J. Biomedical Science and Engineering, 2009, 2, 606-611
doi: 10.4236/jbise.2009.28087 Published Online December 2009 (http://www.SciRP.org/journal/jbise/ JBiSE
Published Online December 2009 in SciRes. http://www.scirp.org/journal/jbise
Influence of sampling on face measuring system based on
composite structured light
Yang Shen1,2, Hai-Rong Zheng1,2*
1Institute of Biomedical and Health Engineering, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences,
Shenzhen, China;
2Key Laboratory of Biomedical Informatics and Health Engineering, Chinese Academy of Sciences, Shenzhen, China.
Email: hr.zheng@siat.ac.cn
Received 7 August 2009; revised 4 September 2009; accepted 7 September 2009.
Human face can be rebuilt to a three-dimensional (3
D) digital profile based on an optical 3D sensing sys-
tem named Composite Fourier-Transform Profilo-
metry (CFTP) where a composite structured light
will be used. To study the sampling effect during the
digitization process in practical CFTP, the pectinate
function and convolution theorem were introduced to
discuss the potential phase erro rs caused by sampling
the composite pattern along two orthogonal direc-
tions. The selecting criterions of sampling frequencies
are derived and the results indicate that to avoid
spectral aliasing, the sampling frequency along the
phrase variation direction must be at least four times
as the baseband and along the orthogonal direction it
must be at least three times as the larger frequency of
the two carrier frequencies. The practical experiment
of a model face reconstruction verified the theories.
Keywords: Optical 3D Sensing; Composite Structured
Light; Sampling; Spectral Aliasing
Structured-light illumination is commonly used as an
active optical 3D sensing technique for automated in-
spection and measuring surface topologies. The Fourier-
Transform Profilometry (FTP) [1,2] is one of the classi-
cal 3D acquisition methods and it has been widely inves-
tigated [3,4,5] because of its advantages of obtaining
data from only one frame and analyzing spectrum in
whole-field as well as high resolution. Recently, an im-
proved FTP method called Composite Fourier-Transform
Profilometry (CFTP) was introduced [6,7]. This novel
method prevents spectral aliasing between zero-frequen-
cy and baseband b y u sing o nly on e gr ating na mely Com-
posite Pattern (CP) that generated by integrating multi-
frame ordinary patterns, so that it allows for real-time
implementations [8].
However, the data in both CFTP and FTP are digitally
sampled to discrete signals during the digitization proc-
ess in practice. The discrete images have periodical Fou-
rier spectrum, and the fundamental spectrum including
the useful information would be overlapped by the adja-
cent periodical weight [9]. Furthermore, th e CP in CFTP
is much more complexity than traditional sine grating,
another kind of spectrum aliasing would be brought in.
In this instance, choosing a proper sampling frequency is
very important for the precise survey.
To study the influence caused by sampling, the know-
ledge of pectinate function and convolution theorem was
employed in this article and the suggestion that how to
select proper sampling frequencies was given. The ex
periment verified the theories, and a beautiful 3D digital
profile of a model face was acquired.
2.1. CFTP Theory
A Composite Pattern (CP) in CFTP is generated as
shown in Figure 1. The multiframe sine patterns to be
modulated are as follows.
cos(2 )nGcfy n
 (1)
where a constant is used to offset to be non-nega-
tive values, and cnG
is the baseband, represents the y
Figure 1. A composite pattern formed by simple strips.
depth distortion (i.e., phase dimension) direction, re-
presents the phase-shift index from 0 to 1. These signal
Y. Shen et al. / J. Biomedical Science and Engineering 2 (2009) 606-611 607
SciRes Copyright © 2009 JBiSE
patterns are multiplied with different carrier frequencies
respectively along the orthogonal direction. Accumulate
all channels such that
(, ){[cos(2)]cos(2)
[cos( 2)]cos(2 )}
xyabcf yfx
cfy fx
 
