Image reconstruction from edges based on a wavelet frame of Gaussian derivatives
Chengho Hsin, Yung-Cheng Chen, Shaw‐Jyh Shin · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2005
Edge detection provides a representation that is used by all later stages of image processing. An edge representation must be perceptually complete. This means that a perceptually accurate estimate of the original image can be reconstructed from its edges. We present an algorithm for image reconstruction from edges using a redundant filter bank derived by a wavelet frame composed of derivatives of Gaussian functions. Edges of an image can be extracted by any edge detection method. The band-pass filtered image from this filter bank contains complete information of the original image. A two-stage scheme of image reconstruction from edges is established. First, the band-pass filtered image is approximated by a set of elementary functions specified by the initial edge parameters. The elementary functions comprise of the first three orders of Gaussian derivatives. Second, the optimally approximated band-pass filtered image plus the average of the image is applied to reconstruct the original image. We adopt a conjugate gradient algorithm for the reconstruction. The major contribution of this paper is to lay down a theory of edge-based image reconstruction scheme.