TELKOMNIKA, Vol.10, No.8, December 2012, pp. 2075~2080 e-ISSN: 2087-278X accredited by DGHE (DIKTI), Decree No: 51/Dikti/Kep/2010
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A Sub-pixel Detection Algorithm of the MEMS Dynamic Fuzzy Image Yuan LUO, Chao JI, Yi Zhang,Zhangfang HU Photoelectric engineering college，The Chongqing University of Posts and Telecommunications, Chongqing 400065, China *corresponding author, e-mail:
[email protected]
Abstract The testing images have a certain degree of ambiguity when Application of machine vision method for MEMS dynamic parameters was measured. This paper presents a sub-pixel algorithm: using selfsimilar characteristics of fractal interpolation to overcome the problem that can not be accurate interpolation and the edge of the image reconstruction. Then, because of abilities of high resolution and anti-noise, the wavelet transform is used to obtain the image edge detection. The experimental results show that the algorithm can reach 0.02 pixel accuracy. Keywords: MEMS, Dynamic testing, Fractal interpolation, Sub-pixel, image edge detection.
Copyright © 2012 Universitas Ahmad Dahlan. All rights reserved.
1. Introduction MEMS (micro electro mechanical system, MEMS) is a emerging discipline.Its development has opened up a whole new area of technology and industry,the use of MEMS technology production come into contact with almost all areas in aviation, aerospace, automotive, biomedical, environmental monitoring, military, and very broad application prospects. With the MEMS from the research stage gradually into the industry stage, their test systems has become increasingly urgent [1] . MEMS dynamic testing technology have been many domestic and foreign research institutions attach great importance, and many of them are applying machine vision inspection technology into the MEMS dynamic testing[2,3]. The use of machine vision methods for MEMS dynamic parameters were measured, usually get the test images have a certain degree of ambiguity. The fuzzy band may reflect the MEMS devices in a specific driving voltage (or frequency) plane micro-motion movement amplitude, so the fuzzy measure with precision positioning is significance. The general image edge detection and localization algorithm is based on differential technology, such as Laplacian operator, Sobel operator and LOG operator, etc, but their edge detection and location accuracy can only achieve a pixel precision, and differential operator for noise very sensitive, often produce some fake edge, etc.So subpixel edge detection and localization problem gets much attention. Currently, there are many sub-pixel edge detection methods, such as interpolation, polynomial fitting, geometric moment method, spatial moment method, the existence of most of these methods calculate the principle error or a large amount of defects and poor anti-noise performance. As to the problems, in order to be able to measure accurately the image with the length of the fuzzy,we need to fuzzy belt on the subpixel precision of edge detection. We propose a fuzzy image of subpixel edge extraction of the new algorithm, to achieve sub-pixel blur with length testing.
2. Fuzzy image In the continuous light illumination of high speed movement MEMS devices are collected motion state, because electric coupler a camera collection rate not so high, the obtained image is fuzzy(shown in Figure.1), the image of fuzzy zone is produced due to the device in this area formed by reciprocating motion, although it is unable to correctly reflect the MEMS device on a particular movement position of the motion state, but it can express in particular driver
Received September 29, 2012; Revised November 4, 2012; Accepted November 13, 2012
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frequency or specific drive voltage MEMS device plane micro movement of the maximum amplitude of movement. Based on the above principle, the acquisition of MEMS device motion image sequence using fractal wavelet transform the subpixel image detection technology, can get MEMS device plane micro of movement movement amplitude and resonance frequency and dynamic characteristic parameters.
