3D OBJECT MEASUREMENT BY SHADOW MOIRÉ

Yun-Long Lay

Hui-Jen Yang

, Chern-Sheng Lin

and Wei-Yu Chen

Dept. of Electronic Engineering, National Chin-Yi University of Technology, Taichung, Taiwan

Dept. of Information Management, National Chin-Yi University of Technology, Taichung, Taiwan

Institute of Automatic Control Engineering, Feng Chia University, Taichung, Taiwan

Keywords: Shadow Moiré, Optical measurement system, Mouth shape measurement, Image processing.

Abstract: In order to get the 3 dimensional data of an object, this research applied a shadow Moiré method to build an

optical measurement system without touching the object to measure the contour for getting a 3D data. A

digital camera was used to capture the Moiré images through an image processing to get the texture of each

contour line. After calculated the texture of each contour line, the correspondence values are then filled.

Each correspondence value will make smooth contour interpolation and then three-dimensional image of the

object was plotted. This method for 3D measurement is simple and does not need an expensive

measurement device to get precisely image information for a 3D rebuilt implementation.

1 NON-TOUCHING

3-DIMENSIONAL

MEASUREMENT METHOD

Non-touching measurement method is to use a laser

or light interference measuring the objects. There

will be no touching wear or contact vibration to

cause bias. This method is very suitable to measure

the soft materials. In addition, its application domain

is wide, such as industrial model design process,

reverse engineering, medical engineering, surgery

simulation, 3D animation and so on. The followings

are some common non-touching three-dimensional

profile measurement methods (Fu, 1997).

Shadow Moiré is the method applied in this

study, shown in Figure 1. The experimental devices

include a reference grating, light source and digital

camera. The light source projects on the grating with

a specific angle. This grating is called as the

reference grating. The shadow of straight-line

projected onto the testing object called as the

shadow grating which overlapped with original

reference grating and generated the circular textures.

Applying the image extracting equipment to obtain

images shall be the interception of two grating lines

forming the moiré image, which can be the most

cost-saving, but also the easiest way to set up. In

order to allow the observers intuitively understand

the ups and downs of surface with contour lines. The

measurement resolution could be changed by setting

the light angle or the grating pitch.

Figure 1: Shadow Moiré Measurement.

2 METHOD

2.1 Shadow Moiré

Moiré grating is forming by two overlapped grating

with low spatial frequency textures (Batouche, 1992).

Shadow Moiré is only using a single grating as the

reference grating placed on the front of object. After

the light projection on the reference grating through

the test object which generates a distorted shadow

called shadow grating. The shadow grating overlaps

with the reference grating formed a shadow moiré.

Figure 2 is the framework of shadow Moiré

measurement. The shadow moiré is composed of the

original grating and the grating shadow. The grating

161

Lay Y., Yang H., Lin C. and Chen W. (2010).

3D OBJECT MEASUREMENT BY SHADOW MOIRÉ.

In Proceedings of the International Conference on Data Communication Networking and Optical Communication Systems, pages 161-164

DOI: 10.5220/0002936101610164

 SciTePress

size can’t too thin or dense to produce diffraction

effects (Glassner, 1999).

From the observation, the overlapped Moiré of

two gratings of AC and AD were recognized

simultaneously. The number of AB straight stripes

has m lines and AD has n lines, then

mpAC = , npAB

NppnmABACBC =−

−= )(

)tan(tan

+= dBC

N: the number of Moiré fringe within the scope of

AC.

p: pitch of grating.

: incidence of light.

:Observation angle of image.

tantan

θθ

oNp ×

(1)

d: Distance of a testing object and reference grating.

Figure 2: Enlargement of Shadow Moiré measurement

framework (Tran etc., 1996).

From the equation 2.1, each moiré fringe can be

calculated. It can be seen that each Moiré is a

contour, in which we can label each moiré fringe in

order to facilitate the depth calculation of the

measurement surface.

2.2 The Image Processing Methods

2.2.1 Remove the Reference Grating Stripes

In the Moiré image, if the reference grating pitch is

too large then the reference grating stripes will be

very obvious, which is not the required information.

The impact of stripes on the images are

comprehensive and can be seen as a periodical

signal in the whole image. It must use a low pass

filter to remove (Batouche, 1992).

Suppose the original matrix is f (x , y), x and y

are matrix elements. Through Fourier transformed,

the output matrix is F(u ,v). Suppose index the

matrix is M×N, the x-index ranges are from 0 to M-1

and the y-index ranges are from 0 to N-1. Equations

2.2 and 2.3 are the two-dimensional discrete Fourier

transformation formula:

∑∑

−

⎥

⎦

⎤

⎢

⎣

⎡

⎟

⎠

⎞

⎜

⎝

⎛

+−=

2exp),(),(

iyxfvuF

(2)

the reversed transformation is

∑∑

−

⎥

⎦

⎤

⎢

⎣

⎡

⎟

⎠

⎞

⎜

⎝

⎛

2exp),(

),(

ivuF

yxf

(3)

Figure 3 (a) is a stripe of its Fourier transformed

images shown in Figure 3 (b), which could be

observed out of several star shapes. The more close

of the distance represents more thin and dense of

straight line, that is the frequency is more higher.