 
 (2)
where 1
and 2
are carrier frequencies along the
orthogonal direction
, and the projection constants
and are used to make sure the projection intensity of
CP falls into the range of
b(, )
xy [6,7]. Ideally, the
reflected image of the specimen surface can be counted
as follows
(, )(, )(, ){
[cos(2( ,))]cos(2)
[cos(2( ,))]cos(2)}
Pxyarxy brxy
cfyxy fx
cfyxy f
 
 
where and
(,)rxy (,)
represent the albedo ra-
diation and distorted phase respectively. By means of
2D Fourier-transform and predigestion, the expression
(3) will be translated into (4) shown as follows, where
, (,A)
, (,)B
and (,)
the two-dimension Fourier spectrum of (, )
xy ,
, and
(,ar x)ybcr(,x y)1
2(,br x
)exp[y j
(, )]x y re-
11 1
11 1
22 2
22 2
(,) (,) (1/2){
[(,)(, )*(, )]
[( ,)(,)*( ,)]
Bff ff f
Bff ff f
Bff ff f
Bff ff f
 
 
 
 
 
Expression (4) suggests that the two carrier frequen-
cies are evenly distributed and are separated by spectral
frequency of background reflectance. Therefore, a smooth
and flat background had better be selected to minimize
the influence to the carrier spectrums. The distorted im-
age is processed as a set of 1-D signal vectors by
band-pass filters to separate out each channel. Cutoff
frequencies of each band represent the individual pat-
terns like that in traditional
Phase Shift FTP and are
used to retrieve the depth of the measured object based
on the traditional
Phase Shift FTP method [7] as
0(, )(, )/2hxyxyLf d
where and are experimental setup parameters,
represents the reconstructed height.
2.2. Influence of Sampling on CFTP
Expression (3) indicates the continuous image, but in
practical experiment it will be digitally sampled to dis-
crete signals by projector and camera, and the discrete
distorted pat te r n is captured as
(, )Sxy
(, )(, )(/,/)
SxyPxycombxxy y
Pxy combxx combyy
where is Pectinate Function, (/ ,/ )comb xxyy
and are sampling spacing along phase direction
and orthogonal direction respectively so that
and represent the sampling frequency along
the two directions respectively. Here suppose
1/ (max{,})
fxnff ff
  (7)
where and are multiple units, respectively
represents the multiple relationship between sampling
frequency and the selected experimental setup frequen-
cies along the two orthogonal axes, and both them are
positive numbers. These two introduced parameters en-
able us to calculate the proper sampling frequencies
based on the known baseband and carrier frequencies,
and the selecting criterions of sampling frequencies are
determined as long as and n are definitely.
m n
Eq.4 shows that besides the frequency of background
reflectance (i.e. (,) A
), there are four peak values
along the orthogonal direction, namely 1, 2ff
; in
each peak
there are three peak spectrums along the
phase direction, namely 0, f
. To simplify the
investigation, we will discuss the sampling effects along
the two orthogonal directions respectively.
2.2.1. Sampling Analysis along Pha s e Dire ct i on
Any a peak value of
was selected, e.g.1
, there
are three peak spectrums in the channel along the phase
1111(,)(,) (,)*(,)
fBfff ff
 
The discrete spectrums of 1(,)Ff
can be calculated
608 Y. Shen et al. / J. Biomedical Science and Engineering 2 (2009) 606-611
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(,)(,) | |()
*(,) ]
fFf ycomby
Bf Nmf
 
 
where is the convolution operator and is integer.
Eq.9 indicates that the spectrums of
1(,Ff )
periodically. To against the overlapping of spectrums, we
must make sure
is separated from *
in the same
period, and also make sure (*)
is separated from
*( )
comes from the adja cent periods, in another word,
the sampling fr equency is restricted, there must be at le ast
four sampling dots in one period [9] so that
4 , or 4yfmf fm
 (10)
2.2.2. Sampli n g An al ysi s along the Orthogonal
Any a peak value of
was selected to study the cor-
responding four peak spectrums of
along the or-
thogonal direction, e.g.
(, )(, )(, )
 
