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S+-trees: an efficient structure for the representation of large pictures
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Efficient secondary memory processing of window queries on spatial data
Information Sciences—Informatics and Computer Science: An International Journal
Encoding and decoding the Hilbert order
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Analysis of the Hilbert curve for representing two-dimensional space
Information Processing Letters
Time and space efficient secondary memory representation of quadtrees
Information Systems
Space-filling curves and their use in the design of geometric data structures
Theoretical Computer Science - Special issue: Latin American theoretical informatics
Efficient processing of window queries in the pyramid data structure
PODS '90 Proceedings of the ninth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Discrete Mathematics
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
IEEE Transactions on Knowledge and Data Engineering
Neighbor-finding based on space-filling curves
Information Systems
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Manipulation and Presentation of Multidimensional Image Data Using the Peano Scan
IEEE Transactions on Pattern Analysis and Machine Intelligence
Processing count queries over event streams at multiple time granularities
Information Sciences: an International Journal
Space-filling curves: Their generation and their application to bandwidth reduction
IEEE Transactions on Information Theory
A new approach to vector median filtering based on space filling curves
IEEE Transactions on Image Processing
An algorithm for encoding and decoding the 3-D Hilbert order
IEEE Transactions on Image Processing
Space-filling approach for fast window query on compressed images
IEEE Transactions on Image Processing
A globally adaptive pixel-decimation algorithm for block-motion estimation
IEEE Transactions on Circuits and Systems for Video Technology
All-nearest-neighbors finding based on the Hilbert curve
Expert Systems with Applications: An International Journal
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Previously, several efficient Hilbert scan-based operations were presented, but they all suffer from the constraint that the image size must be 2^rx2^r. Considering an image with arbitrary size I"1xI"2, this paper first presents an efficient snake scan-based algorithm for coding the Hilbert curve of the given image. The proposed coding algorithm takes O(k+logU) time to code the Hilbert order of one pixel where k denotes the number of the quadrants and U=min(I"1,I"2). Next, a memory-saving Hilbert curve representation called HCGL is presented for representing the encoded Hilbert curve and it can be constructed in O(L^2logL) time where L=max(I"1,I"2). Based on the HCGL representation of arbitrary-sized image, an application to window query is presented and the proposed window query algorithm takes O(MlogL+P) time where M denotes the number of generated maximal quadtree blocks and P denotes the number of output codes. Under the same PSNR (Peak Signal to Noise Ratio), experimental results demonstrate that our proposed HCGL representation outperforms some existing related algorithms in terms of execution-time and BPP (Bit Per Pixel). In addition, our proposed window query algorithm has been justified in the GIS (Geographical Information System) application.