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(BV-SIGGRAPH'99)A Morphable__ Model__ For The Synthesis Of 3D Faces.pdf 2.74MB

CVPR2010.pdf 2.03MB

(BV-PAMI2003)Face recognition____ based on fitting a 3D morphable model.pdf 907KB

张锋硕士论文.pdf 2.53MB

A Morphable Model For The Synthesis Of 3D Faces

Volker Blanz Thomas Vetter

Max-Planck-Institut f¨ur biologische Kybernetik,

T¨ubingen, Germany



Abstract

In this paper, a new technique for modeling textured 3D faces is

introduced. 3D faces can either be generated automatically from

one or more photographs, or modeled directly through an intuitive

user interface. Users are assisted in two key problems of computer

aided face modeling. First, new face images or new 3D face mod-

els can be registered automatically by computing dense one-to-one

correspondence to an internal face model. Second, the approach

regulates the naturalness of modeled faces avoiding faces with an

“unlikely” appearance.

Starting from an example set of 3D face models, we derive a

morphable face model by transforming the shape and texture of the

examples into a vector space representation. New faces and expres-

sions can be modeled by forming linear combinations of the proto-

types. Shape and texture constraints derived from the statistics of

our example faces are used to guide manual modeling or automated

matching algorithms.

We show 3D face reconstructions from single images and their

applications for photo-realistic image manipulations. We also

demonstrate face manipulations according to complex parameters

such as gender, fullness of a face or its distinctiveness.

Keywords: facial modeling, registration, photogrammetry, mor-

phing, facial animation, computer vision

1 Introduction

Computer aided modeling of human faces still requires a great deal

of expertise and manual control to avoid unrealistic, non-face-like

results. Most limitations of automated techniques for face synthe-

sis, face animation or for general changes in the appearance of an

individual face can be described either as the problem of ﬁnding

corresponding feature locations in different faces or as the problem

of separating realistic faces from faces that could never appear in

the real world. The correspondence problem is crucial for all mor-

phing techniques, both for the application of motion-capture data

to pictures or 3D face models, and for most 3D face reconstruction

techniques from images. A limited number of labeled feature points

marked in one face, e.g., the tip of the nose, the eye corner and less

prominent points on the cheek, must be located precisely in another

face. The number of manually labeled feature points varies from



MPI f¨ur biol. Kybernetik, Spemannstr. 38, 72076 T¨ubingen, Germany.

E-mail:

volker.blanz, thomas.vetter

@tuebingen.mpg.de

Modeler

Morphable

Face Model

Face

Analyzer

3D Database

2D Input 3D Output

Figure 1: Derived from a dataset of prototypical 3D scans of faces,

the morphable face model contributes to two main steps in face

manipulation: (1) deriving a 3D face model from a novel image,

and (2) modifying shape and texture in a natural way.

application to application, but usually ranges from 50 to 300.

Only a correct alignment of all these points allows acceptable in-

termediate morphs, a convincing mapping of motion data from the

reference to a new model, or the adaptation of a 3D face model to

2D images for ‘video cloning’. Human knowledge and experience

is necessary to compensate for the variations between individual

faces and to guarantee a valid location assignment in the different

faces. At present, automated matching techniques can be utilized

only for very prominent feature points such as the corners of eyes

and mouth.

A second type of problem in face modeling is the separation of

natural faces from non faces. For this, human knowledge is even

more critical. Many applications involve the design of completely

new natural looking faces that can occur in the real world but which

have no “real” counterpart. Others require the manipulation of an

existing face according to changes in age, body weight or simply to

emphasize the characteristics of the face. Such tasks usually require

time-consuming manual work combined with the skills of an artist.

