Tosiyasu L. Kunii

Topology matching for fully automatic similarity estimation of 3D shapes

There is a growing need to be able to accurately and efficiently search visual data sets, and in particular, 3D shape data sets. This paper proposes a novel technique, called Topology Matching, in which similarity between polyhedral models is quickly, accurately, and automatically calculated by comparing Multiresolutional Reeb Graphs (MRGs). The MRG thus operates well as a search key for 3D shape data sets. In particular, the MRG represents the skeletal and topological structure of a 3D shape at various levels of resolution. The MRG is constructed using a continuous function on the 3D shape, which may preferably be a function of geodesic distance because this function is invariant to translation and rotation and is also robust against changes in connectivities caused by a mesh simplification or subdivision. The similarity calculation between 3D shapes is processed using a coarse-to-fine strategy while preserving the consistency of the graph structures, which results in establishing a correspondence between the parts of objects. The similarity calculation is fast and efficient because it is not necessary to determine the particular pose of a 3D shape, such as a rotation, in advance. Topology Matching is particularly useful for interactively searching for a 3D object because the results of the search fit human intuition well.

A Skeleton-based Approach for Detection of Perceptually Salient Features on Polygonal Surfaces

The paper presents a skeleton‐based approach for robust detection of perceptually salient shape features. Given ashape approximated by a polygonal surface, its skeleton is extracted using a three‐dimensional Voronoi diagramtechnique proposed recently by Amenta et al. [ 3 ]. Shape creases, ridges and ravines, are detected as curvescorresponding 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 methodsfor skeleton denoising and for selecting perceptually important ridges and ravines, and uses a topological analysisof the skeleton for detection of salient shape regions.

Bounded blending for function-based shape modeling

New analytical formulations of bounded blending operations can enhance function-based constructive shape modeling. In this article, we introduce bounded-blending operations that we define using R-functions and displacement functions with the localized area of influence. We define the shape and location of the blend by control points on the surfaces of two solids or by an additional bounding solid. We can apply our proposed blending using a bounding solid to a single selected edge or vertex. We also introduce new multiple blends and a partial edge blend. Our description supports set-theoretic operations on blends and blends on blends - that is, recursive blends. In this sense, our proposed operations could replace pure set-theoretic operations in the construction of a solid without rebuilding the entire construction tree data structure. Our proposed blending method can have application in interactive design.

Bounded blending operations

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 the 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 a vertex. We introduce new types of blends such as a multiple blend with the disconnected bounding solid and a partial edge blend. It is shown to have versatile applications in interactive design.

A New Method for Developing Business Applications: The Cellular Data System

Currently, in the development of business applications, difficulties occasionally arise between the customer side and the supplier side, causing delays and higher development costs. To deal with this, we propose a new development method for business applications to validate them by invariant preservation based on equivalence relations. We have realized it by designing an algebraic expression called formula expression and applying the algebra to the design of each space in the cellular model. The system is called a cellular data system (CDS). It can become a common tool for both sides to make agreements efficiently in the future. Moreover, because you can manage data which has any form by using CDS, it is appropriate when dealing with data not only in business application development but in the cyberworld where no data manager exists

Nijimi rendering algorithm for creating quality black ink paintings

We present an interactive painting system for generating high quality and artistic calligraphy characters and black ink paintings. The system is based on our original algorithm that is unique in physically simulating the dynamic diffusion of liquid ink into absorbent painting paper. The algorithm creates remarkably realistic strokes efficiently. For rendering 20 strokes in different size, it takes only 30 seconds on a personal computer, fast enough for interactive performance. By using this system, the users can create realistic strokes with delicate Nijimi-rendering, kasure-rendering effects, which are essential to black ink painting and modern calligraphy.

Cellular-functional modeling of heterogeneous objects

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 frameworks inherent multidimensionality allowing, in particular, to deal naturally with time dependence promises to model complex dynamic objects composed of different materials with constructive building of their geometry and attributes. 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 - a 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 function representation is used to describe object geometry and density of elements in the cellular model of the mesh. The examples have been implemented by using a specialized modeling language and software tools being developed by the authors.

The potentials of cyberworlds - an axiomatic approach

Considering the increasingly large impacts and potentials of cyberworlds as seen in e-financing that trades GDP equivalent in a day, we human beings living in the real world are at the stage of needing to firmly identify the nature of cyberworlds. It is clear that if we continue to deal with cyberworlds as we have been, they grow chaotic beyond human understanding and control, endangering the real world. In an effort to make cyberworlds an academic discipline to overcome the critical situation, we axiomatize cyberworlds and then theorize them as Euclid did in identifying shapes in the real world.

Cultural Heritage Preservation Using Constructive Shape Modeling

Issues of digital preservation of shapes and internal structures of historical cultural objects are discussed. An overview of existing approaches to digital preservation related to shape modeling is presented and corresponding problems are considered. We propose a new digital preservation paradigm based on both constructive modeling reflecting the logical structure of the objects and open standards and procedures. Constructive Solid Geometry (CSG) and Function Representation (FRep) are examined and practically applied as mathematical representations producing compressed yet precise data structures, thus providing inter‐operability between current and future computer platforms crucial to archiving. Examples of CSG reconstruction of historical temples and FRep modeling of traditional lacquer ware are given. We examine the application of fitting of a parameterized FRep model to a cloud of data points as a step towards automation of the modeling process. Virtual venues for public access to cultural heritage objects including real time interactive simulation of cultural heritage sites over the Web are discussed and illustrated.

Web-based shape modeling with HyperFun

In this article, we have developed an open system architecture and Web-based shape-modeling applications using HyperFun, a high-level programming language for specifying implicit surfaces and FRep objects. We based our system on empirical modeling principles to allow for implementation of realistic behavior of shape models situated in multiagent environments, providing open-ended exploration and experimentation with shared models. Shape modeling systems based on HyperFun modeling language treat Internet-based shape modeling as a resource and let users collaborate in shape development.