Compression of Phase Image for Three-dimensional Object

Han-Yen Tu, Ching-Huang Hsieh, and Huong-Giang Hoang Department of Electrical Engineering, Chinese Culture University, Taipei 11114, Taiwan

E-mail: DHY@ulive.pccu.edu.tw

We present the performances of compression analysis for the phase image resulted from different phase unwrapping algorithms applied to

fringe projection profilometry. Since three-dimensional (3D) surface shape information of objects can be extracted from the phase maps of

objects, the phase unwrapping is critical to many 3D applications for obtaining accurate phase. To reduce the size of storage and processing

for 3D data, these phase images are fed to the compression algorithms. The efficiency is evaluated and compared with compression ratio and

normalized root mean square (NRMS) error. Our simulation and experimental results show that the H.264/AVC codec method can maintain

low NRMS error while with higher compression ratio than the other methods investigated in this paper.

1. Introduction

Three-dimensional noncontact optical technologies are applied

to many approaches, such as 3D imaging and display technology.

The main advantages of these technologies are noncontact and high

accuracy. Fringe analysis technique is one of most used in 3D shape

topography. The structured-light method has been widely adopted

in scientific study and industry applications to our daily life. We can

use the designed structured light fringe analysis technique for 3D

object measurement. It has high automation degree that can be

projected the designed patterns onto the objects for 3D objects

measurement. The distorted patterns of the fringe patterns contain

height information varied with the surface shape of objects because

the phase modulation resulted from the varying of objects height

distribution. 3D surface information of objects can be reconstructed

by the full-field wrapped phase distribution from the phase to height

conversion. Their 3D information of height information through the

phase difference conversion algorithms can be retrieved.

Fringe projection profilometry can adopt phase unwrapping

schemes to obtain the height information through phase to height

phase difference computation. 3D shape information can be

analyzed successfully using phase unwrapping algorithm for getting

true phase of objects. We convert the 3D data caught from fringe

projection techniques into2D images, then find efficient image

processing for transporting and storing these enormously large 3D

data. The phase unwrapping is a core task for 3D height information

in optical interferometry. For this reason, many phase unwrapping

algorithms have been proposed. This paper investigates the results

of compression analysis for the phase images resulted from popular

phase unwrapping algorithms. However, these enormous 3D shape

information processes demand huge storage and processing to

digital computer. Therefore, it is an important issue to study the

crucial computation for fringe projection techniques. The purpose of

this paper is to investigate the performances of compression for the

phase images resulted from different phase unwrapping algorithms

applied to fringe projection schemes. The compression method can maintain low NRMS error while with higher compression ratio for 3D shape information than the other methods investigated in this paper.

Due to the development in three-dimensional display and

networking techniques, new 3D image applications are significantly

attracted in many fields. In order to capture 3D shape information of

objects, digital image compression became more and more

important in the limited transmission and storage conditions.

However, it needs large storage for massive data processing and the

storage is not desirable for image processing applications in many

previous approaches for real-time applications. We cannot get high

compression if 3D surface shape information has many

discontinuities in the corresponding image. Phase unwrapping and

compression techniques are very important for 3D image

processing in fringe projection schemes. Instead of designing new

schemes without modifications, we utilize the existing 2D image

compression techniques for 3D objects. We convert the 3D

information of objects from fringe projection techniques into 2D

shape images, then finding image processing for transporting and

storing enormous 3D data efficiently. This paper is organized as

follows. In Section 2 fringe projection technique and phase

unwrapping schemes will be briefly introduced. In Section 3 we

report and discuss the experimental results to the performances of

P-8

AM-FPD '14 97

the phase unwrapping algorithms applied to popular compression

analysis. Finally, conclusions are made in Section 4.

2. Principle

The fringe projection optical method has been extensively employed for 3D object reconstruction. Figure 1 shows the schematic diagram of a 3D shape measurement system using fringe projection technique. It uses a projector to project a series of sinusoidal structured patterns onto objects. Then the image acquisition unit captures these projected images by the CCD or CMOS camera. The modulated phases of objects from height distribution can be captured by the fringe projection technique. Because deformed fringes contain corresponding 3D information about the recorded object. We can obtain the 3D surface information in phase image by phase shifting scheme [1]. Many phase shifting algorithms have been developed including three-step, four-step, least-square algorithms, etc. [2]. This paper employed a three-step phase-shifting algorithm is for 3D image processing. To obtain the phase image from the recovered images, the camera captures the shift patterns I1(x,y), I2(x,y), and I3(x,y) described with the following equations:

