Aztec curve: proposal for a new space-filling curve
Different space-filling curves (SFCs) are briefly reviewed in this paper, and a new one is proposed. A century has passed between the inception of this kind of curves, since then they have been found useful in computer science, particularly in data storage and indexing due to their clustering properties, being Hilbert curve the most well-known member of the family of fractals. The proposed Aztec curve, with similar characteristics to the Hilbert's curve, is introduced in this paper, accompanied by a grammatical description for its construction. It yields the possibility of creating bi-dimensional clusters, not available for Hilbert nor Peano curves. Additional to this, a case of application on the scope of Compressed Sensing is implemented, in which the use of Hilbert curve is contrasted with Aztec curve, having a similar performance, and positioning the Aztec curve as viable and a new alternative for future exploitation on applications that make use of SFC's.
Code (0)
등록된 구현이 없습니다.
Tasks
compressed sensingSimilar Papers 제목 키워드 기반
Space-filling Curves for High-performance Data Mining
Space-filling curves like the Hilbert-curve, Peano-curve and Z-order map natural or real numbers from a two or higher dimensional space to a one dimensional space preserving locality. They have numerous applications like…
ClusteringVocal Bursts Intensity PredictionPointSCNet: Point Cloud Structure and Correlation Learning Based on Space Filling Curve-Guided Sampling
Geometrical structures and the internal local region relationship, such as symmetry, regular array, junction, etc., are essential for understanding a 3D shape. This paper proposes a point cloud feature extraction network…
3D Point Cloud ClassificationSemantic SegmentationUnsupervised Panoptic Interpretation of Latent Spaces in GANs Using Space-Filling Vector Quantization
Generative adversarial networks (GANs) learn a latent space whose samples can be mapped to real-world images. Such latent spaces are difficult to interpret. Some earlier supervised methods aim to create an interpretable …
Data AugmentationQuantizationDetecting Curve Text with Local Segmentation Network and Curve Connection
Curve text or arbitrary shape text is very common in real-world scenarios. In this paper, we propose a novel framework with the local segmentation network (LSN) followed by the curve connection to detect text in horizont…
SegmentationText DetectionText SegmentationSpace filling positionality and the Spiroformer
Transformers excel when dealing with sequential data. Generalizing transformer models to geometric domains, such as manifolds, we encounter the problem of not having a well-defined global order. We propose a solution wit…