Publications(January 2002 - December 2002)

1. Masayuki Hisada, Alexander G. Belyaev, and Tosiyasu L. Kunii, "Towards A Singularity-Based Shape Language: Ridges, Ravines, and Skeletons for Polygonal Surfaces", Soft Computing, Vol. 7, No. 1, 2002, pp. 45-52, Springer-Verlag, Heidelberg, Germany.
   Abstract - High demands on digital contents have posing strong needs on visual languages on three-dimensional (3D) shapes for improved human communication. For a visual language to effectively communicate essential 3D shape information, shape features defined in terms of singularity signs have been recognized as key shape descriptors. In this paper, we study salient shape features defined via distance function singularities: ridges, ravines, and a skeleton. We propose a method for robust extraction of the 3D skeleton of a polygonal surface and detection of salient surface features, ridges and ravines, corresponding to the skeletal edges. The method adapts the three-dimensional Voronoi diagram technique for skeleton extraction, explores singularity theory for ridge and ravine detection, and combines several filtering methods for skeleton denoising and for selecting perceptually salient ridges and ravines. We demonstrate that the ridges and ravines convey important shape information and, in particular, can be used for face recognition purposes.
   Key words and phrases: Polygonal surface, 3D Voronoi diagram, Skeleton, Ridges and ravines.
2. Yoshihisa Shinagawa, Ryoji Kawamichi, Tosiyasu L. Kunii and Shegeru Ohwada, "Developing Surfaces", Proceedings of the International Conference on Shape Modeling and Applications, May 17-22, 2002, Banff, Canada}, pp.253-260, IEEE Computer Society Press, Los Alamitos, California, May 2002.
   Abstract - To transform a three-dimensional object or to map texture to its surface, it is necessary to introduce a coordinate system. If the surface can be cut and developed, it is easy to identify each point on the surface with the coordinate values. According to a theory in topology, any closed polygonalized two-dimensional surface can be represented by a canonical development. However, no efficient algorithm to actually develop a given surface has been presented, and theory sounds abstract. This paper proposes a method to develop an arbitrary polygonal closed surface and to establish the correspondence between each point on the surface and a point on a regular polygon. Educational software is developed using the algorithm that visualizes the coordinate system by texture mapping or by allowing a user to paint on the surface.
   Key words and phrases: development, algebraic topology, groups, homology, texture mapping, transformation.
3. Galina Pasko, Alexander Pasko, Makoto Ikeda and Tosiyasu L. Kunii, "Bound Blending Operations", Proceedings of the International Conference on Shape Modeling and Applications, May 17-22, 2002, Banff, Canada, pp.95-103, IEEE Computer Society Press, Los Alamitos, California, May 2002.
   Abstract - New analytical formulations of bounded blending for functionally defined set-theoretic operations are proposed. The blending set operations are defined using R-functions and displacement functions with localized area of influence. The shape and location of the blend is defined by control points on the surfaces of two solids or by an additional bounding solid. The proposed blending using a bounding solid can be applied to a single selected edge or vertex. We introduce new types of blends such as a multiple blend with the disconnected bounding solid and a partial edge blend.
4. Noriko Kitani and Tosiyasu L. Kunii, "Web-based Design Databases", Proceedings of NICOGRAPH International 2002, May 30, 2002, Tokyo, Japan, pp.103-114, The Society for Art and Science, May 2002.
   Abstract - A new flexible and well-defined method was developed to turn objects in the real world, designed to satisfy users' taste, into reusable design resources on the Web by virtually decomposing the original design into parts. We show that we can repeat design processes efficiently by storing the information on part cell attachment as design information as well as by making the cell design processes of the parts homotopically equivalent. We then show the possibility of a new architecture of Web-based design databases management systems to support flexible design and redesign. To demonstrate the power of the new method, bag design is selected as an example
   Key words and phrases: Web-based design databases, cell model, cell attachment, cell decomposition, homotopy equivalence, redesign.
5. Valery Adzhiev, Elena Katasheva, Tosiyasu L. Kunii, Alexander Pasko and Benjamin Schmitt, "Cellular-Functional Modeling of Heterogeneous Objects", Proceedings of 7th ACM Symposium on Solid Modeling and Applications, June 17-21, 2002, pp. 192-203, ACM Press, 1515 Broadway, New York, NY, 10036, USA.
   Abstract - The paper presents an approach to modeling heterogeneous objects as multidimensional point sets with multiple attributes (hypervolumes). A theoretical framework is based on a hybrid model of hypervolumes combining a cellular representation and a constructive representation using real-valued functions. This model allows for independent but unifying representation of geometry and attributes, and makes it possible to represent dimensionally non-homogeneous entities and their cellular decompositions. Hypervolume model components such as objects, operations and relations are introduced and outlined. The framework's inherent multidimensionality allowing, in particular, to deal naturally with time dependence promises to model complex dynamic objects composed of different. Attributes given at each point can represent properties of arbitrary nature (material, photometric, physical, statistical, etc.). To demonstrate a particular application of the proposed framework, we present an example of multimaterial modeling - the multilayer geological structure with cavities and wells. Another example illustrating the treatment of attributes other than material distributions is concerned with time-dependent adaptive mesh generation where the function representation is used to describe object geometry and density of elements in the cellular model of the mesh. The examples have been implemented with using a specialized modeling language and software tools being developed by the authors.
   Key words and phrases: Multidimensional point sets, attributes, heterogeneous models, function representation, cellular representation, volume modeling.
