Date of release: Wednesday, July 1, 2015

Sport Science academics revive 'Ancient Mathematical Methods, developed by Pappus of Alexandria' to analyse modern-day film of the moving athlete and present their findings at a major conference this week.

Dr Mark Colpus and Dr Mark Goss Sampson have been invited to attend the 33rd International Conference on Biomechanics in Sports in Poitiers, France this week, to present their latest research in  Modern Performance Technology.

A key aspect of Sports Science involves the analysis of human movement, using mechanical principles (Biomechanics). The most common way to make measurements of human movement in biomechanics is to use sophisticated video filming techniques. One of the most advanced methods involves filming human movement from a number of different angles, so that a 3-D image of the human being in motion, can be reconstructed on a computer.

However, getting accurate measurements when using this multi-angle type of filming and analysis is very challenging. That's because the human being might be moving away from, or towards, the cameras. Often the movements are at unusual angles, relative to the camera.

A mathematical method to deal with this challenge was first introduced centuries ago (by Pappus of Alexandria, c.290 – c.350 AD) and was updated in modern times (in 1803) by a person called Lazare Carnot. He called this mathematical film analysis technique the 'cross-ratio' technique. No-one has really used this technique (despite its existence for a couple of centuries) to analyse the moving sports person when they are filmed using modern-day technology.

For the mathmeticians, the cross-ratio measures the projective invariance of four collinear points in Euclidean Space and directly links the object and image space.

Dr Colpus explains his area of expertise and its relevance to the conference.

"People are easy to observe but difficult to measure.  The common approach is to take a measurement technique and look for a situation in which to apply it.  I work in the opposite direction, starting with the situation and then finding the best way to measure it.  This means I spend a lot of time studying esoteric mathematical methods that do not lend themselves easily to modern digital techniques but do accurately reflect the situation I am looking at.  There is  a tendency now to collect lots of data, blindly process it through a 'black' box and then look for answers in the rather non-specific output".

"I will try a more basic and intuitive approach.  So, if data is coming from more than one camera, it makes sense to switch cameras so I am always using the best image for what is being measured.  Also most human action is 'linked', so there are multiple indicators of the same action – I will try to identify all the indicators to get a more complete story.  For example, given the footage of the top half of a runner, it is usually possible to say if he/she is a heel or forefoot striker without seeing the legs".

"The research paper introduces the concept of cross-ratio, a projective invariant measure that gives the same answer for all images".

The conference itself attracts a huge audience of expertise from around the world showcasing the latest research in Biomechanics.

They will be presenting their research on Friday 3 July 2015.