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Generalized Sampling: A Variational Approach. Part I: Theory
 IEEE Transactions on Signal Processing, 2001. In preparation
, 2002
"... We consider the problem of lconstructing a multidimensional vector function fln: "* from a finite set of linear measures. These can be irregularly sampled responses of several linear filters. Traditional approaches reconstruct in an a priori given space, e.g., the space of bandlimited functions ..."
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Cited by 13 (5 self)
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We consider the problem of lconstructing a multidimensional vector function fln: "* from a finite set of linear measures. These can be irregularly sampled responses of several linear filters. Traditional approaches reconstruct in an a priori given space, e.g., the space of bandlimited functions. Instead, we have chosen to specify a reconstruction that is optimal in the sense of a quadratic plausibility criterion J. First, we plsent the solution of the generalized interpolation problem. Latel; we also consider the approximation plblem, and we show that both lead to the same class of solutions.
Realtime 3D Deformations by Means of Compactly Supported Radial Basis Functions
 In Short papers proceedings of Eurographics
, 2002
"... We present an approach to realtime animation of deformable objects. Optimization of algorithms using compactly supported radial basis functions (CSRBF) allows us to generate deformations performed fast enough for such realtime applications as computer games. The algorithm described in detail in ..."
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Cited by 12 (5 self)
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We present an approach to realtime animation of deformable objects. Optimization of algorithms using compactly supported radial basis functions (CSRBF) allows us to generate deformations performed fast enough for such realtime applications as computer games. The algorithm described in detail in this paper uses space mapping technique. Smooth local deformations of animation objects can be defined by only a moderate number of control vectors and locality of deformations can be defined by radius of support. We also present examples of animations and speed benchmarks.
K.: Direct surface extraction from 3d freehand ultrasound images
 In Proceedings of the conference on Visualization 2002 (2002), IEEE
"... Surface extraction from ultrasound data is challenging for a number of reasons, including noise and artifacts in the images and nonuniform data sampling. This thesis presents a new technique for the extraction of surfaces from freehand 3D ultrasound data. Most available 3D medical visualization met ..."
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Cited by 12 (1 self)
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Surface extraction from ultrasound data is challenging for a number of reasons, including noise and artifacts in the images and nonuniform data sampling. This thesis presents a new technique for the extraction of surfaces from freehand 3D ultrasound data. Most available 3D medical visualization methods fall into two categories: volume rendering and surface rendering. Surface rendering is chosen here because one of the long term goals of this thesis is explicit modelling of organs. Recent progress has been made in surface extraction for a range data or an unorganized data set, by using Radial Basis Functions (RBFs) to represent the whole space with a signed distance function. Instead of using geometric distance as in previous work, this thesis proposes to use pixel intensity directly as a distance function. A new implementation of a freehand 3D ultrasound acquisition system is also introduced in this thesis using a trinocular optical tracking system with lightemitting diodes (LEDs) attached to an ultrasound probe. To calibrate the transformation between the ultrasound image coordinate system and the LED coordinate system, an Nwire calibration phantom was designed. High accuracy
An Approach to Blend Surfaces
 Advances in Modeling, Animation and Rendering
, 2002
"... In this paper, we present an application of a space mapping technique for surface reconstruction (more precisely: reconstruction of missing parts of a real geometric object represented by volume data). Using a space mapping technique, the surface of a given model, in particular tooth shape is fitted ..."
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Cited by 11 (1 self)
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In this paper, we present an application of a space mapping technique for surface reconstruction (more precisely: reconstruction of missing parts of a real geometric object represented by volume data). Using a space mapping technique, the surface of a given model, in particular tooth shape is fitted by a shape transformation to extrapolate the remaining surface of a patient's tooth with occurring damage such as a “drill hole. ” The genetic algorithm minimizes the error of the approximation by optimizing a set of control points that determine the coefficients for spline functions, which in turn define a space transformation. The fitness function to be minimized consists of two components. First one is the error between the blended surface of an object and the surface of the object to be blended in some predefined points. The second is a component that is responsible for the bending energy being minimized.
Motion fields to predict play evolution in dynamic sport scenes
 In CVPR
"... Videos of multiplayer team sports provide a challenging domain for dynamic scene analysis. Player actions and interactions are complex as they are driven by many factors, such as the shortterm goals of the individual player, the overall team strategy, the rules of the sport, and the current contex ..."
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Cited by 10 (4 self)
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Videos of multiplayer team sports provide a challenging domain for dynamic scene analysis. Player actions and interactions are complex as they are driven by many factors, such as the shortterm goals of the individual player, the overall team strategy, the rules of the sport, and the current context of the game. We show that constrained multiagent events can be analyzed and even predicted from video. Such analysis requires estimating the global movements of all players in the scene at any time, and is needed for modeling and predicting how the multiagent play evolves over time on the field. To this end, we propose a novel approach to detect the locations of where the play evolution will proceed, e.g. where interesting events will occur, by tracking player positions and movements over time. We start by extracting the ground level sparse movement of players in each timestep, and then generate a dense motion field. Using this field we detect locations where the motion converges, implying positions towards which the play is evolving. We evaluate our approach by analyzing videos of a variety of complex soccer plays. 1.
