Local injectivity conditions of 2D and 3D uniform cubic B-spline functions
Uniform cubic B-spline functions have been used for mapping functions in various areas such as image warping and morphing, 3D deformation, and volume morphing. The injectivity (one-to-one property) of a mapping function is important to obtain good results in these areas. We consider the local injectivity conditions of 2D and 3D uniform cubic B-spline functions. We propose a geometric interpretation of the local injectivity of a uniform cubic B-spline function, with which 2D and 3D cases can be handled in a similar way. Based on the geometric interpretation, we present sufficient conditions for the local injectivity that are represented in terms of control point displacements. These sufficient conditions are simple and easy to check and will be useful to guarantee the injectivity of mapping functions in application areas.

title: Motif analysis of noisy regular textures
abstract: A regular texture contains a periodic arrangement of a determinable pattern. Motifs of a regular texture are the minimal parallelogrammic sub-regions that can reproduce the texture by tiling. A motif extracted from a regular texture can be used for texture reproduction, texture recognition, and texture compression. However, it is not simple to accurately capture a motif of a regular texture, as the motif may be non-rectangular or arranged in an arbitrary direction. Moreover, when the texture contains additive noises, such as are created by the scanning process, motif analysis becomes more difficult. In this paper, we present an algorithm to obtain a motif of a noisy regular texture in O( mn log mn ) time, where m × n is the size of the texture. The analysis examples demonstrate that the proposed algorithm can robustly derive motifs of noisy regular textures.

title: Out-of-Core Remeshing of Large Polygonal Meshes
abstract: We propose an out-of-core method for creating semi-regular surface representations from large input surface meshes. Our approach is based on a streaming implementation of the MAPS remesher of Lee et al. Our remeshing procedure consists of two stages. First, a simplification process is used to obtain the base domain. During simplification, we maintain the mapping information between the input and the simplified meshes. The second stage of remeshing uses the mapping information to produce samples of the output semi-regular mesh. The out-of-core operation of our method is enabled by the synchronous streaming of a simplified mesh and the mapping information stored at the original vertices. The synchronicity of two streaming buffers is maintained using a specially designed write strategy for each buffer. Experimental results demonstrate the remeshing performance of the proposed method, as well as other applications that use the created mapping between the simplified and the original surface representations

title: Scattered Data Interpolation with Multilevel B-Splines
abstract: The paper describes a fast algorithm for scattered data interpolation and approximation. Multilevel B-splines are introduced to compute a C/sup 2/ continuous surface through a set of irregularly spaced points. The algorithm makes use of a coarse to fine hierarchy of control lattices to generate a sequence of bicubic B-spline functions whose sum approaches the desired interpolation function. Large performance gains are realized by using B-spline refinement to reduce the sum of these functions into one equivalent B-spline function. Experimental results demonstrate that high fidelity reconstruction is possible from a selected set of sparse and irregular samples.

title: Mesh parameterization with a virtual boundary
abstract: Parameterization of a 3D triangular mesh is a fundamental problem in various applications of meshes. The convex combination approach is widely used for parameterization because of its good properties, such as fast computation and one-to-one embedding. However, the approach has a drawback: most boundary triangles have high distortion in the embedding compared with interior ones. In this paper, we present an extension of the convex combination approach that resolves the drawback by using a virtual boundary. Since the virtual boundary is fixed onto a given convex polygon instead of the real boundary, the real boundary triangles can better reflect the shape of the corresponding 3D triangles. The proposedapproach obtains a parameterization of a 3D mesh with less d istortion than with the original convex combination approach.

title: Light field morphing using 2D features
abstract: We present a 2D feature-based technique for morphing 3D objects represented by light fields. Existing light field morphing methods require the user to specify corresponding 3D feature elements to guide morph computation. Since slight errors in 3D specification can lead to significant morphing artifacts, we propose a scheme based on 2D feature elements that is less sensitive to imprecise marking of features. First, 2D features are specified by the user in a number of key views in the source and target light fields. Then the two light fields are warped view by view as guided by the corresponding 2D features. Finally, the two warped light fields are blended together to yield the desired light field morph. Two key issues in light field morphing are feature specification and warping of light field rays. For feature specification, we introduce a user interface for delineating 2D features in key views of a light field, which are automatically interpolated to other views. For ray warping, we describe a 2D technique that accounts for visibility changes and present a comparison to the ideal morphing of light fields. Light field morphing based on 2D features makes it simple to incorporate previous image morphing techniques such as nonuniform blending, as well as to morph between an image and a light field.

