[{"_id":"5801","title":"Fast and Efficient Incremental Algorithms for Circular and Spherical Propagation in Integer Space","author":[{"first_name":"Shivam","last_name":"Dwivedi","full_name":"Dwivedi, Shivam"},{"full_name":"Gupta, Aniket","last_name":"Gupta","first_name":"Aniket"},{"last_name":"Roy","full_name":"Roy, Siddhant","first_name":"Siddhant"},{"orcid":"0000-0002-5372-7890","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","first_name":"Ranita","full_name":"Biswas, Ranita","last_name":"Biswas"},{"full_name":"Bhowmick, Partha","last_name":"Bhowmick","first_name":"Partha"}],"doi":"10.1007/978-3-319-66272-5_28","abstract":[{"text":"Space filling circles and spheres have various applications in mathematical imaging and physical modeling. In this paper, we first show how the thinnest (i.e., 2-minimal) model of digital sphere can be augmented to a space filling model by fixing certain “simple voxels” and “filler voxels” associated with it. Based on elementary number-theoretic properties of such voxels, we design an efficient incremental algorithm for generation of these space filling spheres with successively increasing radius. The novelty of the proposed technique is established further through circular space filling on 3D digital plane. As evident from a preliminary set of experimental result, this can particularly be useful for parallel computing of 3D Voronoi diagrams in the digital space.","lang":"eng"}],"alternative_title":["LNCS"],"year":"2017","date_updated":"2022-01-27T15:34:25Z","publication_identifier":{"isbn":["978-3-319-66271-8"],"issn":["0302-9743"],"eisbn":["978-3-319-66272-5"],"eissn":["1611-3349"]},"publication":"20th IAPR International Conference","place":"Cham","page":"347-359","status":"public","publication_status":"published","month":"08","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","citation":{"short":"S. Dwivedi, A. Gupta, S. Roy, R. Biswas, P. Bhowmick, in:, 20th IAPR International Conference, Springer Nature, Cham, 2017, pp. 347–359.","ama":"Dwivedi S, Gupta A, Roy S, Biswas R, Bhowmick P. Fast and Efficient Incremental Algorithms for Circular and Spherical Propagation in Integer Space. In: <i>20th IAPR International Conference</i>. Vol 10502. Cham: Springer Nature; 2017:347-359. doi:<a href=\"https://doi.org/10.1007/978-3-319-66272-5_28\">10.1007/978-3-319-66272-5_28</a>","ista":"Dwivedi S, Gupta A, Roy S, Biswas R, Bhowmick P. 2017. Fast and Efficient Incremental Algorithms for Circular and Spherical Propagation in Integer Space. 20th IAPR International Conference. DGCI: International Conference on Discrete Geometry for Computer Imagery, LNCS, vol. 10502, 347–359.","apa":"Dwivedi, S., Gupta, A., Roy, S., Biswas, R., &#38; Bhowmick, P. (2017). Fast and Efficient Incremental Algorithms for Circular and Spherical Propagation in Integer Space. In <i>20th IAPR International Conference</i> (Vol. 10502, pp. 347–359). Cham: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-319-66272-5_28\">https://doi.org/10.1007/978-3-319-66272-5_28</a>","ieee":"S. Dwivedi, A. Gupta, S. Roy, R. Biswas, and P. Bhowmick, “Fast and Efficient Incremental Algorithms for Circular and Spherical Propagation in Integer Space,” in <i>20th IAPR International Conference</i>, Vienna, Austria, 2017, vol. 10502, pp. 347–359.","chicago":"Dwivedi, Shivam, Aniket Gupta, Siddhant Roy, Ranita Biswas, and Partha Bhowmick. “Fast and Efficient Incremental Algorithms for Circular and Spherical Propagation in Integer Space.” In <i>20th IAPR International Conference</i>, 10502:347–59. Cham: Springer Nature, 2017. <a href=\"https://doi.org/10.1007/978-3-319-66272-5_28\">https://doi.org/10.1007/978-3-319-66272-5_28</a>.","mla":"Dwivedi, Shivam, et al. “Fast and Efficient Incremental Algorithms for Circular and Spherical Propagation in Integer Space.” <i>20th IAPR International Conference</i>, vol. 10502, Springer Nature, 2017, pp. 347–59, doi:<a href=\"https://doi.org/10.1007/978-3-319-66272-5_28\">10.1007/978-3-319-66272-5_28</a>."