(a) Resonator still images
(b) Resonator motion of fuzzy image
Figure 1. Capture images MEMS resonator 3. Fractal interpolation In order to accurately measure the length of the image of fuzzy zone, it is necessary to fuzzy zone on the accuracy of the subpixel edge detection. The current implementation and pixel Orientation method mainly interpolation method, the moment moment estimation method and the least square method, etc. This paper, by using fractal interpolation combining wavelet transform of edge detection technology to realize the fuzzy zone length of the pixel detection. 3.1 Random midpoint displacement method Mandelbrot elbrot applied fractal dimension to quantitative descripte the image as a whole and partial similarity, and proposed the concept of Fractional Brownian Motion[4,5]. Motion[ ]. Brownian Motion trajectory is a no rules fractal curve, it also has self-similarity, self similarity, but this similarity with statistical properties, and Fractal Brownian motion (FBM) is the promotion of Brownian Motion, can be obtained by FBM theory random midpoint displacement displacement method[8].So, this article applied the midpoint of the random fractal interpolation method. Random midpoint displacement method can use a simple formula to express the interpolation points :
x m i = ( xi + xi +1 ) / 2 + s ⋅ w ⋅ r a n d ( ) y m i = ( y i + y i + 1 ) / 2 + s ⋅ w ⋅ r a n d () (1) In the equation (1), s ， w are respectively, left and right to control the direction and distance of the control parameters, rand () is random variables. 3.2 Fractal interpolation algorithm The random midpoint displacement method principle, can use normal stochastic function stdev ∗ N (0,1) indicate random variable s ⋅ w ⋅ rand () , H is a parameter indicate the standard deviation of change in new interval , also can generate various FBM curve. H is the measurement of generated curve in the fractal dimension. Similarly you can generate FBM surface (shown in Figure 1) from the initial four white pixel pixel point, the iteration generates (shadow) interpolation points.And then ,iterative can get FBM surface.
Figure 2. Fractal interpolation TELKOMNIKA Vol. 10, No. 8, 8 December 2012 : 2075 – 2080
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As shown in Figure 2, the recursive fractal interpolation formula can be expressed as follows. Pixel in the image set (i, j ) , when i ， j are odd, I (i, j ) is known; i ， j are even, the gray value interpolation points:
I ( x, y ) = [ I (i − 1, j − 1) + I (i + 1, j + 1) + I (i − 1, j + 1) + I (i + 1, j − 1)] / 4 + ∆I When
i is a odd and j is even, or i is even and j is a odd, gray value interpolation points: I ( x, y ) = [ I (i − 1, j ) + I (i, j + 1) + I (i, j + 1) + I (i + 1, j )] / 4 + ∆I
∆I = 1 − 2 2 H − 2 ⋅ H σ G (2) Where G is Gaussian random variables, obey N (0,1) distribution. Traversing images, ∆I −H /2
multiplied by the factor 2 desired spatial resolution.
each cycle, and repeating the iteration until the image achieve the
4. Based on wavelet transform modulus maxima edge sub-pixel positioning The following description is the traditional wavelet transform modulus maxima edge detection method of sub-pixel positioning[6]. Taking into account the gray value change of the MEMS motion blur image edge was a gradual process, with characteristics similar to the edge of the slope. And with the CCD is integral device, its output grey value and photographic surface about the light intensity distribution. Let said imaging system point spread function, usually with a Gaussian function approximation, the imaging system get a good image which has a ideal noise-free edge as follow: f1 ( x ) = f ( x ) ∗ G ( x )
= A
− x0
∫
G ( x + ε )d ε
−∞ − x0
1
(3) dε πδ 2 −∞ where f ( x) is ideal edge model, A is constant and x0 is the edge of the ideal position.
= A
The threshold value
∫
e − ( x +ε )
2
/( 2 δ 2 )
T greater than the mean of wavelet coefficients Wf1 ( s, x) : E =
+∞
∫
xp ( x)dx
−∞ +∞
=
∫
x [ µ ( ε / s ) G ( x − x 0 − ε )d ε ] d x
−∞ +∞ +∞
∫ ∫
µ ( ε / s ) G ( x − x 0 − ε )d ε d x
−∞ −∞
(4) = x0 In other words, the value of mean is that the ideal edge image obtained by the imaging system the exact location of the edge.In the equation (4), p ( x ) is greater than the threshold T the wavelet coefficients Wf1 ( s, x ) of the probability. Of actual signals are sampled by the discrete signal after. And theory and experiment can prove that this principle also applies for discrete signals. The edge of the location of the mean calculation formula is as follows[7]: n n
E = ∑ kp (k ) = k =1
∑ kWf (s, k ) k =1 n
1
(5)
∑Wf ( s, k ) k =1
1
A Sub-pixel Detection Algorithm of the MEMS Dynamic Fuzzy Image (Yuan LUO)
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The resulting mean of the wavelet coefficients E , that is, the exact location of the edge. However, experimental results show that the tradition based on wavelet transform modulus maxima edge sub-pixel pixel positioning accuracy positioning algorithm is difficult to meet their high-precision precision measurement and its large number of measurement data obtained is not stable enough[8].. Therefore, to improve the traditional algorithm,we proposed a fractal based subpixel image edge detection algorithm. This algorithm can be fine to keep the original image texture features, to achieve sub-pixel sub pixel edge location to improve the accuracy and stability.
