First Mode of Variation

Second Mode of Variation

Third Mode of Variation

Statistical analysis of 2D shapes based on "Generalized Procrustes Analysis" (Gower, J.C.) and "Active Shape Models - Their Training and Application" (Cootes et al.)

The dataset of 2D face images is publicly available here: IMM Face Database.
Download the data from the above link, place the files data_clean.sh and to_mat.py in the root directory of the downloaded data and run:

1. bash data_clean.sh
2. python3 to_mat.py

This will create faces2D.mat in the data directory.

• See code/main_1.mlx for approach based on Generalized Procrustes Analysis and code/main_2.mlx for approach based on Active Shape Models.

• code/main_1.mlx : Main script for the approach based on Generalized Procrustes Analysis
• code/main_2.mlx : Main script for approach based on Active Shape Models
• code/align1.m : Align two given pointsets of equal cardinality via similarity transformations assuming that the pointset representations are standardized to pre-shape space
• code/align2.m : Align two given pointsets of equal cardinality via similarity transformations, solving for the scale, translation, and rotation jointly
• code/optimize1.m : Runs the algorithm in the pre-shape space and uses align1.m
• code/optimize2.m : Runs the algorithm in the original space and uses align2.m
• code/toPreshape.m : Standardizes the pointset to pre-shape space
• code/updateMean.m : Finds the optimal shape mean given the aligned pointsets
• code/plotPointsets.m : Plots the set of pointsets as a scatter plot, each pointset in a different color
• code/plotWithMode.m : Plots the pointsets along with two sets of variation about the mean along the given mode of variation