• Journal of Advanced Navigation Technology
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• v.13 no.6
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• pp.984-990
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• 2009

Halftoning is very important image processing techniques in the digital printing industry which is a process of converting a continuous-tone image to bi-level tone image. In this paper we introduce a new digital halftoning method based on maze generation algorithm as a replacement algorithm of halftoning with space-filling curve. Previous error-diffusion methods based on space-filling curve suffer from regular pattern artifacts from uniform scan pattern. We use maze generation algorithm to remove this undesirable pattern of space-filling curve method.

• Journal of Digital Convergence
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• v.12 no.1
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• pp.415-421
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• 2014

In this paper, we proposed problem and improvement of halftoning using random space filling curve. Random space filling curve is developed as a solution for shortcoming which space filling curve has self-similarity. It is used to reduce regular pattern can be occurred in constant brightness area in order that randomness apply to scanning path. But there is a problem that some area along scanning path can show too bright result in halftoning using random space filling curve. In this paper, we analyzed cause of problem and proposed single pixel error diffusion as a solution method. This method can avoid over-accumulated error and show better result in halftoning.

• Proceedings of the IEEK Conference
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• 2002.07a
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• pp.38-41
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• 2002

Many scientifc applications include manipulation of data points tying in a space. We describe a method, based on sector labeling to generate a space-filling curve for partitioning such given data points. Our method is straightforward and flexible, equipping a one-one correspondence between point-values on the curve and data points in space in more efficient than designated methods found in the literature. It is widely believed that the Hilbert curve achieves the desired properties on linear mappings due to the locality between data points. Therefore we focus on the Hilbert curve since, later on, we identify it as the most suitable for our application. We demonstrate on using our method for the data particles of an n-body simulation that based on Barnes-Hut algorithm.

• The KIPS Transactions:PartD
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• v.11D no.1
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• pp.23-30
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• 2004

In order to approximate the spatial query result size we partition the input rectangles into subsets and estimate the query result size based on the partitioned spatial area. In this paper we examine query result size estimation in skewed data. We examine the existing spatial partitioning techniques such as equi-area and equi-count partitioning, which are analogous to the equi-width and equi-height histograms used in relational databases, and examine the other partitioning techniques based on spatial indexing. In this paper we propose a new spatial partitioning technique based on the Hilbert space filling curve. We present a detailed experimental evaluation comparing the proposed technique and the existing techniques using synthetic as well as real-life datasets. The experiments showed that the proposed partitioning technique based on the Hilbert space filling curve achieves better query result size estimation than the existing techniques for space query size, bucket numbers, skewed data, and spatial data size.

• Proceedings of the KOSOMBE Conference
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• v.1991 no.11
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• pp.54-56
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• 1991

Many techniques have been used for medial image compression. Its first requirement is "Errorless" or, "Completely Reversible". Under this condition, we have increased the performance of compression using Space Filling Curve. This method converts source image in direction of Hilbert's curve path in order to ate average length longer thar in traditoinal horizental normal path. After that, we have applied RLC and reduced statistical redundancy by Huffman Coding. By this method, we have obtained more efficient results of RLC.

• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.585-595
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• 2024

We show that a pseudo-Anosov map constructed as a product of the large power of Dehn twists of two filling curves always has a geodesic axis on the curve graph of the surface. We also obtain estimates of the stable translation length of a pseudo-Anosov map, when two filling curves are replaced by multicurves. Three main applications of our theorem are the following: (a) determining which word realizes the minimal translation length on the curve graph within a specific class of words, (b) giving a new class of pseudo-Anosov maps optimizing the ratio of stable translation lengths on the curve graph to that on Teichmüller space, (c) giving a partial answer of how much power is needed for Dehn twists to generate right-angled Artin subgroup of the mapping class group.

• 한국HCI학회:학술대회논문집
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• 2008.02a
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• pp.733-738
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• 2008

Serial Music, introduced by A. Sch nberg, is a one of the important composition techniques. This music style has features of pantonality and atonality, so it generates unique atmosphere of modern music. In this paper, we introduce an method of generating serial music using mathematical algorithm. This method generates music that satisfy the requirement that the number of pitches belonged to each pitch class are exactly same, though the requirement is less strict than Sch nberg's definition. To do this, our method uses space-filling curves traversing the twelve tone matrix, which is constructed by the serial series, its inversion and its transpose. Using these curves, we can generate a music that has all notes in the matrix exactly once and adequate repeatness because of the curve's locality. Result music, therefore, can be more suitable for people that are not familiar with modern music, while maintaining the features of pantonality and atonality. This paper also introduces a method of generating extended serial music that uses serialism of duration and dynamic of notes, using multi-dimensional space-filling curves.

• Journal of Korea Spatial Information System Society
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• v.8 no.2 s.17
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• pp.13-38
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• 2006

Range query is one of the most important operations for spatial objects, it retrieves all spatial objects that overlap a given query region in multi-dimensional space. The DOT(DOuble Transformation) is known as an efficient indexing methods, it transforms the MBR of a spatial object into a single numeric value using a space filling curve, and stores the value in a $B^+$-tree. The DOT index is possible to be employed as a primary index for spatial objects. However, the range query processing based on the DOT index requires much overhead for spatial transformations to get the query region in the final space. Also, the detailed range query processing method for 2-dimensional spatial objects has not been studied yet in this paper, we propose an efficient multi-dimensional range query processing technique based on the DOT index. The proposed technique exploits the regularities in the moving patterns of space filling curves to divide a query region into a set of maximal sub-legions within which space filling curves traverse without interruption. Such division reduces the number of spatial transformations required to perform the range query and thus improves the performance of range query processing. A visual simulator is developed to show the evaluation method and the performance of our technique.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.5 no.1
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• pp.38-43
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• 2004

We designed and implemented a medical image query system, including a relational database and DBMS (database management system), which can visualize image data and can achieve spatial, attribute, and mixed queries. Image data used in querying can be visualized in slice, MPR(multi-planner reformat), volume rendering, and overlapping on the query system. To reduce spatial cost and processing time in the system. brain images are spatially clustered, by an adaptive Hilbert curve filling, encoded, and stored to its database without loss for spatial query. Because the query is often applied to small image regions of interest(ROI's), the technique provides higher compression rate and less processing time in the cases.

• Journal of Korea Game Society
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• v.9 no.6
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• pp.191-196
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• 2009

Volume rendering is a method which extracts meaningful information from volume data and visualizes those information. In general, since the size of volume data gets larger, it is very important to devise acceleration methods for interactive rendering speed. Min-max octree is data structure for high-speed volume rendering, however, its creation time becomes long as the data size increases. In this paper, we propose acceleration method of min-max octree generation using CUDA. Firstly, we convert one-dimensional array from volume data using space filling curve. Then we make min-max octree structures from the sequential array and apply them to acceleration of volume ray casting.