title: Reconstruction of nonuniformly sampled images in spline spaces.
abstract: This paper presents a novel approach to the reconstruction of images from nonuniformly spaced samples. This problem is often encountered in digital image processing applications. Nonrecursive video coding with motion compensation, spatiotemporal interpolation of video sequences, and generation of new views in multicamera systems are three possible applications. We propose a new reconstruction algorithm based on a spline model for images. We use regularization, since this is an ill-posed inverse problem. We minimize a cost function composed of two terms: one related to the approximation error and the other related to the smoothness of the modeling function. All the processing is carried out in the space of spline coefficients; this space is discrete, although the problem itself is of a continuous nature. The coefficients of regularization and approximation filters are computed exactly by using the explicit expressions of B-spline functions in the time domain. The regularization is carried out locally, while the computation of the regularization factor accounts for the structure of the nonuniform sampling grid. The linear system of equations obtained is solved iteratively. Our results show a very good performance in motion-compensated interpolation applications.
authors.affiliation: Department of Electrical and Computer Engineering, Concordia University, Montréal, QC H3G 1M8 Canada. cvazquez@ieee.org
authors.forename: Carlos
authors.initials: C
authors.lastname: Vázquez
authors.forename: Eric
authors.initials: E
authors.lastname: Dubois
authors.forename: Janusz
authors.initials: J
authors.lastname: Konrad
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods*; D008954:Models, Biological; D015233:Models, Statistical; D009716:Numerical Analysis, Computer-Assisted; D010363:Pattern Recognition, Automated / Q000379:methods; D010781:Photography / Q000379:methods; D015203:Reproducibility of Results; D018401:Sample Size; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted; D013382:Subtraction Technique; D014741:Video Recording / Q000379:methods*