Spacefilling curves and the planar travelling salesman problem
Journal of the ACM (JACM)
Digital image processing (2nd ed.)
Digital image processing (2nd ed.)
Iterative reconstruction of multivariate band-limited functions from irregular sampling values
SIAM Journal on Mathematical Analysis
Space diffusion: an improved parallel halftoning technique using space-filling curves
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
A sampling approach to ultra-fast object location
Real-Time Imaging
A Gray Image Compression Using a Hilbert Scan
ICPR '96 Proceedings of the International Conference on Pattern Recognition (ICPR '96) Volume III-Volume 7276 - Volume 7276
Alternative Algorithm for Hilbert's Space-Filling Curve
IEEE Transactions on Computers
Detection of Moving Objects in Image Sequences using 3D Velocity Filters
International Journal of Applied Mathematics and Computer Science - Applied Image Processing
Nonlinear Image Processing and Filtering: A Unified Approach Based on Vertically Weighted Regression
International Journal of Applied Mathematics and Computer Science - Applied Image Processing
International Journal of Applied Mathematics and Computer Science - Applied Image Processing
Generalised sampling theorem for band-limited functions
Mathematical and Computer Modelling: An International Journal
A new approach to vector median filtering based on space filling curves
IEEE Transactions on Image Processing
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A new method of equidistributed (EQD) sampling of nD signals is proposed and investigated. Equidistributed or quasi-random (QR) sequences are deterministic sequences, which cover nD space more evenly than uniformly distributed random sequences. We propose to generate quasi-random nD sample sites using space-filling curves, which propagate their measure and neighborhood preserving properties to sample points. It is proved that these points are not only equidistributed but also well distributed, which results in a good volume approximation from samples of 2D and 3D images. A general way of reconstructing output of a linear system from QR samples of its input nD signals is also proposed and proved to be convergent. As an example of applications of the theory, a double radial basis neural network is proposed, which allows for the reconstruction of 2D cross-sections from samples of 3D image or from a video sequence of 2D images.