 
  (11)
Here suppose 21
. Consider expression (7) and
Pectinate Function along the orthogonal
direction, the discrete spectrums of
(/ )xx
can be
calculated as (12):
22 12
12 22
(,)(,) ||( )
[ (,)(,)
(,)(,) ]
Ff Ffxcombx
fNnff fNnff
 
 
 
Expression (12) indicates that the spectrums of
repeat periodically with period of . As
shown in Figure 2, the real lines represent the starboard
, and the dashed represent the larboard
spectrums of the adjoining period.
Figure 2 indicates that to escape the overlapping of
spectrums, there must be have
1max 2min
2max2 2max
() ()
() ()
 (13)
Imitating the definition of instantaneous frequency in
domain of signal processing [5], we get
1 max1max
2min 2max
2max 2max
()(1/2)|/ |
()(1/2)|/ |
()(1/2)|/ |
ff x
ff x
ff x
 
 
 
Eq.13 can be m o di f i e d by (5) and (14) such that
Figure 2. Replicated spectrum distribution.
max21 0
max2 0
|/|()(/2 )
|/|(2)(/2 )
hxffL fd
hxnfL fd
 
  (15)
According to (15), we can get
212( )/nff 2f
If the condition 22
is selected in survey, there
mus t be , so there has
nf f.
2.3. Experiment
To support the analysis above, a model face was used as
a tentative test. The projector used was a Panasonic (PT-
P2500) digital projector with resolution of 1024×768.
The image sensor used was a low-aberrance color CCD
camera (Prosilica, EC1350C, made in Canada) with
resolution of 1360×1024 and pixel size of 4.65um×
1.65um, and the maximum frame rate is 18fps. The fo-
cus of the camera lens (KOWA, LM12JCM, made in
Japan) was 12mm. The image board was a 1394 card
(KEC, 1582T, made in Taiwan). The reference plane as
background was a piece of smooth and white board.
Figure 3 illustrates the experimental setup, in which the
geometric parameters were set as =73mm and
=18mm, and the carrier frequencies
and 2
were set as 3/40 line/pixel and 6/40 line/pixel respec-
tively and the baseband
was given as 60/600 line/
pixel. The lens of projector and camera must be at a
same geometric plane surface and here they were setup
coplanar at vertical curve. The horizontal beam con-
tained CP illuminated over against model face, and the
sho o t ing angle of camera was setup as 45 degree w hich is
Y. Shen et al. / J. Biomedical Science and Engineering 2 (2009) 606-611 609
SciRes Copyright © 2009 JBiSE
Figure 3. The diagram of the experimental setup.
the optimal angle value [4,5]. Because the specimen was
a model face, the gesture and expression could be with-
out consideration, however, with regard to a real human
face, eyes exposure and shadows caused by gesture must
be considered carefully.
According to the analysis above, to avoid spectral
aliasing, there must be have and . Figure 4
shows the captured distortion composite pattern. Figure
5 indicates the reconstructed profile. From the drawings,
we can find that when sampling frequencies do not sat-
isfy the sampling request, i.e. (a) when
, the rebuilt errors were big and the details of face
were lost. However, when and , the de-
tails could be retrieved as shown in (b) and (c) with good
The accurate acquisition of 3D human face appearance
characteristics is very important for designing a facial
contouring surgery, and a good work is based on an ex-
act 3-D face modeling [10]. People hope to find a non-
ontact, rapid, precise way to acquire 3-D digital face
depth, and then based on it to simulate and design an
optimal plan for face surgery by modem technologies
such as computer aided design etc [11].
Figure 4. The captured distortion composite pat-
tern modulated by height of the face model.
Figure 5. The rebuild shape, (a) when m=3, n=2; (b) when
m=4, n=3; (c) m=5, n=5.
610 Y. Shen et al. / J. Biomedical Science and Engineering 2 (2009) 606-611
SciRes Copyright © 2009 JBiSE
At present, there are about three types of 3D face
modeling method to extract human face profile: one is
the method based on computer tomography (CT) tech-
nology [12,13,14] and another one is based on passive
optical 3D sensing technique [15,16,17] and the other is
