# Mini-projects for the advanced Masters degrees

## Ela Claridge

My research area is image understanding and computer vision, especially in application
to medicine and biology. The projects on offer are all related to current research
and would be an ideal introduction for students wishing to pursue doctoral studies
in medical image analysis. Most projects involve mathematics and the students choosing
them will have to be prepared to master the necessary background and techniques
- if needed I shall provide support and guidance. I also very much welcome discussions
with students interested in medical image analysis who have their own project ideas
in this domain.

### Parametrising models of tissue histology using Manifold learning

Imagine a set of points (x,y,z) forming a “swiss roll” with values f(x,y,z) increasing from
the centre of the roll outwards. Parametrising such sets (i.e. finding a functional
form of f) in Cartesian space is quite hard, especially if the geometry of the point
set is not known a priori (unlike knowing that the points form a swiss roll). If
you could unwrap the roll to form a rectangle g(x’,y’) parametrisation would be
trivial as g increases monotonically as a function of (say) y’. Manifold learning
is a family of methods based on non-linear dimensionality reduction
(see e.g.
a Wikipedia page )
that we would like to use to learn a lower-dimensional functional form of abstract
models of tissue histology. This could then be used for classification of tissue
properties and, further on, for detection of abnormal areas such as early cancer.
The project will explore various methods of dimensionality reduction, initially
on the swiss roll model.

### Optimisation for quantifying distribution of the macular pigment in retinal images using Zernike polynomials

Macular pigment (MP) plays an important role in maintaining health of a retina. The amount of pigment as well
as its distribution can be used for early diagnosis of eye diseases such as Age-related
Macular Degeneration (AMD). Our group has developed a novel method for extracting
maps showing the distribution of macular pigment from multispectral images
(see an example of the map).
The challenge remains in deriving quantitative parameters characterising the
distribution of MP.
Zernike polynomials
form an orthogonal basis function set that seems particularly
compatible with the kind of shapes we see in MP maps. This project will use optimisation
methods to fit Zernike polynomials (ZP) to the MP distribution maps. It is anticipated
that the coefficients of ZP will provide a quantitative parametrisation of the macular
pigment distribution.

*Maintained by Ela Claridge*

*Last update: 2 March 2018*