High resolution image formation from low resolution frames using Delaunay triangulation

An algorithm based on spatial tessellation and approximation of each triangle patch in the Delaunay (1934) triangulation (with smoothness constraints) by a bivariate polynomial is advanced to construct a high resolution (HR) high quality image from a set of low resolution (LR) frames. The high resolution algorithm is accompanied by a site-insertion algorithm for update of the initial HR image with the availability of more LR frames till the desired image quality is attained. This algorithm, followed by post filtering, is suitable for real-time image sequence processing because of the fast expected (average) time construction of Delaunay triangulation and the local update feature.

[1]  Nirmal K. Bose,et al.  Recursive reconstruction of high resolution image from noisy undersampled multiframes , 1990, IEEE Trans. Acoust. Speech Signal Process..

[2]  Bobby R. Hunt,et al.  Super‐resolution of images: Algorithms, principles, performance , 1995, Int. J. Imaging Syst. Technol..

[3]  Peyman Milanfar,et al.  Efficient generalized cross-validation with applications to parametric image restoration and resolution enhancement , 2001, IEEE Trans. Image Process..

[4]  Peyman Milanfar,et al.  A computationally efficient superresolution image reconstruction algorithm , 2001, IEEE Trans. Image Process..

[5]  H. Saunders.  Book Reviews : FINITE ELEMENT ANALYSIS FUNDAMENTALS R.H. Gallagher Prentice Hall, Inc., Englewood Cliffs, New Jersey (1975) , 1977 .

[6]  Robert L. Scot Drysdale,et al.  A Comparison of Sequential Delaunay Triangulation Algorithms , 1997, Comput. Geom..

[7]  Adrian Bowyer,et al.  Computing Dirichlet Tessellations , 1981, Comput. J..

[8]  Steve Mann,et al.  Video orbits of the projective group a simple approach to featureless estimation of parameters , 1997, IEEE Trans. Image Process..

[9]  Mark Andrews,et al.  Asymmetric iterative blind deconvolution of multiframe images , 1998, Optics & Photonics.

[10]  Nirmal Kumar Bose,et al.  Reconstruction of 2-D bandlimited discrete signals from nonuniform samples , 1990 .

[11]  D. F. Watson.  Computing the n-Dimensional Delaunay Tesselation with Application to Voronoi Polytopes , 1981, Comput. J..

[12]  Max Born,et al.  Principles of optics - electromagnetic theory of propagation, interference and diffraction of light (7. ed.) , 1999 .

[13]  Rex A. Dwyer.  Higher-dimensional voronoi diagrams in linear expected time , 1991, Discret. Comput. Geom..

[14]  Robert J. Hanisch,et al.  Deconvolution of Hubbles Space Telescope images and spectra , 1996 .

[15]  François Malgouyres,et al.  Edge Direction Preserving Image Zooming: A Mathematical and Numerical Analysis , 2001, SIAM J. Numer. Anal..

[16]  D. Sandwell.  BIHARMONIC SPLINE INTERPOLATION OF GEOS-3 AND SEASAT ALTIMETER DATA , 1987 .

[17]  A. K. Garga,et al.  A neural network approach to the construction of Delaunay tessellation of points in R/sup d/ , 1994 .

[18]  L. Poletto,et al.  Enhancing the spatial resolution of a two-dimensional discrete array detector , 1999 .

[19]  J. C. Dainty,et al.  Iterative blind deconvolution method and its applications , 1988 .

[20]  Larry L. Schumaker,et al.  Triangulation Methods , 1987, Topics in Multivariate Approximation.

[21]  Michael Elad,et al.  A fast super-resolution reconstruction algorithm for pure translational motion and common space-invariant blur , 2001, IEEE Trans. Image Process..

[22]  Peyman Milanfar,et al.  A wavelet-based interpolation-restoration method for superresolution (wavelet superresolution) , 2000 .

[23]  S Peled,et al.  Superresolution in MRI: Application to human white matter fiber tract visualization by diffusion tensor imaging , 2001, Magnetic resonance in medicine.

[24]  D. Donoho.  Smooth Wavelet Decompositions with Blocky Coefficient Kernels , 1993 .

[25]  Helmuth Späth,et al.  Two-dimensional spline interpolation algorithms , 1993 .

[26]  Seunghyeon Rhee,et al.  Discrete cosine transform based regularized high-resolution image reconstruction algorithm , 1999 .

[27]  Henry T. Y. Yang.  Finite Element Structural Analysis , 1985 .

[28]  R. Franke.  Smooth Interpolation of Scattered Data by Local Thin Plate Splines , 1982 .

[29]  Michael Elad,et al.  Superresolution restoration of an image sequence: adaptive filtering approach , 1999, IEEE Trans. Image Process..

[30]  Deepa Kundur,et al.  Blind Image Deconvolution , 2001 .

[31]  Nirmal K. Bose,et al.  Neural network design using Voronoi diagrams , 1993, IEEE Trans. Neural Networks.

[32]  D. M. Etter,et al.  Wavelet basis reconstruction of nonuniformly sampled data , 1998 .

[33]  Kacem Chehdi,et al.  Parametric Blur Estimation Using the Generalized Cross-Validation Criterion and a Smoothness Constraint on the Image , 1999, Multidimens. Syst. Signal Process..

[34]  P. Koeck.  Ins and outs of digital electron microscopy , 2000, Microscopy research and technique.

[35]  Franz Aurenhammer,et al.  Voronoi diagrams—a survey of a fundamental geometric data structure , 1991, CSUR.

[36]  Nirmal K. Bose,et al.  High‐resolution image reconstruction with multisensors , 1998, Int. J. Imaging Syst. Technol..

[37]  Deepa Kundur,et al.  Blind image deconvolution revisited , 1996 .

[38]  Thomas Strohmer,et al.  Computationally attractive reconstruction of bandlimited images from irregular samples , 1997, IEEE Trans. Image Process..

[39]  Michael Elad,et al.  Restoration of a single superresolution image from several blurred, noisy, and undersampled measured images , 1997, IEEE Trans. Image Process..

[40]  Michael K. Ng,et al.  Constrained total least‐squares computations for high‐resolution image reconstruction with multisensors , 2002, Int. J. Imaging Syst. Technol..

[41]  Atsuyuki Okabe,et al.  Spatial Tessellations: Concepts and Applications of Voronoi Diagrams , 1992, Wiley Series in Probability and Mathematical Statistics.

[42]  S. Lertrattanapanich.  Latest Results on High-Resolution Reconstruction from Video Sequences , 1999 .

[43]  J. R. Higgins.  Sampling theory in Fourier and signal analysis : foundations , 1996 .

[44]  A. Murat Tekalp,et al.  Superresolution video reconstruction with arbitrary sampling lattices and nonzero aperture time , 1997, IEEE Trans. Image Process..

[45]  John C. Davis,et al.  Contouring: A Guide to the Analysis and Display of Spatial Data , 1992 .

[46]  Michal Irani,et al.  Improving resolution by image registration , 1991, CVGIP Graph. Model. Image Process..