In this paper, we present a parametric face modeling technique

that assists in both problems. First, arbitrary human faces can be

created simultaneously controlling the likelihood of the generated

faces. Second, the system is able to compute correspondence be-

tween new faces. Exploiting the statistics of a large dataset of 3D

face scans (geometric and textural data,

C yberware

) we built

a morphable face model and recover domain knowledge about face

variations by applying pattern classiﬁcation methods. The mor-

phable face model is a multidimensional 3D morphing function that

is based on the linear combination of a large number of 3D face

scans. Computing the average face and the main modes of vari-

ation in our dataset, a probability distribution is imposed on the

morphing function to avoid unlikely faces. We also derive paramet-

ric descriptions of face attributes such as gender, distinctiveness,

“hooked” noses or the weight of a person, by evaluating the distri-

bution of exemplar faces for each attribute within our face space.

Having constructed a parametric face model that is able to gener-

ate almost any face, the correspondence problem turns into a mathe-

matical optimization problem. New faces, images or 3D face scans,

can be registered by minimizing the difference between the new

face and its reconstruction by the face model function. We devel-

oped an algorithm that adjusts the model parameters automatically

for an optimal reconstruction of the target, requiring only a mini-

mum of manual initialization. The output of the matching proce-

dure is a high quality 3D face model that is in full correspondence

with our morphable face model. Consequently all face manipula-

tions parameterized in our model function can be mapped to the

target face. The prior knowledge about the shape and texture of

faces in general that is captured in our model function is sufﬁcient

to make reasonable estimates of the full 3D shape and texture of a

face even when only a single picture is available. When applying

the method to several images of a person, the reconstructions reach

almost the quality of laser scans.

1.1 Previous and related work

Modeling human faces has challenged researchers in computer

graphics since its beginning. Since the pioneering work of Parke

[25, 26], various techniques have been reported for modeling the

geometry of faces [10, 11, 22, 34, 21] and for animating them

[28, 14, 19, 32, 22, 38, 29]. A detailed overview can be found in

the book of Parke and Waters [24].

The key part of our approach is a generalized model of human

faces. Similar to the approach of DeCarlos et al. [10], we restrict

the range of allowable faces according to constraints derived from

prototypical human faces. However, instead of using a limited set

of measurements and proportions between a set of facial landmarks,

we directly use the densely sampled geometry of the exemplar faces

obtained by laser scanning (

C yber w ar e

). The dense model-

ing of facial geometry (several thousand vertices per face) leads

directly to a triangulation of the surface. Consequently, there is no

need for variational surface interpolation techniques [10, 23, 33].

We also added a model of texture variations between faces. The

morphable 3D face model is a consequent extension of the interpo-

lation technique between face geometries, as introduced by Parke

[26]. Computing correspondence between individual 3D face data

automatically, we are able to increase the number of vertices used

in the face representation from a few hundreds to tens of thousands.

Moreover, we are able to use a higher number of faces, and thus

to interpolate between hundreds of ’basis’ faces rather than just a

few. The goal of such an extended morphable face model is to rep-

resent any face as a linear combination of a limited basis set of face

prototypes. Representing the face of an arbitrary person as a linear

combination (morph) of “prototype” faces was ﬁrst formulated for

image compression in telecommunications [8]. Image-based linear

2D face models that exploit large data sets of prototype faces were

developed for face recognition and image coding [4, 18, 37].

Different approaches have been taken to automate the match-

ing step necessary for building up morphable models. One class

of techniques is based on optic ﬂow algorithms [5, 4] and another

on an active model matching strategy [12, 16]. Combinations of

both techniques have been applied to the problem of image match-

ing [36]. In this paper we extend this approach to the problem of

matching 3D faces.

The correspondence problem between different three-

dimensional face data has been addressed previously by Lee

et al.[20]. Their shape-matching algorithm differs signiﬁcantly

from our approach in several respects. First, we compute the

correspondence in high resolution, considering shape and texture

data simultaneously. Second, instead of using a physical tissue

model to constrain the range of allowed mesh deformations, we use

the statistics of our example faces to keep deformations plausible.

Third, we do not rely on routines that are speciﬁcally designed to

detect the features exclusively found in faces, e.g., eyes, nose.

Our general matching strategy can be used not only to adapt the

morphable model to a 3D face scan, but also to 2D images of faces.