title: Universality of mobility-gate field characteristics of electrons in the inversion charge layer and its application in MOSFET modeling
abstract: A mobility curve for electrons in a MOSFET inversion charge layer is determined from measured drain current of transistors produced by a wide range of MOS technologies. A comparison between this mobility curve and previously published results shows that a truly universal mobility curve does not exist and only local universal mobility curves can be expected, i.e. unique mobility curves which are valid over a finite range of MOS technologies and/or over a particular set of fabrication facilities. The curve's basic characteristic of being technology-independent over a wide range of process variation points out the potential of using such a local universal mobility curve as a powerful basis for developing predictive device modeling tools. This potential is demonstrated for an analytical MOSFET model and a two-dimensional device simulator where the mobility models have the general characteristics of experiment-based local universal mobility curves.

title: Scalability study of the ad hoc on-demand distance vector routing protocol
abstract: As mobile networking continues to experience increasing popularity, the need to connect large numbers of wireless devices will become more prevalent. Many recent proposals for ad hoc routing have certain characteristics that may limit their scalability to large networks. This paper examines five different combinations of modifications that may be incorporated into virtually any on-demand protocol in order to improve its scalability. The scalability of current on-demand routing protocols is evaluated through the selection of a representative from this class of protocols. The performance of the un-modified on-demand protocol is compared against that of it combined with each of the scalability modifications. Each scheme's behavior is analyzed in networks as large as 10,000 nodes through detailed simulation. Based on the observations, conclusions are drawn as to the expected scalability improvement that can be achieved by each modification.

title: Closed smooth piecewise bicubic surfaces
abstract: Two classes of closed piecewiee bicubic surfaces are considered. These surfaces are geometrically smooth about each extraordinary point and, for a large mesh and a large control polyhedron, they are parametrically smooth away from the extraordinary points. Furthermore, free parameters are available for manipulating the shape of the surface without changing the control polyhedron. The control is local for a large control polyhedron.

title: Scale-Space Derived From B-Splines
abstract: This paper proposes a scale-space theory based on B-spline kernels. Our aim is twofold: 1) present a general framework, and show how B-splines provide a flexible tool to design various scale-space representations. In particular, we focus on the design of continuous scale-space and dyadic scale-space frame representations. A general algorithm is presented for fast implementation of continuous scale-space at rational scales. In the dyadic case, efficient frame algorithms are derived using B-spline techniques to analyze the geometry of an image. The relationship between several scale-space approaches is explored. The behavior of edge models, the properties of completeness, causality, and other properties in such a scale-space representation are examined in the framework of B-splines. It is shown that, besides the good properties inherited from the Gaussian kernel, the B-spline derived scale-space exhibits many advantages for modeling visual mechanism including the efficiency, compactness, orientation feature and parallel structure.

title: Video Data Indexing by 2D C-Trees
abstract: Video data contains a large amount of spatial and temporal information. The changes of video frames are quite useful for motion analysis and cannot be provided by other media easily. Chang et al. had proposed an effective 2D string approach for spatial indexing of image data. In this paper, we extend this iconic approach and apply it to video data indexing. We propose 2D C-trees to represent the spatial content within individual frames. A video sequence can then be represented and indexed by a temporal set or an ordering set of 2D C-trees. The similarity retrieval of video matching problem becomes the problem of video sequence matching by computing the similarity, or the minimum cost of matched frames. We present three schemes, full-sequence matching, segment matching and subsequence matching, for video information retrieval. The matching schemes can be modified and extended to approximate sequence matching by computing the partial distance for providing a comprehensive retrieval of video data. A prototype video information system is also developed to validate the effectiveness of video data indexing by 2D C-trees.