Review of Subpixel Edge detection

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1 Introduction

The edge detection of digital image is an important foundation of image processing such as segmentation, target recognition and region shape extraction. In the image understanding and analysis, the first step is often edge detection. At present, edge Detection has become one of the most active topics in machine vision, and its research is of great theoretical significance and practical application value. The detection precision of the traditional edge detection method can only reach one pixel level, but with the rapid development of science and technology, the requirement of precision in industrial detection is increasing, the traditional pixel-level edge detection method can not meet the need of actual measurement. Subpixel edge detection, which is highlighted in this paper, can improve the detection accuracy to sub-pixel level.

2 topics

2.1 Sub-pixel positioning principle

Subpixel is a subdivision of the basic unit of pixels, which is a smaller unit than pixels, thus improving the image resolution. in general, sub-pixel edge points exist in the image of the gradual change in the region, we can use polynomial fitting and other methods to obtain the sub-pixel position of the edge point. sub-pixel positioning can be understood as the hardware conditions of the camera system, the use of software algorithms to improve the edge detection accuracy of the method, or is a resolution of less than one pixel image processing technology.

Sub-pixel positioning technology has certain preconditions: 1, the detected target is not composed of isolated, single pixel points, but is composed of a plurality of pixel points, and these pixels should have a certain distribution characteristics, such as gray scale distribution, geometric shape distribution characteristics, etc. 2, under normal circumstances, different goals have their own characteristics, It mainly includes the characteristics of gray distribution based on the target, geometric shape feature, geometric and gray-level coupling characteristics, can analyze and utilize the known target characteristics, and finally determine the exact position of the target by analyzing and recognizing the target image. In the process of locating, the target image is positioned with floating point arithmetic, and the target positioning accuracy is higher than the whole pixel level. This paper analyzes the target characteristics from the image and calculates the target location which is the most consistent with this feature, which is called the image target Subpixel localization technology.

2.2 Subpixel positioning at home and abroad development status

At present, the sub-pixel edge detection algorithm can be summarized into 3 types: Moment method, interpolation method and quasi-legal.

2.2.1 Moment Method

Tabatabai and so on first proposed a sub-pixel edge localization algorithm using the first three-order gray moment, then the method based on the space moment and the zernike orthogonal moment has been proposed successively. The method of Zernike moment is much smaller than that of space moment because only 3 templates need to be calculated. However, these methods are proposed for the ideal edge model. The Shan-moment method is improved, and the fuzzy edge model is used to reflect the edge information more realistically. The advantage of the moment method is that the calculation is simple and the analytic solution can be obtained. However, the moment method is sensitive to image noise, and if the fuzzy edge model is taken into account, the model parameters are added, which makes the determination of analytic solutions very difficult.

2.2.2 interpolation Method

The core of interpolation method is to interpolate the value of gray value or the derivative of gray value of pixel, and increase the information to realize subpixel edge detection. Among them, there are two interpolation, B-spline interpolation and Chebyshev polynomial interpolation to study more methods. The interpolation class has a short operation time, the two-time interpolation algorithm is simple and can be implemented by hardware, which is suitable for on-line detection. When the linear diffusion function of optical system is symmetrical, the accuracy of interpolation edge detection is higher. The interpolation method is similar to the moment-based method, and the calculation process is simple, but it is susceptible to the influence of noise.

2.2.3 quasi-legal

The fitting method is to obtain subpixel edge positioning by fitting the gray value of the assumed edge model. Nalwa The least squares fitting method for the hyperbolic tangent function of the edge model is given, and the edge model of the proposed algorithm is the Gaussian edge function of the ideal edge model and the Gaussian function convolution. Both of these algorithms can provide high subpixel edge positioning accuracy. The fitting method is insensitive to noise, because the fitting does not need numerical differentiation, and fitting the minimum distance of each gray value to the fitting curve, not only makes use of the gray value with error, but also reduces the influence of gray value error. But because the model is complex, its solution speed is slow.

