In this paper

an edge detector based on a B spline smoothing formula of image is proposed.Firstly

a smoothing surface with perfect information of the digital image is presented by using the uniform B spline function.Since the B spline is a locally supported function

the smoothing formula can be strictly limited in some neighborhood of a point

i.e.

S（x

y）=∑（i

j）∈N k

l （x

y）f（i

j）Ω k（x-i）Ω l（y-j） The surface is smooth

and it has the same convexity as that of the original image.secondly

the edge point is detected by either computing the local extreme of the directional derivative or computing zero crossing of the second order directional derivative of the smoothing surface.Finally

and example of the detector performance is given.The numerical experiment suggests that our detection scheme may be used in computer vision

such as feature extraction

segmentation of image

and texture synthesis.