Unlike a previous approach [35], the morphable 3D face model is

now directly matched to images, avoiding the detour of generat-

ing intermediate 2D morphable image models. As a consequence,

head orientation, illumination conditions and other parameters can

be free variables subject to optimization. It is sufﬁcient to use rough

estimates of their values as a starting point of the automated match-

ing procedure.

Most techniques for ‘face cloning’, the reconstruction of a 3D

face model from one or more images, still rely on manual assistance

for matching a deformable 3D face model to the images [26, 1, 30].

The approach of Pighin et al. [28] demonstrates the high realism

that can be achieved for the synthesis of faces and facial expressions

from photographs where several images of a face are matched to a

single 3D face model. Our automated matching procedure could be

used to replace the manual initialization step, where several corre-

sponding features have to be labeled in the presented images.

For the animation of faces, a variety of methods have been pro-

posed. For a complete overview we again refer to the book of

Parke and Waters [24]. The techniques can be roughly separated

in those that rely on physical modeling of facial muscles [38, 17],

and in those applying previously captured facial expressions to a

face [25, 3]. These performance based animation techniques com-

pute the correspondence between the different facial expressions of

a person by tracking markers glued to the face from image to im-

age. To obtain photo-realistic face animations, up to 182 markers

are used [14]. Working directly on faces without markers, our au-

tomated approach extends this number to its limit. It matches the

full number of vertices available in the face model to images. The

resulting dense correspondence ﬁelds can even capture changes in

wrinkles and map these from one face to another.

1.2 Organization of the paper

We start with a description of the database of 3D face scans from

which our morphable model is built.

In Section 3, we introduce the concept of the morphable face

model, assuming a set of 3D face scans that are in full correspon-

dence. Exploiting the statistics of a dataset, we derive a parametric

description of faces, as well as the range of plausible faces. Ad-

ditionally, we deﬁne facial attributes, such as gender or fullness of

faces, in the parameter space of the model.

In Section 4, we describe an algorithm for matching our ﬂexible

model to novel images or 3D scans of faces. Along with a 3D re-

construction, the algorithm can compute correspondence, based on

the morphable model.

In Section 5, we introduce an iterative method for building a mor-

phable model automatically from a raw data set of 3D face scans

when no correspondences between the exemplar faces are available.

2 Database

Laser scans (

C yber w ar e

) of 200 heads of young adults (100

male and 100 female) were used. The laser scans provide head

structure data in a cylindrical representation, with radii

(

h; 

)

surface points sampled at 512 equally-spaced angles



, and at 512

equally spaced vertical steps

. Additionally, the RGB-color values

(

h; 

)

(

h; 

)

,and

(

h; 

)

, were recorded in the same spatial

resolution and were stored in a texture map with 8 bit per channel.

All faces were without makeup, accessories, and facial hair. The

subjects were scanned wearing bathing caps, that were removed

digitally. Additional automatic pre-processing of the scans, which

for most heads required no human interaction, consisted of a ver-

tical cut behind the ears, a horizontal cut to remove the shoulders,

and a normalization routine that brought each face to a standard

orientation and position in space. The resultant faces were repre-

sented by approximately 70,000 vertices and the same number of

color values.

3 Morphable 3D Face Model

The morphable model is based on a data set of 3D faces. Morphing

between faces requires full correspondence between all of the faces.

In this section, we will assume that all exemplar faces are in full

correspondence. The algorithm for computing correspondence will

be described in Section 5.

We represent the geometry of a face with a shape-vector

(

; :::::; Y

)

, that contains the

X; Y; Z

coordinates of its

vertices. For simplicity, we assume that the

number of valid texture values in the texture map is equal to the

number of vertices. We therefore represent the texture of a face by

a texture-vector

; :::::; G

)

,that

contains the

R; G; B

color values of the

corresponding vertices.

A morphable face model was then constructed using a data set of

exemplar faces, each represented by its shape-vector

and texture-

vector

. Since we assume all faces in full correspondence (see

Section 5), new shapes

model

and new textures

model

can be

expressed in barycentric coordinates as a linear combination of the

shapes and textures of the

exemplar faces:

mod

;

mod

;

We deﬁne the morphable model as the set of faces

(

mod

(

)

mod

(

))

, parameterized by the coefﬁcients

= (

:::a

)

and

:::b

)

Arbitrary new faces can be generated by

varying the parameters

and

that control shape and texture.

