The implicit polynomial curves have a lot of merits

such as the capability to describe irregularly shaped objects

object recognition and insensitivity to noise

and are used widely in CAGD and computer graphics. A new method for closed curve construction is introduced which is based on the combination of BP neural network and principle of implicit curve construction. The algorithm

first constructs the input and output of the BP neural network from the constraint points and changes the implicit function that represents object boundary into explicit function

then uses BP neural network to fit the curve of the explicit function

and finally obtains the fitting curves that represent the object boundary from the simulation surface. The algorithm has more advancements than the method of fitting the curves of explicit functions by BP network

which can not fit the closed curves. It has good numerical stability and robustness in dealing with noisy or missing data. The Experimental results are given to verify the effectiveness of recovering incomplete images and object boundary reconstruction.