5. Fractal interpolation Experimental results and analysis Start
I n p u t t h e o r ig in a l im a g e
S e le c t M x M w in d o w t o tr a v e r s e t h e im a g e , e x e c u t in g f r a c ta l in te r p o la tio n
T r a v e r s e im a g e a n d e a c h c o lu m n ( o r lin e s ) e x e c u t e w a v e le t t r a n s fo r m
A c c o r d in g t o th e e q u a t io n ( 3 ) , c a lc u la te d a n d g e t e d g e p o in t s
O b ta in s u b p ix e l e d g e p r o file
Figure 3. Mixed fractal and wavelet transform subpixel image edge detection algorithm process
Mixed fractal and wavelet transform subpixel image edge detection algorithm process as shown in Figure 3. 5.1 Mix fractal and wavelet transform subpixel image edge detection algorithm experiment According to the flow chart, first from the MEMS dynamic fuzzy image (as shown in Figure 1 (b)) near the edge of, we selected 10 × 10 pixel blocks of the size of the window for the fractal interpolation.
(a) The original gray level( level 10 × 10 )
(b)After four times the interpolation gray level ( 145 × 145 )
Figure 4. The interpolation of near the edge TELKOMNIKA Vol. 10, No. 8, 8 December 2012 : 2075 – 2080
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(a)Original Original Image grey plane
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(b)After After four times the interpolation Image grey plane Figure 5. Image grey plane
In Figure 4，color color is the size of grey value .In Figure 5 ，the the same contours of grey value shows the bottom. And the same contours can be approximately as rim profile detected . The planes of original image and image after four times fractal interpolation are shown in Figure 5. Considering above images，the images gray value changes can be seen in the MEMS fuzzy edge image. Among them, the different tonal boundary is the edge of the image. Comparing Figure 5 (a) and (b) shows that after the interpolation ，the the image gray surface do not generate smooth; Also, the interpolated image gray contour contour lines and contour lines of the original gray-scale scale images with good self-similarity, self similarity, so you can maintain the image of the edge detail, avoiding the generation of false edges smooth. Then, each column of the interpolated image executes wavelet transform. From the interpolation image,we choose a column and execute wavelet transform (this paper choose 80 column). Through the large scale wavelet denoising after the curve can be more clearly show dynamic fuzzy image edges presents the characteristics of the edge e of slope.
(a)The The gray curve before wavelet change
(b)The The gray curve after wavelet change
Figure 6.The gray curve after wavelet change
Experimental results verify the wavelet-based wavelet sub-pixel pixel edge detection of anti-noise performance,as shown in Figure 6. 5.2 Comparison and analysis of test results In experiment, generate the ideal slope of ten different edges firstly, and use the image sub-pixel pixel edge detection algorithm presented in this paper to detect the edges. es. And the datas in Table1. Measuring the standard deviation of absolute error to represent the uncertainty of the method, the uncertainty of the new algorithm presented in this paper is 0.0115, while the traditional wavelet transform method is 0.0184[9]. 0.0184[ Obviously, And the new algorithm is more stable. The experimental results showed that the new algorithm can achieve 0.02 pixels subpixel precision. pixel Detection Algorithm of the MEMS Dynamic Fuzzy Image (Yuan LUO) A Sub-pixel
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Table.1 Mixed fractal and wavelet algorithm and the wavelet measuring parameters pixel NO. 1 2 3 4 5 6 7 8 9 10
Real edge position 138.080 138.180 138.280 138.380 138.480 138.580 138.680 138.780 138.880 138.980
Measuring position of the edge 1.380897 138.1749 138.2881 138.3926 138.4659 138.5919 138.6916 138.7741 138.8891 138.9956
Measuring absolute error 0.0097 0.0051 0.0081 0.0126 1.0141 0.0119 0.0116 0.0059 0.0091 0.0156
6. Conclusion Based on MEMS dynamic testing system, this article processes the blur image of planar motion of MEMS devices. For this fuzzy causes, proposes a new image sub-pixel edge detection algorithm, the experimental results show the feasibility of the proposed algorithm and it’s high precision.
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TELKOMNIKA Vol. 10, No. 8, December 2012 : 2075 – 2080
