Abstract
The method of Tikhonov regularization has been widely used to form well-posed inverse problems in low-level vision. The application of this technique usually results in a least squares approximation or a spline fitting of the parameter of interest. This is often adequate for estimating smooth parameter fields. However, when the parameter of interest has discontinuities the estimate formed by this technique will smooth over the discontinuities. Several techniques have been introduced to modify the regularization process to incorporate discontinuities. Many of these approaches however, will themselves be ill-posed or ill-conditioned. This paper presents a technique for incorporating discontinuities into the reconstruction problem while maintaining a well-posed and well-conditioned problem statement. The resulting computational problem is a convex functional minimization problem. This method is compared to previous approaches and examples are presented for the problems of reconstructing curves and surfaces with discontinuities and for estimating image data. Computational issues arising in both analog and digital implementations are also discussed. >
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: IEEE Transactions on Systems, Man, and Cybernetics
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.