortex) which is responsible for most of the bone's strength. However, in order to answer the important questions (what type of cortical thickness distribution might predispose an individual to fracture, does any particular therapy increase cortical thickness in the right regions?) it is necessary to compare cortical thickness maps across many individuals. And before we can compare one individual with another, we need to express all the cortical thickness maps on a common surface mesh.

We do this by taking the common mesh and deforming it until it aligns with each individual. This process is known as spatial registration. The aim of this project is to improve the registration algorithm by making it invariant to bending of the surface. We could do this by generating a bending invariant signature of each surface, in which the Euclidean distance between each pair of vertices approximates the geodesic distance (i.e. the distance measured along the surface). We would then spatially align the two signatures using our existing registration algorithm. Alternatively, we could generate an ensemble of common meshes with different neck-shaft angles using Blender, and then pick the one that best matches each individual. This project would suit a student who has taken Module 3G4. If you take on this project, you will learn a lot about computational geometry and graphics.

Our recent research has shown how to extract cortical thickness maps (top right, pink is thin, blue is thick) from CT data (top left) by deconvolution (bottom). The result is a detailed, accurate map of an individual bone.
For cohort studies, we need to register individual femurs (left, green) onto a common mesh (left, red). We currently do this using a global transformation (left, first seven frames) followed by a nonrigid deformation (left, last seven frames). After registration, the thickness map is transferred across to the common mesh.
This project will look at ways of making the registration invariant to bends in the surface, for example the angle the femoral neck makes with the shaft. We could do this by aligning not the surfaces themselves, but bending invariant signatures of the surfaces. The figure on the left shows two poses of a human being (top). Trying to register these surfaces based on spatial proximity would be doomed to failure. Instead, we could calculate a bending invariant signature of each surface (bottom), where the Euclidean distances approximate the geodesic distances, and then establish vertex correspondences by registering the two signatures.
© Cambridge University Engineering Department
Information provided by Andrew Gee
Last updated: March 2017