固定パラメータ問題に対する高速算法に基づく計算困難問題の解決

金沢大学 / 北陸先端科学技術大学院大学本研究の目的は、最近の計算機環境の下で固定パラメータ問題を高速に解決するための方法論を確立することである。そのために、単なるプログラムテクニックとして解析に反映されなかった側面を数学的に厳密に評価し、従来の解析方法とは全く異なる立場から計算の効率評価を行うことであった。今年度は、トライセクター曲線に関する研究に時間を割いた.平面上に与えられた2点に対する2等分線は容易に計算できるが,2点間に等距離の曲線を描くのは困難である.正確には,任意の精度で近似解を得ることはできるが,正確に曲線上の点を求めることは不可能(代数的でない)であることが予想される.本研究では,そのような曲線が常に存在し,ユニークに定まることを数学的にかつ構成的に証明した.それ以外にも様々な興味深い構造的な性質を明らかにした.この研究の成果は,5月に開かれた理論計算機科学では最高峰の国際会議であるSTOCにおいて発表すると共に,Advances in Mathematicsという数学ではトップクラスのジャーナルにも論文を発表した.非常に基本的な問題でありながら,これまでに全く類似の研究がなかったということはむしろ驚きである.計算幾何学においてボロノイ図は重要な研究課題のひとつである.本研究では,従来のボロノイ図の概念を一般化して,三角形に関する評価尺度に基づいた様々なボロノイ図を定義したが,特に角度ボロノイ図に興味をもち,その構造と複雑さに関する研究を行った.具体的には,線分の集合が与えられたとき,どの線分に対して定義される視角が最も小さいかという関係で平面を分割したものである.この研究では,角度ボロノイ図が通常のボロノイ図と極めて異なる性質をもつことを証明し,さらに最小の視角を最大にする点を効率よく求めるためのアルゴリズムを示している.この結果にっいては,7月に開かれたボロノイ図に関する国際ワークショップにおいて報告した.現在は,そのジャーナルバージョンを執筆中であり,近い将来にジャーナル誌に投稿をする予定である.The purpose of this research is to establish methodology for solving fixed parameter problems in an efficient way under latest computer environment. For the purpose we mathematically evaluate some aspects of programming which has not been reflected to analysis as just simple programming techniques and then analyze computational performance from a completely different standpoint from the existing ones.In this year we spent much time for the study of distance trisector curves. Given two points in the plane, it is easy to draw perpendicular bisector, but it is hard to draw two curves equidistant from each other. More exactly, we can approximate points on the curves at any precision, but it is impossible to compute their coordinates exactly without any error. In fact we conjecture that the curves are non-algebraic. In this research we proved that such curves exist and they are unique, mathematically in a constructive manner. We also found many interesting properties of the curves. The resu lts were presented at an international symposium STOC, one of the top conference in the world in this area and also published in a top mathematical journal, Advances in Mathematics. It is rather surprising that it is quite simple and fundamental problem while there is no study on the curves. We also applied the idea to Voronoi diagrams, which is one of the most important research topics in computational geometry. In this research we defined various Voronoi diagrams based on criteria on goodness of triangles by generalizing the traditional Voronoi diagrams. More concretely, given a set of line segments in the plane, an angular Voronoi diagram is a partition of the plane into regions by the relation on which line segment gives the smallest visual angle. We have shown that this Voronoi diagram has properties which are quite different from those of the exisiting ones. We also gave an efficient algorithm for finding a point that maximizes the smallest visual angle. The results were presented at an international symposium on Voronoi diagrams We are now preparing journal version of those papers to submit them to international journals.研究課題/領域番号:15300003, 研究期間(年度):2003 - 2006出典：「固定パラメータ問題に対する高速算法に基づく計算困難問題の解決」研究成果報告書　課題番号15300003（KAKEN：科学研究費助成事業データベース（国立情報学研究所）） （https://kaken.nii.ac.jp/ja/report/KAKENHI-PROJECT-15300003/153000032006kenkyu_seika_hokoku_gaiyo/）を加工して作

A comparison of 2D and 3D Delaunay triangulations for fingerprint authentication

The two-dimensional (2D) Delaunay triangulation-based structure, i.e., Delaunay triangle, has been widely used in fingerprint authentication. However, we also notice the existence of three-dimensional (3D) Delaunay triangulation, which has not been extensively explored. Inspired by this, in this paper, the features of both 2D and 3D Delaunay triangulation-based structures are investigated and the findings show that a 3D Delaunay structure, e.g., Delaunay tetrahedron, can provide more feature types and a larger number of elements than a 2D Delaunay structure, which was expected to provide a higher discriminative capability. However, higher discrimination does not necessarily lead to better performance, especially in biometric applications, when biometric uncertainty is unavoidable. Experimental results show that the biometric uncertainty such as missing or spurious minutiae causes more negative influence on the 3D Delaunay triangulation than that on the 2D Delaunay triangulation in three out of four experimental data sets

