Research On The Algorithms Of The Edge Detection Based On Singular Function And Curve Fitting

Edge detection is one of the important steps in image processing and the computer vision system. It plays an important role on many aspects such as feature extraction, object recognition, motion analysis etc. Although various algorithms of the edge detection have been proposed, many problems still exist. It is of important significance to image analysis and recognition that the algorithms of the edge detection are researched further. The work pointed on the theory of the image edge detection in this paper is as follows:Kinds of classic algorithms of the image edge detection are summarized and analyzed. These include the Roberts edge operator, the Sobel edge operator, the Prewitt edge operator, the Robinson edge operator and the Laplace edge operator. Advantage, disadvantage and practicability are compared by theory analysis and computer simulation.With convolution in the context of the theory of distribution, the paper improves on a singular kernel and constructs Shannon's delta kernel used in edge detection, proposes the discrete singular convolution algorithm accordingly. The reasonable threshold of the image segment can be achieved by statistic characteristic of the gradients value which is obtained by image convolution moreover.Discussing the kind of edge and lease square estimation used in curve fitting, the paper proposes a curve fitting algorithm which fits pixels'value using curve and judges the edge by correlation coefficient and the property of the curve.On the basis, computer simulation and experiment on two algorithms proposed above are done, especially anti-noise experiment on noise-adding image. The result illustrates the following: The adaptive separate methods proposed in the paper, which are based on singular function and curve fitting, have more apparent improvement in effect than the traditional one, narrower edge, higher resolution analysis, more accurate edge location, more obvious increase in edge loss (rift), better property of anti-noise.In conclusion, the methods based on singular function and curve fitting are proposed in the paper with the comparison of the various edge-detecting methods. Further more the selection of threshold is also studied, a kind of the rules of threshold selection is given in the paper. The superiority of the two methods is validated by the edge-detecting result of standard image and noise-adding image.