based on active optical 3D sensing technique [18,19,20].
The 3D reconstruction method based on CT technol-
ogy is sensitively to skeleton and is convenient to be
used for craniofacial plastics and oral and maxillofacial
correction of abnormality and such fields, however, 3D
profile of soft tissue is difficult to rebuilt by CT tech-
nology, especially the human face surface features.
The passive optical 3D sensing technique such as ste-
reo vision uses two or more camera systems to capture
the scene in ambient light from different viewpoints and
to determine the height by matching image features of
the corresponding surface features. In this method, a lot
of factors need to be noticed, such as ambient light,
background, vision angle and face gesture, expression
and shading and so on, for they would influence the
measuring accuracy directly. Besides, there always need
to process a mass of data operation like correlation
analysis and matching operation etc. Generally, the pas-
sive optical 3D sensing technique is more often used for
3D object recognition and understan ding. Alo ng with the
development of computing technique, arithmetic speed
is no longer a key limiting factor, and the passive optical
3D sensing technique is widely used in the field of ma-
chine vision.
The active optical 3D sensing technique employs
structured light to illuminate the specimen. The time or
space in structured light will be modulated by height,
and then the 3D information can be extracted from the
observation light by certain unwrapping algorithm [5].
For its feature of non-contact, high resolution and highly
automated, the active optical 3D sensing technique is
used in most 3D sensing systems with the purpose of 3D
surface-shape measurement.
Phase Measuring Profilometry (PMP) is one i mportant
method of active optical 3D sensing technique [5]. In
PMP, sinusoidal fringes and phase shifting technique are
employed to acquire the height information that we
wanted. A flaw of PMP is that it has to capture at least
three continuous modulated phase shifting fringes cor-
responding to a static profile and therefore there will be
some trouble for real-time dynamic measurement, and
during the shooting process a little movement or facial
expression changes of the target human face will poten-
tially bring errors to the demodulated results. By using
fast digital grating projection approach, a series of phase
shifting fringes can be projected and shot within a short
span of time. However, the images photographed by
CCD camera would easily cause drawbacks such as
trailing and distortion etc. due to rapid rotation of the
phase shifting fringes, and then the inaccuracy of meas-
urement will be raised. A one-shot technique, therefore,
becomes a trend [19,20].
Here a novel one-shot approach for 3D human face
profile measurement is introduced. A composite pattern
(CP) is used in place of the series phase shifting fringes
in PMP, and only a single frame of CP is needed to pro-
ject and capture. The CP efficiently combines some
phase shifting fringes and the same number of carrier
gratings, and so that the phase shifting technique can be
also utilized in this approach. This one-shot technique
can avoid some unwanted troubles such as trailing and
distortion etc. that happened in PMP for needing only
one projection and corresponding one capture. Based on
the proposed approach, 3D digital model of real human
face could be acquired more conveniently and exactly.
Here we used this novel method to reconstruct a
model face and acquired a good stereogram under the
proper sampling frequencies which were the focus of our
investigation. Because of the comp lexity of the compos-
ite pattern, another kind of spectrum overlapping would
be brought in by the two modulating gratings during the
digitization process. In this instance, choosing a proper
sampling frequency is very important for the precise
reconstruction. In the paper we discussed the sampling
conditions along two directions and pointed ou t the rules,