2.2.4 Related improved algorithm

1 subpixel Edge detection method based on improved morphological gradient and zernike moment

The algorithm first uses the improved mathematical morphology gradient operator to locate the edge point, the coordinates and the gradient direction of the edge point at the pixel level, and then the subpixel edge detection is realized by using the Zernike moment algorithm to reposition the edge point based on the constructed edge point vector and reference threshold. This composite image edge Subpixel detection algorithm can well combine the advantages of mathematical morphology gradient operator and Zernike moment algorithm, has good anti-noise performance and sub-pixel precise positioning ability, the calculation amount is relatively small, can quickly realize the subpixel edge detection of CCD image measurement system. In addition, because the general measurement image is simple and the contrast is high, if the appropriate template window is used, the algorithm can have good processing effect.

Rate can meet the real-time and sub-pixel precise measurement requirements of general image measurement system, and has good application prospect.

2 spline interpolation subpixel edge detection method based on improved morphological gradient

This improved method is to combine the improved morphological gradient filter operator with the three-order spline interpolation method to detect the edge, firstly using the improved mathematical morphology gradient filter operator to locate the edge point, and get the pixel-level edge of the image, then using three-time spline interpolation method to interpolate the edge image, That is, sub-pixel fine positioning. Finally, the interpolated edge is refined to obtain sub-pixel edge image.

3 subpixel edge detection algorithm based on Bezier edge model

Firstly, the modified parameter T is introduced into the existing Bessel point diffusion function, and the modified Bessel edge Gray model is obtained by convolution with the ideal edge model. Then, using the information of the edge of the image to

Model for least squares fitting, in the fitting process, the Edge model is modified by modifying the parameter T, finally obtains the accurate edge model, and considers the influence of factors such as digital sampling on the gray distribution, and obtains the subpixel position of the image edge.

There are many improved algorithms for subpixel edge detection, such as the new image subpixel detection method proposed by Hu Shujie, an improved new method based on orthogonal Fourier transform is proposed, which improves the accuracy of subpixel edge detection in some digital images. A fast sub-pixel image registration algorithm, such as Landsky, is proposed, and the speed is higher than that of similar algorithm, etc.

3 Summary

In general, the most straightforward way to improve the accuracy of the detection system is to increase the camera's hardware resolution, but the price is quite expensive. If the 512x512 camera resolution to 1024x1024, will be several times, or even more than 10 times times the price, while the system's image storage capacity and image transmission speed should be increased, otherwise it will cause hardware mismatch. Therefore, it is not economical to improve the accuracy of the measurement system by improving the hardware resolution, and it is also limited in the application of various visual systems. Therefore, it is of great significance to study the method of software processing to improve the detection precision of measurement system, that is, subpixel edge detection.

The combination of multiple algorithms is a way to improve the detection accuracy, such as morphology and zernike moment, improved morphology gradient and spline interpolation.

In sub-pixel edge detection, the predecessors have done a lot of work, but often only for some specific areas more effective, the general method is relatively small, different areas need to use different methods.

4 references

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[3] Zhao Future Dunchen Dengshanxi Yang Yongyue. Subpixel Edge detection based on space moment and Zernike moment [J]. 2004.

[4] Zheng, Luojun wen Experts, et. Research on subpixel edge location method based on curve fitting [J]. Optical technology. 2007 (03): 386-389.

[5] Wang, Pu Zhaobong, Yin Ji-co. Study on the subdivision algorithm of space moment sub-pixel [J]. Optical technology. 1999 (04): 3-6.

[6] Sheng, Tri Xianyu, Gao. Universal Subpixel Edge detection algorithm [J]. Journal of Shanghai Jiaotong University. 2007, 41 (6): 911-915.

[7] Sunqiucheng, Tan Qingchang, Ann was first, et. A Subpixel precision edge detection method [J]. Journal of Beijing University of Technology. 2009, 35 (10): 1332-1337.

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[10] Landsky, Li Chengjin, Zhao Shunjie, et. A fast sub-pixel image registration algorithm [J]. Infrared technology. 2013, 35 (1): 27-30.

Review of Subpixel Edge detection