)],(2cos[),(),(),(),( 00001 yxxfyxryxByxAyxI o φπ ++= (1)

]3

2),(2cos[),(),(),(),( 00002πφπ +++= yxxfyxryxByxAyxI o

(2)

]3

4),(2cos[),(),(),(),( 00003πφπ +++= yxxfyxryxByxAyxI o

(3)

where A0(x,y), is the average intensity, B0(x,y) is the intensity modulation and f0 represents the spatial frequency of the projected fringe patterns. By solving Eqs.(1) to (3), the wrapped phase �0(x,y) is

��

���

−−

−=321

230 2

3arctanIII

IIφ (4)

We can take a reference plane to reduce the background and noise for 3D shape measurement. The range of the wrapped phase in equation is limited from 0 to 2� and with 2� discontinuities. Many conventional phase unwrapping algorithms can be adopted to remove these 2� phase jumps [6]. The wrapped phase were resolved to obtain continuous phase maps. Thus 3D surface shape information can be scanned into 2D images and retrieved by the conversion of height variation. The depth map of varying height can be recovered pixel by pixel using the triangulation based algorithm [3]

( ) ( )( ) dfyx

yxdyxh

0

0

2,,

,πφ

φ+Δ

Δ= (5)

where h(x,y) is height variation relative to the reference plane. d0 is

the distance from the reference plane to the CCD and projector

plane and d represents the distance between the CCD camera and

the projector. ��(x,y) is the phase map evaluated between the

reference plane to the projected surface. To obtain continuous phase

images, phase unwrapping algorithms play an important role for

finding the true phase of 3D objects. These acquired but restricted

wrapped phase values can be unwrapped well by phase unwrapping

algorithms. Many unwrapping problems and algorithms have been

proposed to provide phase unwrapping solutions [2]. Wrapping

phase maps can be valued by proper schemes or functions of

algorithms to derive true phase variance. Since phase images are

made up of pixels, phase unwrapping applied gradient, quality maps

and masks etc. to integrate the phase variance over the chosen path

or region in the phase domain. In this paper five of them will be

tested to the phase image of objects for the compression application.

Flynn method and quality guided path following are the algorithms

belonging to the path-following groups. Preconditioned conjugate

gradient and minimum Lp-norm methods represent minimum

-norm groups.

The scanned 3D shape information can be converted into 2D

images. To reduce the size of the signal, we store and compress

these deformed fringes information, and then decompress and

recover into original 3D surface of objects. We analyze the

performance of compression for 3D object reconstruction using 2D

compression schemes for the phase maps of objects in this paper.

Fig.1. Schematic diagram for three-dimensional object reconstruction by

using fringe projection profilometry

.

98 AM-FPD '14

Previous research groups have investigated many compression and achieved effective and reliable performance, such as wavelets [4], JPEG and JPEG2000 image compression [5], and H.264 [6] etc. Wavelets transforms have been widely used in signal process [4] and can provide specific purposes for image representations. An arbitrary function can be expressed by a mother wavelet function and setting translation and dilation scaling factors to define. They split the sample space into approximate subspace. Architectures of discretized wavelet transform based on the classical implementation have been applied to signal processing and image compression [4], such as Daubechies and Haar wavelet functions. JPEG is based on the discrete cosine transform standard, and JPEG 2000 is wavelet-based method image compression standard system [5]. Hence, they have been adapted for the compression of multidimensional image information. JPEG 2000 offers both loss and lossless compression in the same file. Thus, when high quality is the concern, JPEG 2000 proves to be a much better compression tool. H.264 (MPEG-4 Part 10) is advanced coding format. It was created to provide good video quality at lower bit rates than previous standards but without increasing complex design. In order to compress these projected patterns more efficient, how to maintain low NRMS error while with higher compression ratio, with low storage and transmission for 3D object reconstruction will be investigated. We present the results of compression methods for the phase images of 3D objects in the following.

