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Deformable models in medical image analysis: A survey
 Medical Image Analysis
, 1996
"... This article surveys deformable models, a promising and vigorously researched computerassisted medical image analysis technique. Among modelbased techniques, deformable models offer a unique and powerful approach to image analysis that combines geometry, physics, and approximation theory. They hav ..."
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Cited by 590 (7 self)
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This article surveys deformable models, a promising and vigorously researched computerassisted medical image analysis technique. Among modelbased techniques, deformable models offer a unique and powerful approach to image analysis that combines geometry, physics, and approximation theory. They have proven to be effective in segmenting, matching, and tracking anatomic structures by exploiting (bottomup) constraints derived from the image data together with (topdown) a priori knowledge about the location, size, and shape of these structures. Deformable models are capable of accommodating the significant variability of biological structures over time and across different individuals. Furthermore, they support highly intuitive interaction mechanisms that, when necessary, allow medical scientists and practitioners to bring their expertise to bear on the modelbased image interpretation task. This article reviews the rapidly expanding body of work on the development and application of deformable models to problems of fundamental importance in medical image analysis, includingsegmentation, shape representation, matching, and motion tracking.
A survey of freeform object representation and recognition techniques
 Computer Vision and Image Understanding
, 2001
"... Advances in computer speed, memory capacity, and hardware graphics acceleration have made the interactive manipulation and visualization of complex, detailed (and therefore large) threedimensional models feasible. These models are either painstakingly designed through an elaborate CAD process or re ..."
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Cited by 200 (1 self)
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Advances in computer speed, memory capacity, and hardware graphics acceleration have made the interactive manipulation and visualization of complex, detailed (and therefore large) threedimensional models feasible. These models are either painstakingly designed through an elaborate CAD process or reverse engineered from sculpted prototypes using modern scanning technologies and integration methods. The availability of detailed data describing the shape of an object offers the computer vision practitioner new ways to recognize and localize freeform objects. This survey reviews recent literature on both the 3D model building process and techniques used to match and identify freeform objects from imagery. c ○ 2001 Academic Press 1.
Discrete Fairing and Variational Subdivision for Freeform Surface Design
 The Visual Computer
, 2000
"... The representation of freeform surfaces by sufficiently refined polygonal meshes has become common in many geometric modeling applications where complicated objects have to be handled. While working with triangle meshes is flexible and efficient, there are difficulties arising prominently from the l ..."
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Cited by 41 (2 self)
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The representation of freeform surfaces by sufficiently refined polygonal meshes has become common in many geometric modeling applications where complicated objects have to be handled. While working with triangle meshes is flexible and efficient, there are difficulties arising prominently from the lack of infinitesimal smoothness and the prohibitive complexity of highly detailed 3Dmodels. In this paper we discuss the generation of fair triangle meshes which are optimal with respect to some discretized curvature energy functional. The key issues are the proper definition of discrete curvature, the smoothing of high resolution meshes by filter operators, and the efficient generation of optimal meshes by solving a sparse linear system that characterizes the global minimum of an energy functional. Results and techniques from differential geometry, variational surface design (fairing), and numerical analysis are combined to find efficient and robust algorithms that generate smooth meshes of...
On Transfinite Barycentric Coordinates
, 2006
"... A general construction of transfinite barycentric coordinates is obtained as a simple and natural generalization of Floater's mean value coordinates [Flo03, JSW05b]. The GordonWixom interpolation scheme [GW74] and transfinite counterparts of discrete harmonic and WachspressWarren coordinate ..."
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Cited by 20 (0 self)
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A general construction of transfinite barycentric coordinates is obtained as a simple and natural generalization of Floater's mean value coordinates [Flo03, JSW05b]. The GordonWixom interpolation scheme [GW74] and transfinite counterparts of discrete harmonic and WachspressWarren coordinates are studied as particular cases of that general construction. Motivated by finite element/volume applications, we study capabilities of transfinite barycentric interpolation schemes to approximate harmonic and quasiharmonic functions. Finally we establish and analyze links between transfinite barycentric coordinates and certain inverse problems of di#erential and convex geometry.
