Application of an improved high order PDE in image edge detection

Yu Bowen

The two order partial differential equation in the image edge detection, has good edge holding ability, but there will be a "piecewise constant" effect, leading to false edges produced. Partial differential equation of higher order is very good to overcome the "piecewise constant" effect, but the ability of keeping edge drop, resulting in blurred edge. Therefore, this paper proposes a model for edge detection fusion of two order partial differential equation with four order partial differential equations, gives the Euler Lagrange equation and the gradient descent flow, and introduces the numerical discretization method.Finally a numerical validation is performed by the edge detection of objective evaluation index. Experiments show that, this method is very effectively in the image edge extraction, and overcome "piecewise constant" effect , edge blur and other shortcomings, improving the extraction results.