Yüz Tanıma ve Uygulamaları Prof.Dr. Muhittin Gökmen İstanbul Teknik Üniversitesi Bilgisayar Mühendisliği Bölümü.

Yüz Tanıma ve Uygulamaları

Prof.Dr. Muhittin Gökmen İstanbul Teknik Üniversitesi

Bilgisayar Mühendisliği Bölümü

Yüz Tanıma

Resim alma

Sayısallaştırma

Yüz yerini bulma

Yüz tanıma

Zorluklar

Poz değişimleriAydınlatma değişimleriYüz ifadesindeki değişimlerÖlçek değişimleriZamanla yüzde oluşan değişimlerTanınacak kişi sayısının çokluğuHesaplama hızı

Yüz tanıma yöntemleri

1. Şablon eşleme Representing a whole face using templates like a 2-D array of intensity Combine with some features like eyes, nose and mouth. Simple but large memory and inefficient matching algorithm

2. Özniteliklere dayalı yöntemler Geometric features, position/width of eyes, noses, mouth, face breadth, etc Small memory, higher recog speed but hard feature extraction

3. Özyüzlere dayalı yöntemler Project face images into a linear subspace with low dimensions Eigenface

EigenfacesEigenfaces

w1 w2 w3 w4u1 u2 u3 u4

original face mean face caricature face

Each face is a linear composition of the maximum eigenvalued eigenvectors (eigenfaces),

I.T.U. CVIP Lab.I.T.U. CVIP Lab. November, 1999November, 1999Alper YILMAZ M.Sc. Thesis

EigenFaces

EigenFaces0. Initialization: acquire the training set of face images and calculate the eigenfaces, which define the face space

•Each image is N by N

•Set of training images Γ1, Γ2, … , Γm, (Γi is a column vector of size N2 *1 )

•150 images of 15 individuals

EigenFaces0. Initialization: acquire the training set of face images and calculate the eigenfaces, which define the face space

•Each image is N by N

•Average face of the training Set

• Ψ = ( Σ Γi )/M

EigenFaces0. Initialization: acquire the training set of face images and calculate the eigenfaces, which define the face space

Each training image differs from the average face by: Φi = Γi – ΨA total number of N2 pairs of eigenvectors μi and eigenvalues λi of the covariance matrix

C = (ΣΦiΦi T)/M = AAT (C: N2 * N2 matrix) Eq. (1)

where A = [Φ1 Φ2 Φ3 … ΦM] (A: N2 * M matrix) ??

It is Computationally Intractable

EigenFaces0. Initialization: acquire the training set of face images and calculate the eigenfaces, which define the face space

For Computational Feasibility -- Only M-1 eigenvectors are meaningful M< N2

eigenvectors νi and eigenvalues λi of the covariance matrix L = ATA ATA νi = λi νi

A ATA νi = λi Aνi

Therefore, Aνi are the eigenvalues of C = A AT , λi are the associated eigenvalues

μi = A νi The associated eigenvalues allow us to rank the eigenvectors according to their usefulness in characterizing the variation among the images

EigenFaces0. Initialization: acquire the training set of face images and calculate the eigenfaces, which define the face space

The first 15 eigenfaces corresponding to the 15 largest eigenvalues.

EigenFaces

Construction of Known Individuals’ Face Classes -- Each image Γi of known individuals is projected onto “face space” by a simple operation ωk = μk

T * ( Γi - Ψ ) , where i=1, 2, ……, M represents the ith individual, The pattern vector of the ith individual is

Ωi = [ω1 … ωM’ ] -- If an individual has more than one image, take the average of the pattern vectors of this person

EigenFaces0. Initialization: acquire the training set of face images and calculate the eigenfaces, which define the face space

Γf = ω1μ1 + … + ωM’ μM ’

Γ1

EigenFaces1. Calculate a set of weights based on the input image and M’ eignefaces by projecting the input image onto each of the eigenfaces

Γf = ω1μ1 + … + ωM’ μM ’

Input Γωk = μk

T * ( Γ - Ψ ) Ω = [ω1 … ωM’ ]

EigenFaces2. Determine if the image is a face at all by checking to see if the image is sufficiently close to face space.

Γf = ω1μ1 + … + ωM’ μM ’

Input Γωk = μk

T * ( Γ - Ψ ) Ω = [ω1 … ωM’ ]

Φ = Γ - Ψ ε2 = |Φ- Γf |2

If ε < θ ( θ is a threshold)Then Γ is a faceElse Γ is not a face

EigenFaces3. If it is a face, classify the weight pattern as either a know person or as unknown.

Γf = ω1μ1 + … + ωM’ μM ’

Input Γωk = μk

T * ( Γ - Ψ ) Ω = [ω1 … ωM’ ]

Ωi is a vector for an existing face class ε = | Ω - Ωi |2

If ε < θ ( θ is a threshold)Then Γ is a known faceElse Γ is not a known face