Reviewing eigenfaces

Ok, yesterday night I was trying to implement the eigenface algorithm [1] on MATLAB, using the AT&T [2] database, but I had some issues with it...
Let me explain myself what I did:

For a given face like this one:

This face can be thought as , so the mean face should be the sum of n samples of faces divided by n. So, the mean face just defined, can looks like as follows:

Now, given the mean face, we can get the difference between the mean face and the original face, in therms of the spatial domain and their intensity values, and it looks like this:

The eigenvalues of the the covariance matrix are defined as:

So then, the eigenvalues just obtained have been multiplied by the image obtained differencing the mean face and the original face, obtainig something like this:

This is called eigenface, however, this doesn't looks like the eigenfaces introduced on the journal articles regarding eigenfaces, therefore, I have to ask myself some questions, to get fully understanding of the main idea of the eigenfaces:

• "The eigenvector of the covariance matrix..." <--about which covariance matrix are they talking about? the original face covariance matrix? or the differenced face covariance matrix?
• The eigenface is the product between the eigenvalues and the differenced face?
• What the Karhunen-Loeve Transform does exactly?
• Is the eigenface part of the Karhunen-Loeve Transform?
• Where does the Principal Component Analysis (PCA) ends? Doues it ends getting the Karhunen-Loeve Transform; or, ends obtaining the eigenface?
• Do I deserve to eat today?

Well, I hope to get the answers to some of my questions, if someone want to comment, anything, I'll appreciate it.

[1] M. Turk, A. Pentland, "Eigenfaces for recognition", Journal of Cognitive Neuroscience, Massachusetts Institute of Technology, Vol. 3, No. 1, 1992.
[2] Face database propietary of AT&T Research laboratories.

Research Update

These past few days I’ve been writing down a table with some interesting information of the current state of the art, this information is: Name of the publication (transaction papers, journal papers, etc), PIE robustness, % of recognition, type of clasiffier, facial features extracted, year, database tested, and application. The papers done until now are this ones:

Deformation Analysis for 3D Face Matching Discriminative Common Vectors for Face Recognition
Face Recognition Using Laplacianfaces
High-Speed Face Recognition Based on Discrete Cosine Transform and RBF Neural Networks
Locally Linear Discriminant Analysis for Multimodally Distributed Classes for Face recognition with a Single Model Image
Wavelet-based PCA for Human Face Recognition
Real-time Embedded Face Recognition for Smart Home
Acquiring Linear Subspaces for Face Recognition under Variable Lighting
Appearance-Based Face Recognition and Light-Fields Bayesian Shape Localization for Face Recognition Using Global and Local Textures
A Unified Framework for Subspace Face Recognition
PROBABILISTIC MATCHING FOR FACE RECOGNITION
Face Recognition Based on Fitting a 3D Morphable Model
Appearance-Based Face Recognition and Light-Fields
Face Recognition Using Artificial Neural Network Group-Based Adaptive Tolerance (GAT) Trees
Face Recognition by Applying Wavelet Subband Representation and Kernel Associative Memory
Face Recognition Using Kernel Direct Discriminant Analysis Algorithms
Face Recognition Using Fuzzy Integral and Wavelet Decomposition Method
Face Recognition Using Line Edge Map
Face Recognition Using the Discrete Cosine Transform
Face Recognition System Using Local Autocorrelations and Multiscale Integration
Face Recognition Using the Weighted Fractal Neighbor Distance
Gabor-Based Kernel PCA with Fractional Power Polynomial Models for Face Recognition Gabor Wavelet Associative Memory for Face Recognition
N-feature neural network human face recognition
GA-Fisher: A New LDA-Based Face Recognition Algorithm With Selection of Principal Components
Kernel Machine-Based One-Parameter Regularized Fisher Discriminant Method for Face Recognition

Some authors try to get the reader confused about the results, trying to make himself look the best methodology with the best recognition rate. Here is where I loose the big part of the time, discovering the real % of recognition.

The first blog

The very first blog...

Well, well, well, this thing looks nice, I'll try to put some stuff as soon as possible.
Maybe I should call it "Pablog" <--- it's funny, doesn't it?

Ok, c-you.

SonoraEs...

This was a magazine citation from a concourse I have participated in. Date: July 2004
Original Hyperlink:
SonoraEs...: NOGALES

Destaca a ITN a nivel Nacional.
Estudiantes del Instituto Tecnológico de Nogales (ITN) obtuvieron primeros lugares, en concursos nacionales de creatividad, en los estados de Veracruz y Baja California. En Orizaba, Veracruz el primer lugar a nivel posgrado, fue para Julio César Ramírez, de la maestría en Ciencias Computacionales con el proyecto “Sistema experto borroso en diagnóstico”. En Mexicali, en la etapa regional de este concurso, los primeros lugares fueron para Pablo Rivas Perea con el proyecto “Reconocedor de rostros en movimiento mediante preceptores multicapa” del área de Sistemas Computacionales y en el área de Ingeniería Civil “Neruva” desarrollado por Gabriel Ruiz, Karla Morales y Carmen Rodríguez fue el proyecto ganador."

RECONOCIMIENTO DE ROSTROS MEDIANTE PERCEPTRONES MULTICAPA

This was my first keynote speech, on SINATI (Simposium Nacional de Tecnologias Informaticas)

RECONOCIMIENTO DE ROSTROS MEDIANTE PERCEPTRONES MULTICAPA
By Pablo Rivas Perea

ABSTRACT
El reconocimiento de rostros es un tema específico generalizado y clasificado en los problemas de visión por computadora conocido como detección, rastreo y clasificación. La tarea es detectar, localizar e identificar un rostro humano en una secuencia de video de tiempo real, que es obtenida de una cámara conectada a la computadora. Se han sugerido diferentes enfoques para resolver esta tarea; muchos de estos enfoques pueden ser divididos en dos grupos:
Escaneo exhaustivo. Cada uno de los frames-imagen es escaneado en al menos cada tamaño de subframe y el clasificador determina en cada subframe si un rostro está presente o no.
Movimiento y análisis de imágenes a bajo nivel. Mediante el análisis de movimiento de una secuencia de video (por ejemplo diferencia-frame) y técnicas de análisis de imágenes tal como orilla u operadores gradiente, un rostro es sensado presente después de aplicar cierta heurística (análisis de imágenes a alto nivel), junto con información del color.
Basado en tecnologías de redes neuronales, con este trabajo se demuestra que mediante el perceptrón multicapa se pueden identificar rostros reduciendo el porcentaje de error; usando metodos heuristicos para mejorar el aprendizaje de la red neuronal, el porcentaje de error para el MLP se redujo aun más. Esta investigación se basó principalmente en tres aspectos, la detección de movimiento, rostro y seguimiento,
preprocesamiento de la imagen, y reconocimiento del rostro, previamente la red neuronal fue entrenada en base a 100 imágenes de diez personas diferentes, en diferentes posiciones. Probado en diferentes instalaciones y situaciones reales, demostró ser capaz de reconocer rostros, y otros objetos visibles para los cuales haya sido previamente entrenada la red neuronal, por ejemplo, camiones de combate, armas automáticas, aviones, etc.

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