Surface mesh segmentation and smooth surface extraction through region growing
 COMPUTER AIDED GEOMETRIC DESIGN
, 2005
"... Laser rangescanners are used in fields as diverse as product design, reverse engineering, and rapid prototyping to quickly acquire geometric surface data of parts and models. This data is often in the form of a dense, noisy surface mesh that must be simplified into piecewisesmooth surfaces. The me ..."
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Cited by 16 (2 self)
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Laser rangescanners are used in fields as diverse as product design, reverse engineering, and rapid prototyping to quickly acquire geometric surface data of parts and models. This data is often in the form of a dense, noisy surface mesh that must be simplified into piecewisesmooth surfaces. The method presented here facilitates this timeconsuming task by automatically segmenting a dense mesh into regions closely approximated by single surfaces. The algorithm first estimates the noise and curvature of each vertex. Then it filters the curvatures and partitions the mesh into regions with fundamentally different shape characteristics. These regions are then contracted to create seed regions for region growing. For each seed region, the algorithm iterates between region growing and surface fitting to maximize the number of connected vertices approximated by a single underlying surface. The algorithm finishes by filling segment holes caused by outlier noise. We demonstrate the algorithm effectiveness on real data sets.
Multivariate Bernstein polynomials and convexity
 Comp. Aided Geom. Design
"... It is well known that in two or more variables Bernstein polynomials do not preserve convexity. Here we introduce two variations, one stronger than the classical notion, the other one weaker, which are preserved. Moreover, a weaker sufficient condition for the monotony of subsequent Bernstein polyno ..."
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Cited by 14 (0 self)
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It is well known that in two or more variables Bernstein polynomials do not preserve convexity. Here we introduce two variations, one stronger than the classical notion, the other one weaker, which are preserved. Moreover, a weaker sufficient condition for the monotony of subsequent Bernstein polynomials is given. x1 Introduction Consider m+1 points p 0 ; : : : ; pm 2 R d in general position; i.e., the vectors p k \Gamma p 0 , k = 0; : : : ; m, are linearly independent, in the course of which d has to be greater than or equal to m. A point p in the affine hull of p 0 ; : : : ; pm can be uniquely written as p = m X k=0 u k p k ; where u 0 + \Delta \Delta \Delta + um = 1: The coefficients of u = (u 0 ; : : : ; um ) 2 R m+1 are called the barycentric coordinates of p with respect to p 0 ; : : : ; pm . Moreover, the points of the simplex [p 0 ; : : : ; pm ], spanned by the vertices p 0 ; : : : ; pm have nonnegative barycentric coordinates and vice versa. In other words, we can...
A subdivisionbased implementation of the hierarchical bspline finite element method
 Computer Methods in Applied Mechanics and Engineering
"... A novel technique is presented to facilitate the implementation of hierarchical bsplines and their interfacing with conventional finite element implementations. The discrete interpretation of the twoscale relation, as common in subdivision schemes, is used to establish algebraic relations between ..."
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Cited by 9 (1 self)
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A novel technique is presented to facilitate the implementation of hierarchical bsplines and their interfacing with conventional finite element implementations. The discrete interpretation of the twoscale relation, as common in subdivision schemes, is used to establish algebraic relations between the basis functions and their coefficients on different levels of the hierarchical bspline basis. The subdivision projection technique introduced allows us first to compute all element matrices and vectors using a fixed number of samelevel basis functions. Their subsequent multiplication with subdivision matrices projects them, during the assembly stage, to the correct levels of the hierarchical bspline basis. The proposed technique is applied to convergence studies of linear and geometrically nonlinear problems in one, two and three space dimensions.
Subdivision shells with exact boundary control and nonmanifold geometry
 International Journal for Numerical Methods in Engineering
"... We introduce several new extensions to subdivision shells that provide an improved level of shape control over shell boundaries and facilitate the analysis of shells with nonsmooth and nonmanifold joints. To this end, modified subdivision schemes are used that enable to relax the continuity of the ..."
