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eigenfaces's Introduction

Eigenfaces

R Project by Marcel Fischer, Ida Jandl and Aaron Osburg

within the course "Programming Language R" - Summersemester 2020.

Table of contents

General info

This Project contains the principle component method on a large set of images of different human faces (here: Olivetti Dataset). The derived eigenvectors are called eigenfaces. They can be used for human face recognition.

Technologies

Project is created with:

  • R Version: 4.0.2

Setup

To run this project, we recommend using RStudio.

Illustration

Nine examples of the images in the Olivetti Dataset: (plots created with this code.)

Example of Images in Olivetti Dataset

First nine eigenfaces of the Olivetti Dataset: (plots created with this code.)

Nine Eigenfaces of the Olivetti Dataset

Projection of images onto the first two eigenfaces: (plots created with this code.)

Projection on eigenfaces Projection on eigenfaces

Furthermore, a classifcation algortihm is implemented. Here it is performed on picture 33 of the dataset.

3 Closest neighbor

Additional content:

  • Shiny App
  • Vignette
  • Extensive documentation

We recommend reading the vignette for additional details.

Sources

This Project is inspired by Marinovsky F., Wagner P., Gesichtserkennung mit Eigenfaces, FH Zittau/Görlitz

eigenfaces's People

Contributors

ida-droid avatar osburg avatar mafi2 avatar

Stargazers

Christof Schötz avatar

Watchers

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eigenfaces's Issues

Unklarheit zur Hauptkomponentenanalyse

Wie in dieser Arbeit beschrieben, wird nicht das Eigenwertproblem für C = A * A^T gelöst, sondern stattdessen das für C' = A^T * A. Aus den Eigenvektoren C' lässt sich eine (unechte!) Teilmenge der Eigenvektoren von C bestimmen. Damit werden als Eigenfaces diejenigen Eigenvektoren von C (bzw. C') bestimmt, die die größten Eigenwerte (innerhalb der Teilmenge) haben. Da jedoch nur eine unechte Teilmenge der Eigenvektoren von C betrachtet wird, ist aber nicht sichergestellt, dass es sich tatsächlich um die Eigenvektoren von C mit den größten Eigenwerten handelt (d.h. die optimalen Eigengesichter sind). (Oder übersehe ich hier etwas?)
Das beschriebene Problem lässt sich aber glaube ich nicht so leicht lösen, da das obige Vorgehen sehr viel Rechenzeit spart.

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