Partialdifferential equation based

ImageEdge Detector and Enhancement


 Earlier Work

We were among the very firstwho proposed the use of fourth order and other higher order differentialequations for image processing, see   our paper. The fourth order operator, when combinedwith appropriate nonlinear production (or the so called enhancement) terms,delivers better results for image restoration (including deblurring andenhancement).


Recent Work

Albeit anisotropic diffusiontype of PDEs are very good at image denoising and deblurring, they are not asgood as other standard techniques for image edge detection. In particular, edgedetction of texture images is still a challenging task for all exist methods. Clearly, a different approach is required. We borrow the idea ofsynchronization from nonlinear dynamics. Two coupled nonlinear PDEs are set toevolve with different time scales.  Image edges are obtainedthe synchronization residual. Our results are compared with  those obtained  by using the standardCanny and Sobel detector.  For each original image, one optimal result ispresented in this page.  A large grayscale image can be viewed by clickingon the image. For details, see our paper.

Edge Detection


Edge Detected Images by couple PDEs 



Edges Detected by Sobel Edge Detector

Edges Detected by Canny Edge Detector


                                                                                                           Image Enhancement

 Great edge imag edetection leads to great enhancement, which is obtained by adding the edge to the original image. 


Edge Enhanceed Images by coupled PDEs