中心B样条二进小波多尺度边缘提取

分析了截尾的Canny算子在多尺度边缘提取时对运算速度造成的影响,提出了中心B样条二进小波多尺度边缘提取,详尽地研究了Canny算子与中心B样条函数的若干性质,中心B样条函数具有紧支集,以极快的速度逼近高斯函数,四阶中心B样条函数的导数比Canny算子更接近最佳边缘检测滤波器.四阶中心B样条函数是二阶平滑问题的唯一最优解,并且它的时频测不准关系值非常接近时频测不准关系下界.从对计算结果的讨论中也得出中心B样条二进小波优于Canny算子的结论.

Center B Spline Dyadic Wavelet Multiscale Edge Detection

We first analyse the effect of cutting off the Canny operator on the calculationspeed for multiscale edge detection, and then propose the center B spline spline dyadic waveletmultiscale edge detection algorithm. Some properties of the Canny operator and center B functionare studied in detail: 1) the center B spline function has compact support and the Cannyoperator does not; 2) the center B spline function converges to the Gaussian function and thederivative of center B spline {unction converges to Canny operator; 3) the derivative of thefourth order center B spline function is more like the optimal edge detection filter than theCanny operator is ; and 4) the fourth order center B spline function is the only solution to thesecond order smoothing problem and its time-frequency uncertainty value is very close to theoptimal value. The result of the multiscale edge detection shows that the center B splinedyadic wavelet is superior to the Canny operator.