| Curve fitting is a commonly used data processing method in many fields.It was originally used to study the relationship between multiple variables.It has been applied to computer aided geometric design over time.In recent years,with the development of artificial intelligence technology,the knowledge of curve fitting will be used to describe and track the trajectory of moving objects in the field of computer vision,edge detection and so on.The smoothness of the curve generated by fitting is also an important index for evaluating curve fitting.If the curve generated by fitting has many burrs,the accuracy of the results will be seriously affected.Therefore,the curve smoothing technology is particularly important.Although the principle of the classical curve smoothing algorithm is simple and the effect of the curve generated in some cases is good,the application scope of the algorithm is limited.It can only be used when the data points can be expressed by functional expressions,but it can not be used when the shape of the curve is complex.In recent years,some new algorithms proposed by researchers,such as fairing spline method and penalty spline method,are mostly based on least square method and improved by adding penalty terms.The fairing effect of these algorithms is good,and can be used in the case of complex data points.But these algorithms involve a lot of matrix operations,and with the increase of data points,the time spent on generating curves is also increasing.The common point of these algorithms is that they need to calculate the parameters in the curve expression.In order to calculate these parameters,it takes a lot of time,and a lot of matrix operations are needed to calculate these parameters,which leads to the high time complexity of the algorithm.In this paper,a new non-parametric curve smoothing algorithm is designed.The main principle is that the absolute value of the difference between left and right slope of data points is used as the smoothing criterion to identify noise points in data points,and then the gradient descent method is used to move these noise points continuously to achieve the effect of curve smoothing.The main difference between the idea of this algorithm and other representative algorithms is that it does not need to calculate theparameters in the function expression of the generated curve,which saves a lot of time in the process of calculating the function expression and improves the efficiency of the algorithm significantly.At the same time,the simplified formula of this algorithm only uses simple addition and subtraction method,which is another reason for the low time complexity of this algorithm.In this paper,we use sinusoidal function,circle,chirp function and irregular curve to simulate the experiment.The experimental results show that the fairing effect of this algorithm is similar to that of other representative algorithms.Under the condition that the fairing effect is good,it runs faster than other algorithms,and can also be used when the amount of data is large.More importantly,the time complexity of the proposed algorithm is less than nO)(. |
