Bilinear models for action and identity recognition

Oxford Brookes Vision Group

26/01/2009

Fabio Cuzzolin

Bilinear models for invariant gaitID

The identity recognition problem View-invariance in gaitIDBilinear modelsHMMs and a three-layer modelFour experiments on the Mobo database

Identity recognition from gait

biometrics increasingly popularcooperative methods: face recognition, retinal analysissurveillance context: non-cooperative usersthe problem: recognizing the identity of humans from their gaitmethods: dimensionality

reduction, silhouette analysisissues: nuisance factors,

viewpoint dependence

A brief reviewgait signatures:

silhouettes [Collins 02, Wang 03], optical flow, velocity moments, shape symmetry, static body parameters

“baseline” algorithm [Sarkar 05]computes similarity scores between a probe sequence and each gallery (training) sequence by pairwise frame correlation

methodologies: mostly pattern recognition after dimensionality reduction

eigenspaces [Abdelkader 01], PCA/MDA [Tolliver 03, Han 04]

stochastic models (HMMs): [Kale 02, Debrunner 00]

KL-divergence between Markov models

Bilinear models for invariant gaitID

The identity recognition problem View-invariance in gaitIDBilinear modelsHMMs and a three-layer modelFour experiments on the Mobo database

The view-invariance issue

many different nuisance factorsnuisance factors are involved viewpointilluminationclothes, shoes, carried objectstrajectory

big issue: view-invarianceview-invariancepossible approaches:

3D trackingvirtual view reconstructionstatic body parameters

Approches to view-invariant gait ID

[Cunado 99]: “Evidence gathering” technique coupled oscillators, Fourier description, inclination of thigh and leg

[Urtasun,Fua 04]: fitting 3D temporal motion models to synchronized video sequences

Motion parameters: coefficients of the singular value decomposition of the estimated model angles

[Bhanu,Han 02] matching a 3D kinematic model to 2D silhouettes

extracting a number of feature angles from the fitted model

[Kale 03]: synthetic side-view of the moving person using a single camera[Shakhnarovich 01]: view-normalization from volumetric intersection of the visual hulls[Johnson, Bobick 01]: static body parameters recovered across multiple views

Bilinear models for invariant gaitID

The identity recognition problem View-invariance in gaitIDBilinear modelsHMMs and a three-layer modelFour experiments on the Mobo database

Bilinear models

From view-invariance to “style” invariance“style” invariancemotions usually possess several labels: action, identity, viewpoint, emotional state, etc.Bilinear modelsBilinear models (Tenenbaum) can be used to separate the influence of two of those factors, called “style” and “content” (the label to classify)

ySC is a training set of k-dimensional observations with labels S and CbC is a parameter vector representing content, while AS is a style-specific linear map mapping the content space onto the observation space

CSSC bAy

Bilinear models

the “content” (identity, action) of an observation can be thought of as a vector in an abstract “content space” of some dimension J

bC

AS

ySC

observations are then derived from content vector linearly, through a map which depends on the “style” parameter S

Learning an asymmetric bilinear model

given an observation sequence ySC…... an asymmetric bilinear model can fitted to the data through the SVD Y=SUV’ of a stacked observation matrix

the symmetric model can be written as Y=AB where

least-squares optimal style and content parameters are

SCS

C

yy

yy

Y

1

111

]',,[ 1 SAAA ],,[ 1 CbbB

JcolUSA ,...,1][ JrowVB ,...,1]'[

Content classification of unknown style

consider a training set in which persons (content=ID) are seen walking from different viewpoints (style=viewpoint)when new motions are acquired in which a known person is walking from a different viewpoint (unknown style)…… an iterative EM procedure can be set up to classify the content (identity)

E step -> estimation of p(c|s), the prob. of the content given the current estimate s of the style M step -> estimation of the linear map for the unknown style s

2

2~

2),~|(

csbAy

ecsyp

Bilinear models for invariant gaitID

The identity recognition problem View-invariance in gaitIDBilinear modelsHMMs and a three-layer modelFour experiments on the Mobo database

Hidden Markov models

finite-state representation of an observation process

state process {Xk} is a Markov chain

given a sequence os observations (feature matrix)...... EM algorithm for parameter learning (Moore)A->transition probabilities (motion dynamics)C-> means of state-output distributions (poses)

Motions as stacked HMMsinterpretation of the C matrix: columns of C are means of the output distributions associated with the states of the model

in gaitID (cyclic motions) the dynamics is the same for all sequences (A neglected)a sequence can then be represented as a collection of poses: stacked columns of the C stacked columns of the C matrixmatrix

Three-layer model

First layer (feature representation): projection of the contour of the silhouette on a sheaf of lines passing through the center

1

Third layer: bilinear model of HMMs3

2In the second layer each sequence is encoded as a Markov model, its C matrix is stacked in an observation vector, and a bilinear model is trained over those vectors

Bilinear models for invariant gaitID

The identity recognition problem View-invariance in gaitIDBilinear modelsHMMs and a three-layer modelFour experiments on the Mobo database

Mobo database: 25 people performing 4 different walking actions, from 6 cameras

each sequence has three labels: action, id, viewaction, id, view

MOBO database

Four experiments

we can then set up four experiments in which one label is chosen as contentone label is chosen as content, another one as another one as stylestyle, and the remaining is considered as a nuisance factorcontent style nuisance

actionview-invariant

action recognition

view ID

actionID-invariant

action recognition

ID view

IDaction-invariantgaitID

action view

IDview-invariant

gaitID view action

Results – ID versus VIEW

Compared performances with “baseline” baseline” algorithmalgorithm and straight k-NN on sequence HMMs

Results – ID versus action

performance of the bilinear classifier in the ID vs action experimentID vs action experiment as a function of the nuisance (view=1:5), averaged over all the possible choices of the test action the average best-match performance of the bilinear classifier is shown

in solid red, (minimum and maximum in magenta). Best-3 matches ratio in dotted red

Feature extractionType 1: projection of the contourprojection of the contour of the silhouette on a sheaf of lines passing through the center

Type 2: size functions [Frosini 90]

Type 3: Lee’s momentsLee’s moments

Results - influence of features

Left: ID-invariant action recognitionID-invariant action recognition using the bilinear classifier. The entire dataset is considered, regardless the viewpoint. The correct classification percentage is shown as a function of the test identity in black (for models using Lee's features) and red (contour projections). Related mean levels are drawn as dotted lines. Right: View-invariant action recognitionView-invariant action recognition.

Conclusions

covariance factorscovariance factors of paramount importance in gaitID

bilinear-multilinear modelsbilinear-multilinear models provide a way to separate different factorswe proposed a three-layer modelthree-layer model in which sequence are represented through HMMs

some approaches to view-invariance are expensive and sensitiveexpensive and sensitive

experiments on the Mobo database show how much separating factor is effective for motion classificationfuture: multilinear models, testing on more realistic setups (many factors, USF database)