Statistical Shape Analysis

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.)

Data:

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.

Usage:

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

Documentation:

• 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