PDF version of this entire document


Roy Schestowitz1

Image crest


Statistics of disparate and absolute parts of the human face are a complex area of exploration due to high variation which is caused by facial expressions. There have been studies - despite scarcity in numbers - into how this variation can be modeled, but there is not sufficient consideration of different paradigms for studying this variation. Generalised Multi-Dimensional Scaling (GMDS) can overcome this by considering image surface rather than handle the complexity introduced by applying directional decomposition in a high-dimensional hyperspace. In both 2- and 3-D, information about depth can be used, although in the latter case this information is accurate, whereas in the former case there is reliance on estimation based on shadows or stereo vision, i.e. multiple angles. Three-dimensional methodologies usually rely on accurate measures that are not just relative but also absolute, meaning that the location of objects in the image should be capable of alignment wrt other images too. The application of these ideas in areas such as face analysis - including recognition, modeling, synthesis, and interpretation - is seen as promising with the advent of new acquisition equipment and modalities. A lot of data is made available and exploitation of its full potential is made possible by accounting for large sets of data. The more data becomes available, the more viable it becomes to study the statistics of faces and make inference based on the learnt information. Our attempt to reproduce some of the results of F. Al-Osaimi et al. and furthermore improve them using other methods and different datasets (with a 3-D scanner at our disposal), are described in this informal document, which in essence contains research notes for 3-D facial expression analysis through statistics (project starting 2011). It is work in progress2, so this text is eternally an informal draft that deals with comparing a principal component analysis (PCA) approach to a GMDS approach. Shall the goal be met by reasoning about the advantage of the latter, portions of this document may prove handy.

Roy Schestowitz 2012-01-08