3. Experiment results A series of coded proper frequency projected fringe patterns

are arranged to the project and reflect onto the object surface for 3D surface shape measurement in fringe projection profilometry as shown in Fig.2 (a). The image sensor is used to record the distorted fringe patterns caused by the height variation of objects. These patterns contain height information that can be extracted by phase modulation analysis. The wrapped phase of the 3D object can be obtained in Fig.2 (b). 3D surface shape information is recovered from the phase computation. Since the phase distribution may range over than 2�, phase maps must be retrieved and remove discontinuities by proper phase unwrapping algorithms. We employ the phase unwrapping scheme to retrieve the continuous map in Fig. 2(c). Then in Fig. 2(d), the 3D shape of object can be reconstructed by the conversion of triangulation algorithm. Then we adopt 2D compression schemes to the phase maps for 3D object reconstruction analysis.

We upload the phase images resulted from the phase unwrapping algorithms to execute the compression for Daubechies wavelets, Haar wavelets, JPEG, JPEG2000, and H.264 etc. The compression ratio and normalized root mean square (NRMS) error of the

characteristics for the compression are calculated. The compression ratio is calculated by CR (original size / compressed size) and NRMS error is defined as

21

1

0

1

0

2

1

0

1

0

2

|),(|

|}),('||),({|

����

�

�

����

�

−

=

� �

� �−

=

−

=

−

=

−

=x y

x y

N

n

N

m

N

n

N

m

nmU

nmUnmUNRMS

(6)

where U and U’ are the 3D shape of reconstructed image from

original phase and decompressed process maps respectively, and

Nx and Ny are dimensions of phase images. Hence, the

compressed information of an image is reduced but it still can

preserve good quality of 3D shape information. It is efficient for

storage and transmission for 3D object reconstruction. We

compare five different methods of compressed coding

performance for phase images as shown in Fig.3 to Fig.7. In Fig.3,

compression ratio versus NRMS error for DCT method is shown.

Figure 4 and 5 show the algorithms of path-following groups for

the Flynn method and quality guided path following methods

respectively. Fig. 6 and Fig.7 are the compression results of

preconditioned conjugate gradient and minimum Lp-norm

methods for represent minimum-norm groups. They all show that

the advanced coding codec H.264 scheme is considered as an

effective candidate for 3D surface shape information because of its

higher compression ratio in the experiment results of 3D image

reconstruction but still preserves 3D shape information well. The

Fig. 2. 3D object reconstruction using fringe projection profilometry

(a) phase-shifting projected fringes, (b) wrapped phase image,

(c) unwrapped phase images, and (d) 3D surface shape of object.

AM-FPD '14 99

advanced coding codec of H. 264 has the ability to achieve higher

compression ratios than previous standards with little reconstructed

error increase.

Fig.3. Compression ratio versus NRMS error for DCT method.

Fig.4. Compression ratio versus NRMS error for Flynn’s method.

Fig.5. Compression ratio versus NRMS error for quality-guided path

following method.

Fig.6. Compression ratio versus NRMS error for minimum Lp-norm

method.

Fig.7. Compression ratio versus NRMS error for preconditioned conjugate

gradient method.

4. Conclusions This study implemented and experimentally demonstrated the

effective compression for 3D phase images in the fringe projection profilometry system. Since fringe projection techniques have enabled record the 3D shape information in real-time. Effective compression techniques due to the streaming and storing 3D information is a challenge for 3D object reconstruction. The phase images processed from the phase unwrapping procedures are compressed in this study. The efficiency are evaluated and compared in five popular compression schemes under different phase unwrapping algorithms. H.264 codec can achieve effective compression for the phase images of 3D objects under different phase unwrapping algorithms. In our future work, we will apply the advanced video coding codec to the compression of 3D objects captured from fringe projection techniques. The image processing for phase images with 3D surface information has little loss of quality but with higher compression ratios for 3D objects will be advanced to the prospect of 3D video compression.

Acknowledgment This work was financially supported by the National Science Council, Taiwan, R.O.C., under contract No. NSC 101-2221-E-034 -011 -MY2.

References 1) P. Hariharan, B. F. Oreb, and T. Eiju : Appl. Opt. 26(13) (1987)2504. 2) D. C. Ghiglia and M. D. Pritt: Two-dimensional phase unwrapping.

Wiley(1998).

3) M. Takeda and K. Mutoh: Appl. Opt. 22(24) (1983) 3977. 4) I. Daubechies :Ten Lectures on Wavelets ( Capital City Press,

Vermont)(1992). 5) D. Taubman and M. Marcellin: JPEG2000: Image compression

fundamentals, standards, and practice kluwer academic blishers(2001). 6) E. G. Iain and C. Richardson: H.264 and MPEG-4 video compression

video coding for nxt-generation mltimedia.” Wiley, (2003).

100 AM-FPD '14