For a useful face synthesis system, it is important to be able to

quantify the results in terms of their plausibility of being faces. We

therefore estimated the probability distribution for the coefﬁcients

and

from our example set of faces. This distribution enables

us to control the likelihood of the coefﬁcients

and

and conse-

quently regulates the likelihood of the appearance of the generated

faces.

We ﬁt a multivariate normal distribution to our data set of 200

faces, based on the averages of shape

and texture

and the co-

variance matrices

and

computed over the shape and texture

differences



and



A common technique for data compression known as Principal

Component Analysis (PCA) [15, 31] performs a basis transforma-

tion to an orthogonal coordinate system formed by the eigenvectors

and

of the covariance matrices (in descending order according

to their eigenvalues)

model



; T

model



;

(1)

~;



. The probability for coefﬁcients

~

is given by

(

~

)



exp

[

(



=

)

]

;

(2)

with



being the eigenvalues of the shape covariance matrix

The probability

(



)

is computed similarly.

Segmented morphable model: The morphable model de-

scribed in equation (1), has

degrees of freedom for tex-

ture and

for shape. The expressiveness of the model can

Standard morphing between two faces (

) is obtained if the pa-

rameters

are varied between

and

, setting

= 1

and

Due to the subtracted average vectors

and

, the dimensions of

Span



and

Span



are at most

S (− − − +)

T (− − − −)

S (0 0 − +)

T (+ + + +)

S (+ + +.−)

Average

Prototype

Segments

S (+ + + +)

T (+ + + +)

S (0 0 0 0)

T (0 0 0 0)

S (− + + −)

T (0 0 0 0)

S (− − + 0)

S (1/2 1/2 1/2 1/2)

T (1/2 1/2 1/2 1/2)

S (+ − − −)

T (− − − −)

S (− − − −)

S (+ 0 − 0)

T (− − − −)

T (+ + + +)

Figure 2: A single prototype adds a large variety of new faces to the

morphable model. The deviation of a prototype from the average is

added (+) or subtracted (-) from the average. A standard morph (*)

is located halfway between average and the prototype. Subtracting

the differences from the average yields an ’anti’-face (#). Adding

and subtracting deviations independently for shape (S) and texture

(T) on each of four segments produces a number of distinct faces.

be increased by dividing faces into independent subregions that are

morphed independently, for example into eyes, nose, mouth and a

surrounding region (see Figure 2). Since all faces are assumed to

be in correspondence, it is sufﬁcient to deﬁne these regions on a

reference face. This segmentation is equivalent to subdividing the

vector space of faces into independent subspaces. A complete 3D

face is generated by computing linear combinations for each seg-

ment separately and blending them at the borders according to an

algorithm proposed for images by [7] .

3.1 Facial attributes

Shape and texture coefﬁcients



and



in our morphable face

model do not correspond to the facial attributes used in human lan-

guage. While some facial attributes can easily be related to biophys-

ical measurements [13, 10], such as the width of the mouth, others

such as facial femininity or being more or less bony can hardly be

described by numbers. In this section, we describe a method for

mapping facial attributes, deﬁned by a hand-labeled set of example

faces, to the parameter space of our morphable model. At each po-

sition in face space (that is for any possible face), we deﬁne shape

and texture vectors that, when added to or subtracted from a face,

will manipulate a speciﬁc attribute while keeping all other attributes

as constant as possible.

In a performance based technique [25], facial expressions can be

transferred by recording two scans of the same individual with dif-

ferent expressions, and adding the differences



expression

neutral



expression

neutral

, to a different individual

in a neutral expression.

Unlike facial expressions, attributes that are invariant for each in-

dividual are more difﬁcult to isolate. The following method allows

us to model facial attributes such as gender, fullness of faces, dark-

ness of eyebrows, double chins, and hooked versus concave noses

(Figure 3). Based on a set of faces

(

)

with manually assigned

labels



describing the markedness of the attribute, we compute

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