6. Toshio Kodama and Tosiyasu L. Kunii, "Homotopic Database Animation", Proceedings of Computer Animation 2002 (June 19-21, 2002, Geneva, Switzerland) pp. 89-97, IEEE Computer Society Press, Los Alamitos, California, U. S. A.
   Abstract - Very large databases on the Web have been changing dynamically and have become complicated today. This research aims at helping users' understanding of database changes by database animation. As a case study, animating budget management of one company is researched. It shows clearly that database animation help understand the flow of plans and the distribution of the whole budget. Furthermore, it has shown that reverse animation by preserved homotopy realizes the effective reuse of databases.
   Key words and phrases: database animation, cellular databases, homotopic animation, homotopy, cellular model.
7. Tosiyasu L. Kunii, "Cyber Graphics", Proceedings of the First International Symposium on Cyber Worlds (CW2002), November 6-8 2002 Tokyo, Japan, pp. 3-7, IEEE Computer Society Press, Los Alamitos, California, November 2002.
   Abstract - Cyber graphics as an emerging technology has been playing key roles as human interfaces of cyber worlds. With the ever increasing roles of cyber worlds in the real world, as seen in e-financial trading that deals GDP-equivalent in a day, understanding of cyber graphics is becoming essential. To this end, scientific research has been conducted to grasp the foundation as invariants. Cellular modeling has been found to be of key importance. The adjunction spaces and cell attaching functions of cyber graphics are investigated through varieties of examples to find out the invariants successfully.
   Key words and phrases: adjunction spaces, cell attaching functions, a hierarchy of invariants, cellular spatial structures.
8. Pizzanu Kanonchoiyos, Tomoyuki Nishita, Yoshihisa Shinagawa, and Tosiyasu L. Kunii, "Topological Morphing Using Reeb Graphs", Proceedings of the First International Symposium on Cyber Worlds (CW2002), November 6-8 2002 Tokyo, Japan, pp. 465-471, IEEE Computer Society Press, Los Alamitos, California, November 2002.
   Abstract - Metamorphosis between 3D objects is often the transformation between a pair of shapes that have the same topology. This paper presents a new model using Reeb graphs and their contours to create morphing between 3D objects having different topology. The proposed method specifies the correspondence between of the input objects by using the graph isomorphic theory. Then the super Reeb graph, which has the equivalent topological information to the Reeb graphs of the two input objects, is constructed and used to conduct the sequence of the morphing. The evolutions of the topology that occur during the morph can be specified by the transformation of the Reeb graphs and their contours of the input objects. Reeb graph-based modeling allows the users precisely and intuitively control the morph because the topological information of the objects, represented by the structures of the Reeb graphs, is explicit and easy to understand. Moreover, the contours of the Reeb graphs also represent the geometrical information of the objects. The examples of morphing between different topological shapes are demonstrated.
   Key words and phrases: 3D morphing, topological evolutions, Reeb graphs.
9. Kazuteru Matsumoto and Tosiyasu L. Kunii, "A Cellular Design System for Soft- and Varied Sized- Objects", Proceedings of the First International Symposium on Cyber Worlds (CW2002), November 6-8 2002 Tokyo, Japan, pp. 386-393, IEEE Computer Society Press, Los Alamitos, California, November 2002.
   Abstract - After we sketch the design of a product on the Web, we can obtain each part of the product applying a cell decomposition to the sketched design based on the cellular model operations and then applying the homotopy theory to it. When we perform cell decomposition, we can specify the manufacturing procedures of a product as homotopy invariants based on the homotopy theory. Using the parts and the manufacturing procedures of a product, and cell attaching functions accumulated in the cellular design database while these procedures are applied, we show first that we can perform the real design of soft objects, the shapes of which are constantly changing. We then show that the cellular model also can uniformly specify varied sizes. Thus, the cellular model is far more powerful than existing geometric models. The design of bags is taken as an example of soft object and varied sized object design.
   Key words and phrases: 3D morphing, topological evolutions, Reeb graphs.
10. Masayuki Hisada, Alexander G. Belyaev, Tosiyasu L. Kunii, "A Skeleton-based Approach for Detection of Perceptually Salient Features on Polygonal Surfaces," Computer Graphics Forum, Vol. 21, No. 4, pp. 1-12, 2002.
    Abstract -The paper presents a skeleton-based approach for robust detection of perceptually salient shape features. Given a shape approximated by a polygonal surface, its skeleton is extracted using a three-dimensional Voronoi diagram technique proposed recently by Amenta et al. 3 . Shape creases, ridges and ravines, are detected as curves corresponding to skeletal edges. Salient shape regions are extracted via skeleton decomposition into patches. The approach explores the singularity theory for ridge and ravine detection, combines several filtering methods for skeleton denoising and for selecting perceptually important ridges and ravines, and uses a topological analysis of the skeleton for detection of salient shape regions.
11. Tosiyasu L. Kunii, "Web Information Modeling: The Adjunction Space Model", Proceedings of the 2nd International Workshop on Databases in Networked Information Systems (DNIS 2002), pp. 58-63, The University of Aizu, Japan, December 16-18, 2002, Lecture Notes in Computer Science, Subhash Bhalla, Ed., Springer-Verlag, December, 2002.
    Abstract -The nature of Web information is clarified and modeled as the adjunction space model. Practical Web information management requires Web information to be modeled in such a way that the model captures the dynamic changes, present the dynamism visually, and validate the results formally. As the mathematical ground of the model, we have adopted algebraic topology, cellular spatial structures in the homotopic framework and adjunction spaces in particular. The results have been applied successfully to typical Web information systems such e-finance and e-manufacturing to validate the advantages of our Web information modeling over the popular relational model, the entity relationship model, UML, and XML.

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