Fingerprint Direct-Access Strategy Using Local-Star-Structure-based Discriminator Features: A Comparison Study

This paper describes a comparison study of the proposed fingerprint direct-access strategy using local-star-topology-based discriminator features, including internal comparison among different concerned configurations, and external comparison to the other strategies. Through careful minutiae-based feature extraction, hashing-based indexing-retrieval mechanism, variable-threshold-on-score-ratio-based candidate-list reduction technique, and hill-climbing learning process, this strategy was considered promising, as confirmed by the experiment results. For particular aspect of external accuracy comparison, this strategy outperformed the others over three public data sets, i.e. up to Penetration Rate (PR) 5%, it consistently gave lower Error Rate (ER). By taking sample at PR 5%, this strategy produced ER 4%, 10%, and 1% on FVC2000 DB2A, FVC2000 DB3A, and FVC2002 DB1A, respectively. Another perspective if accuracy performance was based on area under curve of graph ER and PR, this strategy neither is the best nor the worst strategy on FVC2000 DB2A and FVC2000 DB3A, while on FVC2002 DB1A it outperfomed the others and even it gave impressive results for index created by three impressions per finger (with or without NT) by ideal step down curve where PR equal to 1% can always be maintained for smaller ER.DOI:http://dx.doi.org/10.11591/ijece.v4i5.658

Improvement of fingerprint retrieval by a statistical classifier

The topics of fingerprint classification, indexing, and retrieval have been studied extensively in the past decades. One problem faced by researchers is that in all publicly available fingerprint databases, only a few fingerprint samples from each individual are available for training and testing, making it inappropriate to use sophisticated statistical methods for recognition. Hence most of the previous works resorted to simple $k$-nearest neighbor ($k$-NN) classification. However, the $k$-NN classifier has the drawbacks of being comparatively slow and less accurate. In this paper, we tackle this problem by first artificially expanding the set of training samples using our previously proposed spatial modeling technique. With the expanded training set, we are then able to employ a more sophisticated classifier such as the Bayes classifier for recognition. We apply the proposed method to the problem of one-to-$N$ fingerprint identification and retrieval. The accuracy and speed are evaluated using the benchmarking FVC 2000, FVC 2002, and NIST-4 databases, and satisfactory retrieval performance is achieved. © 2010 IEEE.published_or_final_versio

Multi-Modal Biometrics: Applications, Strategies and Operations

The need for adequate attention to security of lives and properties cannot be over-emphasised. Existing approaches to security management by various agencies and sectors have focused on the use of possession (card, token) and knowledge (password, username)-based strategies which are susceptible to forgetfulness, damage, loss, theft, forgery and other activities of fraudsters. The surest and most appropriate strategy for handling these challenges is the use of naturally endowed biometrics, which are the human physiological and behavioural characteristics. This paper presents an overview of the use of biometrics for human verification and identification. The applications, methodologies, operations, integration, fusion and strategies for multi-modal biometric systems that give more secured and reliable human identity management is also presented

The Proceedings of 15th Australian Information Security Management Conference, 5-6 December, 2017, Edith Cowan University, Perth, Australia

Conference Foreword The annual Security Congress, run by the Security Research Institute at Edith Cowan University, includes the Australian Information Security and Management Conference. Now in its fifteenth year, the conference remains popular for its diverse content and mixture of technical research and discussion papers. The area of information security and management continues to be varied, as is reflected by the wide variety of subject matter covered by the papers this year. The papers cover topics from vulnerabilities in “Internet of Things” protocols through to improvements in biometric identification algorithms and surveillance camera weaknesses. The conference has drawn interest and papers from within Australia and internationally. All submitted papers were subject to a double blind peer review process. Twenty two papers were submitted from Australia and overseas, of which eighteen were accepted for final presentation and publication. We wish to thank the reviewers for kindly volunteering their time and expertise in support of this event. We would also like to thank the conference committee who have organised yet another successful congress. Events such as this are impossible without the tireless efforts of such people in reviewing and editing the conference papers, and assisting with the planning, organisation and execution of the conference. To our sponsors, also a vote of thanks for both the financial and moral support provided to the conference. Finally, thank you to the administrative and technical staff, and students of the ECU Security Research Institute for their contributions to the running of the conference