and then under the given sampling conditions we ac-
quired a perfect digital 3D face profile.
Composite Fourier Transform Profilometry (CFTP) is an
improved FTP method where a composite structured
light is employed. To study the influence caused by
sampling, the knowledge of pectinate function and con-
volution theorem was used and the suggestion that how
to select proper sampling frequencies was given, that is,
the sampling frequency along the phr ase variation direc-
tion must be at least four times as the baseband and
along the orthogonal direction it must be at least three
times as the larger frequency of the two carrier frequen-
This study was supported by the National 973 Basic Research Program
of China (No. 2010C B7 32600).
[1] M. TAKEDA, K. MUTOH. (1983) Fourier transform
profilometry for the automatic measurement 3-D object
shapes. Appl . Opt., 24, 3977–3982.
[2] M. Takeda, H. Ina. (1982) Fourier-transform method of
fringe-pattern analysis for computer-based topography
and interferometry. J. Opt. Soc. Am, 1, 156–160.
[3] S. Fu, Y. S. Wang, G. B. Han. (2004) Fourier transform
profilometry in 3-D measurement based on wavelet
digital Filter. J.Optoelectronics·Laser, 2, 205–207.
[4] W. J. Chen, X. Y. Su. (2000) Discussion on phase er-
rors caused by frequency leakage in FTP. Acta Optica
Y. Shen et al. / J. Biomedical Science and Engineering 2 (2009) 606-611 611
SciRes Copyright © 2009 JBiSE
Sinica, 10, 1429–1433.
[5] X. Y. Su, J. T. Li. (1999) Information Optics. Publish
House of Science, Beijing, 332–335 (in Chinese).
[6] C. Guan, L. G. Hassebrook. (2003) Composite struc-
tured light pattern for three-dimensional video. Optics
Express, 5, 406–417.
[7] H. M. Yue, X. Y. Su. (2005) Improved fast fourier
transform profilometry based on composite grating.
Acta Optica Sinica, 6, 767–770.
[8] Y. S. Xiao, X. Y. Su, Q. C. Zhang. (2006) 3-D surface
shape restoration for the breaking surface of dynamic
process. Laser Technology, 3, 258–261.
[9] H. Yang, W. J. Chen. (1999) Influence of Sampling on
Fourier-Transform Profilometry. Acta Optica Sinica, 7,
[10] G. L. Murrell, N. K. McIntyre, and B Trotter. (2003)
Facial contouring. Facial Plast Surg Clin North Am, 3,
[11] R. Schmelzeisen and A. Schramm. (2003) Computer-
assisted reconstruction of the facial skeleton. Arch Fa-
cial Plast Surg, 5, 437–440.
[12] S. Prakoonwit, and R. Benjamin. (2007) Optimal 3D
surface reconstruction from a small number of conven-
tional 2D X-ray images. Journal of X-Ray Science and
Technology, 4, 197–222.
[13] M. Deling, W. Biao, F. Peng, and Y. Fuguang. (2007)
Oral Implant Orientation of 3-D Imaging Based on
X-Ray Computed Tomography (CT). Asian J. Inform.
Techno, 11, 1143–1147.
[14] Mahfouz, Badawi, A. Fatah, Kuhn, and Merkl. (2006)
Reconstruction of 3D patient-specific bone models
from biplanar xray images utilizing morphometric
measurements. Proceedings of the 2006 International
Conference on Image Processing, Computer Vision, and
Pattern Recognition, 345–349.
[15] C. Zhang, F. S. Cohen, and H. RVSI. (2002) 3-D face
structure extraction and recognition from images using
3-D morphing and distance mapping. IEEE Transac-
tions on Image Processing, 11, 1249–1259.
[16] H. Hirschmuller, P. R. Innocent, and J. Garibaldi. (2002)
Real-time correlation-based stereo vision with reduced
border errors. Int. J. Comput. Vi s., 1/2/3, 229–246.
[17] S. Huq, B Abidi, A. Goshtasby, and M. A. Abidi. (2004)
Stereo matching with energy-minimizing snake grid for
3D face modeling. Proceedings of SPIE, 5404, pp.
[18] M. Takeda and K. Mutoh. (1983) Fourier transform
profilometry for the automatic measurement 3-D object
shapes. Appl . Opt., 24, 3977–3982.
[19] H. M. Yue, X. Y. Su, and Z. R. Li. (2005) Improved
fast fourier transform profilometry based on composite
grating. Acta Optica Sinica, 6, 767–770.
[20] C. Guan, L. G. Hassebrook, and D. L. Lau. (2003)
Composite structured light pattern for three-dimen-
sional video. Optics Express, 5, 406–417.