},"day":"22","date_created":"2019-01-08T20:42:22Z","oa_version":"None","conference":{"name":"DGCI: International Conference on Discrete Geometry for Computer Imagery","end_date":"2017-09-21","start_date":"2017-09-19","location":"Vienna, Austria"},"extern":"1","date_published":"2017-08-22T00:00:00Z","publisher":"Springer Nature","intvolume":"     10502","article_processing_charge":"No","volume":10502,"quality_controlled":"1","language":[{"iso":"eng"}],"type":"conference"},{"date_published":"2017-08-22T00:00:00Z","extern":"1","date_created":"2019-01-08T20:42:39Z","oa_version":"None","conference":{"location":"Vienna, Austria","start_date":"2017-09-19","end_date":"2017-09-21","name":"DGCI: International Conference on Discrete Geometry for Computer Imagery"},"citation":{"short":"E. Andres, R. Biswas, P. Bhowmick, in:, 20th IAPR International Conference, Springer Nature, Cham, 2017, pp. 388–398.","ista":"Andres E, Biswas R, Bhowmick P. 2017. Digital primitives defined by weighted focal set. 20th IAPR International Conference. DGCI: International Conference on Discrete Geometry for Computer Imagery, LNCS, vol. 10502, 388–398.","ama":"Andres E, Biswas R, Bhowmick P. Digital primitives defined by weighted focal set. In: <i>20th IAPR International Conference</i>. Vol 10502. Cham: Springer Nature; 2017:388-398. doi:<a href=\"https://doi.org/10.1007/978-3-319-66272-5_31\">10.1007/978-3-319-66272-5_31</a>","apa":"Andres, E., Biswas, R., &#38; Bhowmick, P. (2017). Digital primitives defined by weighted focal set. In <i>20th IAPR International Conference</i> (Vol. 10502, pp. 388–398). Cham: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-319-66272-5_31\">https://doi.org/10.1007/978-3-319-66272-5_31</a>","ieee":"E. Andres, R. Biswas, and P. Bhowmick, “Digital primitives defined by weighted focal set,” in <i>20th IAPR International Conference</i>, Vienna, Austria, 2017, vol. 10502, pp. 388–398.","chicago":"Andres, Eric, Ranita Biswas, and Partha Bhowmick. “Digital Primitives Defined by Weighted Focal Set.” In <i>20th IAPR International Conference</i>, 10502:388–98. Cham: Springer Nature, 2017. <a href=\"https://doi.org/10.1007/978-3-319-66272-5_31\">https://doi.org/10.1007/978-3-319-66272-5_31</a>.","mla":"Andres, Eric, et al. “Digital Primitives Defined by Weighted Focal Set.” <i>20th IAPR International Conference</i>, vol. 10502, Springer Nature, 2017, pp. 388–98, doi:<a href=\"https://doi.org/10.1007/978-3-319-66272-5_31\">10.1007/978-3-319-66272-5_31</a>."},"day":"22","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","month":"08","article_processing_charge":"No","volume":10502,"language":[{"iso":"eng"}],"type":"conference","quality_controlled":"1","publisher":"Springer Nature","intvolume":"     10502","abstract":[{"text":"This papers introduces a definition of digital primitives based on focal points and weighted distances (with positive weights). The proposed definition is applicable to general dimensions and covers in its gamut various regular curves and surfaces like circles, ellipses, digital spheres and hyperspheres, ellipsoids and k-ellipsoids, Cartesian k-ovals, etc. Several interesting properties are presented for this class of digital primitives such as space partitioning, topological separation, and connectivity properties. To demonstrate further the potential of this new way of defining digital primitives, we propose, as extension, another class of digital conics defined by focus-directrix combination.","lang":"eng"}],"alternative_title":["LNCS"],"year":"2017","doi":"10.1007/978-3-319-66272-5_31","title":"Digital primitives defined by weighted focal set","author":[{"last_name":"Andres","full_name":"Andres, Eric","first_name":"Eric"},{"first_name":"Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","last_name":"Biswas","full_name":"Biswas, Ranita","orcid":"0000-0002-5372-7890"},{"first_name":"Partha","full_name":"Bhowmick, Partha","last_name":"Bhowmick"}],"_id":"5802","status":"public","publication_status":"published","place":"Cham","page":"388-398","publication":"20th IAPR International Conference","publication_identifier":{"eissn":["1611-3349"],"eisbn":["978-3-319-66272-5"],"issn":["0302-9743"],"isbn":["978-3-319-66271-8"]},"date_updated":"2022-01-27T15:38:35Z"}]