Efficient 3D Data Representation for Biometric Applications

Hassan Ugail and Eyad Elyan

School of Informatics University of Bradford

United Kingdom

Distributed Virtual Environments research Distributed Virtual Environments research

Research in the area of geometric modelling, virtual environments, virtual simulations, 3D modelling and rendering for entertainment and computer games.

11 members of staff,Several post-docsMany PhD and masters students.

Resources include: - 15 camera Vicon motion capture system (same as that used to create Lord of the rings movie. )

- A high end render-farm for rendering high quality geometric scenes.

example

Thanks Thanks

• Modelling and Animation, EPSRC grant value £281,500 + Support from Alias.

• Biharmonic Polynomial Surfaces. EPSRC grant value £10,070.

• 3D FACIS: Higher Education Innovation Fund (HEIF) grant, value £70,000.

• Magic Curves 3D for MAYA - University of Bradfordgrant, value £15,000.

We discuss techniques for representing 3D data for biometric applications.

e.g. It is a common problem to construct a smooth surface for some given point cloud data to adequately describe the shape. (e.g. scan data of a human face)

IntroductionIntroduction

1. Be able to model complex shapes (e.g. human face, body pose, shape of hand, DNA etc.)

2. Be able to parameterise the data (i.e. describe the data using a small parameter set of the underlying representation).

3. Efficient data storage (e.g. point cloud data from a 3D scan face is around 1MB which cannot be used to perform efficient searches)

Requirements of a 3D representation technique Requirements of a 3D representation technique

Existing Methods Existing Methods

A number of techniques currently exist for 3D data representation.

For example,

- Spline based techniques

- Subdivision techniques

Spline based techniques Spline based techniques

Uses polynomial interpolations, For example,

Bézier surfaces

NURBS

Problem: too many control points (difficult to parameterise the geometry)

Subdivision techniques Subdivision techniques

Uses simple set of local rules and can create geometry of arbitrary topology

Problem: generating smooth surfaces is an issue

Partial Differential Equations for 3D Partial Differential Equations for 3D Data Representation Data Representation

Heat

Heat

Imagine the steady state heat distribution of an insulated metal bar

- internal temperature depends on heat applied at the boundary- heat distribution is constant throughout at steady state - temperature will not exceed that supplied at the boundaries

02

2

2

2

2

2

z

H

y

H

x

HMathematically this can be modelled using Laplace Equation

The idea of Partial Differential Equations (PDEs) The idea of Partial Differential Equations (PDEs)

Now if we simply solve Laplace Equation with a set of boundary conditions and plot the resulting solution we will get a surface.

We know that: - surface shape depends on the shape of the boundary- surface is a smooth transition between the boundaries- internal surface points is less or equal to the boundary (a.k.a Min-Max principle)

The idea of Partial Differential Equations (PDEs) The idea of Partial Differential Equations (PDEs)

04

Elliptic operator Min/Max principle

guarantees Smooth transition between the boundaries

The PDE Method for Geometry Generation …The PDE Method for Geometry Generation …

u

v x

y

z

X(u,v)

The PDE Method for Geometry Generation The PDE Method for Geometry Generation

X(u,v) = (x(u,v), y(u,v), z(u,v))

32 )( ER

NoteThe boundary in the (u,v) space is mapped to that in (x,y,z)

n

X

Usually we choose the 4th order elliptic PDE:

0),(2

2

22

2

2

vuXv

au

Boundary conditions are:

variations of ),( vuX and along

• Boundary value approach

• Global smoothing approach

• Small set of design parameters

Advantages

a is a special parameter known as the smoothing parameter

Position Curves curves at u=0 and u=10<=v<=2

u=0

u=1

p1

p2

Derivative Curves

svdvpn

X)]()([

Both size and directioncan be controlled

Interactive Definition of Boundary Conditions Interactive Definition of Boundary Conditions

d2

P2

u=0

d2

Interactive Shape ManipulationInteractive Shape Manipulation

P2

Prototype Demo

u=0

d2

Example PDE GeometryExample PDE Geometry

P2

Biometric Application: Biometric Application: 3D Facial data representation and recognition3D Facial data representation and recognition

Shape reconstruction using the Biharmonic Shape reconstruction using the Biharmonic EquationEquation

For shape reconstruction we use the fourth order PDE based on the Laplace equation.

0),(

2

2

2

2

2

vuXvu

Boundary conditions are:

)(),1(

)(),(

)(),(

)(),0(

1

0

vPvX

vPvuX

vPvuX

vPvX

tt

ss

Note: the PDE is solved explicitly.

Algorithm for reconstructionAlgorithm for reconstruction

For a given shape (e.g. point cloud data).

1. Extract a series of profile curves

2. Arrange the curves in groups of four

3. Assign each group of four curves as boundary conditions for the 4th order PDE

4. Generate a continuous surface

Example Example

Boundary curves Resulting surface

Results Results

Original surface Reconstructed surfaceCurves extracted

Example of reconstruction – 3D face example 1

Results Results

Example of reconstruction – 3D face example 2

Original surface Reconstructed surface

Curves extracted

Results Results

Comparison

As one can see there is good agreement between the original and

reconstructed face.

Original data:

triangulated (green)

Parametric Representation and manipulation Parametric Representation and manipulation

Define a face using a series of

parameters (i.e. a handful of

measures)

1. Define a set of facial features on a template face

2. For every facial feature allocate the set of controls that define its topology and local geometry

3. Define a set of parameters for every feature based on the previous allocated points

4. Adjust these parameters to generate a new face.

Parametric Representation and manipulation Parametric Representation and manipulation

The Generic

template can be

updated based

on the chosen

parameters.

This has applications in other areas. e.g. facial animation

Efficient data storage for the 3D faceEfficient data storage for the 3D face

Our PDE based facial model based on curves which identify key facial

Features enables facial data to be stored very efficiently.

Typical 3D facial scan over 1MB data

PDE model typically 30KB

Face can be saved generated and re-generated very efficiently

Raw data processing and face characterisationRaw data processing and face characterisation

Processing raw data (from scan)

includes

1. Loading the Original Mesh

2. Neutralising the face (i.e. place it in a Cartesian coordinate frame)

3. Extracting a set of boundary curves that represent the vertical profiles of the face

Automatic facial feature identificationAutomatic facial feature identification

Key features such as

Nose tip, nose bridge,eye centre etc are identified.

Facial authentication/detectionFacial authentication/detection

• Define a set of parameters (based on the PDE boundary curves) within the central region.

• These parameters are unique to each face and are used to uniquely identify each face.

Systems disposalSystems disposal

• Many interested commercial parties.

• System was on trial at London Heathrow new Terminal 5. Outperformed Iris based detection.

Conclusion Conclusion

We have discussed techniques for 3D data representation using Partial Differential Equation. These techniques allow us to

• generate smooth surfaces for the given data

• efficiently parameterise the data set

• efficiently store the data

An example, based on 3D face modelling and recognition has been discussed.

Further Readings Further Readings

H. Ugail, M.I.G. Bloor, and M.J. Wilson, Techniques for Interactive Design Using the PDE Method, ACM Transactions on Graphics, 18(2), 195-212, (1999).

J. Monterde and H. Ugail, A General 4th-Order PDE Method to Generate Bézier Surfaces from the Boundary, Computer Aided Geometric Design, 23 (2): 208-225, (2006).

H. Ugail, 3D Facial Data Fitting using the Biharmonic Equation, in Visualization, Imaging and Image Processing, J.J. Villanueva (ed.), ACTA Press ISBN: 0-88986-598-1, pp. 302-307. (2006).

www.ugail.org

Questions ? Questions ?