• Objective here is to visualize the dominant modes of variability in 3D faces mainly, and not focus on facial texture.

• The attached notbook analyzes the variability in given data and also presents some extreme variant of 3D faces generated using eigenfaces, which captures at least 98% variability in the data.  

• Synthetic 3D Face of about 500 faces is available.

• Each of the faces is represented by 7160 dimension 3D coordinates. 

• To compute eigenfaces using Principal Component Analysis (PCA), each 3D face coordinates of N points are arranged in 3N (3*N) dimensions, that is, a 3D face composed of 7160 points by 3 ordnaties is represented by 21470 points (3*7160).

• To get back eigenface from eigenvector the 3N points are reshaped to [N * 3] dimension.

• The average face is mean of all the faces that also acts as template face for visualizing variability in generated 3D faces. 

• where is a new face which is generated using eigenfaces () by varying magnitude of .  
• Variant of faces are generated using average face as template and adding extreme combination of eigenvectors () to show range of faces that can be produced.

• Very few eigenfaces (38) are needed to capture (98%) of variability in data. Although, the data being synthetic with not much variability in it is also playing a role in requiring very few eigenfaces to capture 98% variability.

• One can generate any number of faces using a combination of eigenfaces.  

[1] White, Julie D., et al. "MeshMonk: Open-source large-scale intensive 3D phenotyping." Scientific reports 9.1 (2019): 1-11.

[2] Cootes, Tim, E. R. Baldock, and J. Graham. "An introduction to active shape models." Image processing and analysis (2000): 223-248.