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Cited by 8 (5 self)
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We introduce several new extensions to subdivision shells that provide an improved level of shape control over shell boundaries and facilitate the analysis of shells with nonsmooth and nonmanifold joints. To this end, modified subdivision schemes are used that enable to relax the continuity of the limit surface along prescribed crease edges and to create surfaces with prescribed limit positions and normals. Furthermore, shells with boundaries in form of conic sections, such as circles or parabolas, are represented with rational subdivision schemes which are defined in analogy to rational bsplines. In terms of implementation, the difference between the introduced and conventional subdivision schemes is restricted to the use of modified subdivision stencils close to the mentioned geometric features. Hence, the resulting subdivision surface is in most parts of the domain identical to standard smooth subdivision surfaces. The particular subdivision scheme used in this paper constitutes an improved version of the original Loop’s scheme and is as such based on triangular meshes. As in the original subdivision shells, surfaces created with the modified scheme are used for interpolating the reference and deformed shell configurations. At the integration points, the subdivision surface is evaluated using a newly developed discrete parameterisation approach. In the resulting finite elements the only degrees of freedom are the midsurface displacements of the nodes and additional Lagrange parameters for enforcing normal constraints. The versatility of the newly developed elements is demonstrated with a number of geometrically nonlinear shell examples.
Fair polyline networks for constrained smoothing of digital terrain elevation data
 IEEE TRANS. GEOSC. REMOTE SENSING
, 2006
"... We present a framework for smoothing gridlike digital terrain elevation data, which achieves fair shape by means of minimizing an energy functional. The minimization is performed under the sidecondition of hard constraints which come from available horizontal and vertical accuracy bounds in the e ..."
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Cited by 7 (3 self)
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We present a framework for smoothing gridlike digital terrain elevation data, which achieves fair shape by means of minimizing an energy functional. The minimization is performed under the sidecondition of hard constraints which come from available horizontal and vertical accuracy bounds in the elevation specification. We introduce the framework and demonstrate the suitability of this method for the tasks of accuracyconstrained smoothing, featurepreserving smoothing, and filling of data voids.
EducationDriven Research in CAD
 Computer Aided Design
, 2004
"... We argue for a new research category, named EducationDriven Research (abbreviated EDR), which fills the gap between traditional fieldspecific Research that is not concerned with educational objectives and Research in Education that focuses on fundamental teaching and learning principles and possib ..."
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Cited by 7 (6 self)
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We argue for a new research category, named EducationDriven Research (abbreviated EDR), which fills the gap between traditional fieldspecific Research that is not concerned with educational objectives and Research in Education that focuses on fundamental teaching and learning principles and possibly on their customization to broad areas (such as mathematics or physics), but not to specific disciplines (such as CAD). The objective of EDR is to simplify the formulation of the underlying theoretical foundations and of specific tools and solutions in a specialized domain, so as to make them easy to understand and internalize. As such, EDR is a difficult and genuine research activity, which requires a deep understanding of the specific field and can rarely be carried out by generalists with primary expertise in broad education principles. We illustrate the concept of EDR with three examples in CAD: (1) the Split&Tweak subdivisions of a polygon and its use for generating curves, surfaces, and animations; (2) the construction of a topological partition of a plane induced by an arbitrary arrangement of edges; and (3) a romantic definition of the minimal and Hausdorff distances. These examples demonstrate the value of using analogies, of introducing evocative terminology, and of synthesizing the simplest fundamental building blocks. The intuitive understanding provided by EDR enables the students (and even the instructor) to better appreciate the limitations of a particular solution and to explore alternatives. In particular, in these examples, EDR has allowed the author to: (1) reduce the cost of evaluating a cubic Bspline curve; (2) develop a new subdivision curve that is better approximated by its control polygon than either a cubic Bspline or an interpolating 4point sub...