Reversely, the far of the distance represents the

frequency is low and the pitch of straight stripes is

larger. is shown in Figure 3 (c) is the image after

processing by a notch filter . The straight-line stripes

have been removed, shown in Figure 3 (d).

(a) (b)

Figure 3: Fourier transformed with the notch filter image

processing.

A template mask scanning on the image with the

adjacent grayscale calculates the new grayscale

value. If it uses a linear function to obtain the mask,

this mask can also be called as a linear filter

(McAndrew, 2004).

Too much detail of images in the computer

vision on some specific pattern recognition will

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affect its results. To solve this problem, a low-pass

filter on the image will produce fuzzy results and

also can reduce the noise.

2.2.2 Enhance the Image Contrast

The contrast of a non-obviously image can be

enhanced through the expansion of gray-scale

distributions.

Using histogram equalization, assuming a gray-

scale image has L gray levels, in the histogram of

the i layer has n pixels, and assuming that all the

number of pixels are

110

...

−

+++=

nnnN

the gray-

level i can be replaced by Equation 2.4 (Lin, 2001):

()

...

−

⎟

⎠

⎞

⎜

⎝

⎛

+++

nnn

(4)

A clear contrasted black and white images will be

obtained.

2.2.3 Binarization

After the step of the image contrast enhancement,

the next step is the binary image process. The

required stripes and unnecessary image need to be

split. The change of gray-scale image will be

converted into black and white binary images. A

common method is to set a threshold value of gray-

scale images T to judge the grayscale value of each

pixel, shown as follows.

⎩

⎨

⎧

≥

Tyxg

yxg

),(,0

),(,255

),(

Sometimes, the brightness of image is not consistent.

A single threshold may not be fully extracted the

images. The images can be cut to different blocks

and each image block can have different setting of

threshold value.

2.2.4 Thinning

The Zhang-Suen iterative algorithm was used to

process the thinning (Zhang & Fu, 1984).

1. Odd-iteration was used to remove the right,

bottom and upper-left corner pixels.

2. Even-iteration was used to remove the left, top

and bottom right corner pixels.

However, there is certain condition should be

considered. There is one neighboring pixel which

may be the endpoint of framework and can’t be

removed. if there are 7 or more neighboring pixels,

then it should remove the image object which

probably can destroy the shape of image.

After the thinning step, it should remove the four-

side line to get a contour line graph. The next section

will be the actual measurement results and establish

the three-dimensional graphic.

3 EXPERIMENTAL RESULTS

The pitch of reference grating is 1mm (p = 1mm),

light source is from θ

= 45 ° to project, and the

observation is from θ

= 0 ° to observe, shown in

Figure 4 which is the extracting image of the Moiré.

Through Equation 3.1 calculating the d=1N(mm), it

represents that there is a depth change of 1 mm in

each pixel. The image area was cut appropriately

and the color image was converted into grayscale for

each pixel RGB (www.mathworks.com, 2009).

Gray=0.299×R + 0.587×G + 0.114×B (5)

Cutting the region of interest image and filtering

the reference grating stripes, shown in Figure 4.

(a) (b) (c) (d)

Figure 4: Capture images (a) original image (b) 8-bit

grayscale (c) filtering the grating stripes (d) contrast

enhancement.

After binarization of the image, the unneeded

parts were cut or manual removed, shown as Figure

5(a) Marking on the Moiré lines, Figure 5(b) fill in

the different gray values.

(a) (b) (c)

Figure 5: Remove the unwanted unneeded parts and fill in

the gray-scale value.

Figure 6: Three-dimensional graphic rebuit.

3D OBJECT MEASUREMENT BY SHADOW MOIRÉ

163

(a1) (a2)

(b1) (b2)

Figure 7: (a1) (b1) original photos (a2) (b2) three-

dimensional measurement results.

4 CONCLUSIONS

This research applies shadow Moiré to measure the

shape of the mouth. It can freely adjust the different

grating pitch, light sources and different image

grabbing angle to get different resolutions. The more

the density of the grating is, the higher the resolution

is. However, when the shadow stripe on the object is

not obvious, it will increase the difficulty to process.

If the light is not uniform while projecting, aperture

and shutter exposure are not all the same. The

images can’t be processed by a fixed step of the

camera operation. Sometimes it requires manual

adjustment and handling. In the future, in order to

increase its feasibility of projection Moiré in the

experiment, it can also build more samples of the

moving objects. The further study also needs to use

the measured information matching with the 3D

graphic design software to create animation models.

ACKNOWLEDGEMENTS

The author would like to show appreciation that this

work was supported by the National Science

Council of Taiwan, ROC under Grant No. NSC-96-

2221-E-167-026-MY3.

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