Harmonic volumetric mapping aims to establish a smooth bijective correspondence between two solid shapes with the same topology. In this paper, we develop an automatic meshless method for creating such a mapping between two given objects. With the shell surface mapping as the boundary condition, we first solve a linear system constructed by a boundary method called themethodoffundamentalsolution, and then represent the mapping using a set of points with different weights in the vicinity of the shell of the given model. Our algorithm is a true meshless method (without the need of any specific meshing structure within the solid interior) and the behavior of the interior region is directly determined by the boundary, which can improve the computational efficiency and robustness significantly. Therefore, our algorithm can be applied to massive volume data sets with various geometric primitives and topological types. We demonstrate the utility and efficacy of our algorithm in information transfer, shape registration, deformation sequence analysis, tetrahedral remeshing, and solid texture synthesis.

Polycube T-spline has been formulated elegantly that can unify T-splines and manifold splines to define a new class of shape representations for surfaces of arbitrary topology by using polycube map as its parametric domain. In essense, The data fitting quality using polycube T-splines hinges upon the construction of underlying polycube maps. Yet, existing methods for polycube map construction exhibit some disadvantages. For example, existing approaches for polycube map construction either require projection of points from a 3D surface to its polycube approximation, which is therefore very difficult to handle the cases when two shapes differ significantly; or compute the map by conformally deforming the surfaces and polycubes to the common canonical domain and then construct the map using function composition, which is challenging to control the location of singularities and makes it hard for the data-fitting and hole-filling processes later on.

Harmonic volumetric mapping for two solid objects establishes a one-to-one smooth correspondence between them. It finds its applications in shape registration and analysis, shape retrieval, information reuse, and material/texture transplant. In sharp contrast to harmonic surface mapping techniques, little research has been conducted for designing volumetric mapping algorithms due to its technical challenges. In this paper, we develop an automatic and effective algorithm for computing harmonic volumetric mapping between two models of the same topology. Given a boundary mapping between two models, the volumetric (interior) mapping is derived by solving a linear system constructed from a boundary method called the fundamental solution method. The mapping is represented as a set of points with different weights in the vicinity of the solid boundary. In a nutshell, our algorithm is a true meshless method (with no need of specific connectivity) and the behavior of the interior region is directly determined by the boundary. These two properties help improve the computational efficiency and robustness. Therefore, our algorithm can be applied to massive volume data sets with various geometric primitives and topological types. We demonstrate the utility and efficacy of our algorithm in shape registration, information reuse, deformation sequence analysis, tetrahedral remeshing and solid texture synthesis.

This paper proposes a new concept of polycube splines and develops novel modeling techniques for using the polycube splines in solid modeling and shape computing. Polycube splines are essentially a novel variant of manifold splines which are built upon the polycube map, serving as its parametric domain. Our rationale for defining spline surfaces over polycubes is that polycubes have rectangular structures everywhere over their domains except a very small number of corner points. The boundary of polycubes can be naturally decomposed into a set of regular structures, which facilitate tensor-product surface definition, GPU-centric geometric computing, and image-based geometric processing. We develop algorithms to construct polycube maps, and show that the introduced polycube map naturally induces the affine structure with a finite number of extraordinary points. Besides its intrinsic rectangular structure, the polycube map may approximate any original scanned data-set with a very low geometric distortion, so our method for building polycube splines is both natural and necessary, as its parametric domain can mimic the geometry of modeled objects in a topologically correct and geometrically meaningful manner. We design a new data structure that facilitates the intuitive and rapid construction of polycube splines in this paper. We demonstrate the polycube splines with applications in surface reconstruction and shape computing.

Relevance feedback is a powerful technique to bridge the gap between high-level concepts and low-level features, and has been successfully applied to the field of Content-Based Image Retrieval (CBIR) to improve the query accuracy in recent years. In this paper, we propose a novel model (iSearch) which predicts user's information need based on past retrieval history. Based on the prediction, we then transform the feature space based on the user's feedback and employ an Expectation Maximization (EM) approach to simulate the new space by a mixture of Gaussian distributions. The experimental results show that the proposed method is effective and captures the user's information need more precisely.

Accurate measurement and identification of blood vessels could provide useful information to clinical diagnosis. A piecewise Gaussian model is proposed to describe the intensity distribution of vessel profile in this paper. The characteristic of central reflex is specially considered in the proposed model. The comparison with the single Gaussian model is performed, which shows that the piecewise Gaussian model is a more appropriate model for vessel profile. The obtained model parameters could be utilized in the identification of vessel type. The minimum Mahalanobis distance classifier is employed in the classification. 505 segments of vessels were tested. The success rate is 82.46% and 89.03% for the arteries and veins respectively.