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
progress^{2}, 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.

- Contents
- List of Figures
- Overview

- Existing Work/Literature Survey

- Methods
- Model-building
- Data Alignment
- PCA
- PCA for Animation
- GMDS vs. PCA
- GPCA
- Algorithm
- Outline/Thoughts About Operation
- Systematic Experiments

- Data

- Implementation
- Preparation and Preprocessing
- Normalisation
- Expression Models
- Registration
- Modelling
- Control Files
- Graphical User Interface
- Remote Access to the Program

- Experimental Framework

- Ongoing Progress and Results
- Visualisation
- Statistical Analysis
- Detection
- Automation
- Similarity Measures
- Performance
- Benchmarks
- Full Model (EDM) for FRGC Data
- ICP
- Systematic Experiments
- Residue Adjustments
- ROC Curves
- Initial ROC-based Benchmarks
- Downsampled Images for PCA
- Model-based approach
- ICP Revisited
- New Similarity Measure
- Effects of Lambda Changes
- Debugging ICP
- Translation Explored
- Multi-feature PCA
- Multidimensional Scaling - Animated Example
- Exploratory GMDS Integration
- Full-face PCA
- GMDS on Smaller Face Parts

- Texas Database
- Planning for Final Stages
- Caching Code
- Backporting
- C++ FMM Debugging
- Workaround implemented
- Resolution Increases
- Smoothing
- Resolution increased
- Residuals
- Higher Resolution
- 2006 Experiments and Geodesic Masks
- Preparing Larger Experiments
- False Positive - a Dilemma
- Fallback Discriminant
- Making a More Stable Classifier
- Occlusion Based on FMM for Matching
- More FMM Results
- FMM-based Dissimilarity
- Rotation
- More Data Points
- Geodesic Slices
- Surface Signatures
- Vectorised Signatures
- Hybrid and Bugs
- Alternations to the Algorithm
- Eyes vs Nose
- Exact geodesic_library
- Removing Cases of Uncertainty
- Recognition Results
- Number of Vertices vs Recognition Rates
- Trial and Error in Parallel
- Geodesic lenses
- Weighting for Source Points
- Weighted Similarity Measure
- Early Results With Weighting
- Nose Tip Revisited
- Similarity Measure Variants
- ROC Curve - Without Smoothing
- Spectral Masks

- Diffusion Distance

- Summary and Conclusions
- Bibliography
- About this document ...