Application of Higher Order Partial Differential Equations Based on Diffusion Coefficient Improvement in Image Edge Detection

When edge extraction is performed on images, the method of second-order partial differential equations may result in a phenomenon where a similar feature area undergoes multiple iterations and the first derivative is zero, resulting in the same grayscale value of the image and false edges. Although traditional high-order differential equations can overcome the piecewise constant effect, they also bring about the speckle effect. To overcome this drawback, this paper proposes an improved high-order partial differential equation detection model. This model can effectively solve the false edges caused by the “piecewise constant effect” and the existence of the “speckle effect”, resulting in good extraction results.