Software Tools Using CSRBFs for Processing Scattered Data
, 2003
"... A set of software tools that use compactly supported radial basis functions (CSRBFs) to process scattered data is proposed in this paper. To solve problems concerning the processing of scattered data in such applications as reconstruction of functionaly defined geometric objects, surface retouching, ..."
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Cited by 9 (2 self)
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A set of software tools that use compactly supported radial basis functions (CSRBFs) to process scattered data is proposed in this paper. To solve problems concerning the processing of scattered data in such applications as reconstruction of functionaly defined geometric objects, surface retouching, and shape modifications, we employ a specially designed C++ software library. Thanks to the efficient octree algorithm used in this study, the resulting matrix is a banddiagonal matrix that permits handling of large data sets in a reasonable time.
PetRBF—A parallel O(N) algorithm for radial basis function interpolation
, 909
"... We have developed a parallel algorithm for radial basis function (rbf) interpolation that exhibits O(N) complexity, requires O(N) storage, and scales excellently up to a thousand processes. The algorithm uses a gmres iterative solver with a restricted additive Schwarz method (rasm) as a precondition ..."
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Cited by 8 (2 self)
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We have developed a parallel algorithm for radial basis function (rbf) interpolation that exhibits O(N) complexity, requires O(N) storage, and scales excellently up to a thousand processes. The algorithm uses a gmres iterative solver with a restricted additive Schwarz method (rasm) as a preconditioner and a fast matrixvector algorithm. Previous fast rbf methods — achieving at most O(N log N) complexity—were developed using multiquadric and polyharmonic basis functions. In contrast, the present method uses Gaussians with a small variance (a common choice in particle methods for fluid simulation, our main target application). The fast decay of the Gaussian basis function allows rapid convergence of the iterative solver even when the subdomains in the rasm are very small. The present method was implemented in parallel using the petsc library (developer version). Numerical experiments demonstrate its capability in problems of rbf interpolation with more than 50 million data points, timing at 106 seconds (19 iterations for an error tolerance of 10 −15) on 1024 processors of a Blue Gene/L (700 MHz PowerPC processors). The parallel code is freely available in the opensource model. Key words: radial basis function interpolation, domain decomposition methods, gmres, orderN algorithms, particle methods, parallel computing
Minimally Invasive Holographic Surface Scanning for SoftTissue Image Registration
 IEEE Transactions on Biomedical Engineering
"... Abstract—Recent advances in registration have extended intrasurgical image guidance from its origins in bonebased procedures to new applications in soft tissues, thus enabling visualization of spatial relationships between surgical instruments and subsurface structures before incisions begin. Preo ..."
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Cited by 7 (2 self)
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Abstract—Recent advances in registration have extended intrasurgical image guidance from its origins in bonebased procedures to new applications in soft tissues, thus enabling visualization of spatial relationships between surgical instruments and subsurface structures before incisions begin. Preoperative images are generally registered to soft tissues through aligning segmented volumetric image data with an intraoperatively sensed cloud of organ surface points. However, there is currently no viable noncontact minimally invasive scanning technology that can collect these points through a single laparoscopic port, which limits wider adoption of softtissue image guidance. In this paper, we describe a system based on conoscopic holography that is capable of minimally invasive surface scanning. We present the results of several validation experiments scanning ex vivo biological and phantom tissues with a system consisting of a tracked, offtheshelf, relatively inexpensive conoscopic holography unit. These experiments indicate that conoscopic holography is suitable for use with biological tissues, and can provide surface scans of comparable quality to existing clinically used laser range scanning systems that require open surgery. We demonstrate experimentally that conoscopic holography can be used to guide a surgical needle to desired subsurface targets with an average tip error of less than 3 mm. Index Terms—Image guided surgery, laser scanning, minimally invasive surgery, surface registration. I.
SOBOLEVTYPE APPROXIMATION RATES FOR DIVERGENCEFREE AND CURLFREE RBF INTERPOLANTS
"... Abstract. Recently, error estimates have been made available for divergencefree radial basis function (RBF) interpolants. However, these results are only valid for functions within the associated reproducing kernel Hilbert space (RKHS) of the matrixvalued RBF. Functions within the associated RKHS, ..."
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Abstract. Recently, error estimates have been made available for divergencefree radial basis function (RBF) interpolants. However, these results are only valid for functions within the associated reproducing kernel Hilbert space (RKHS) of the matrixvalued RBF. Functions within the associated RKHS, also known as the “native space ” of the RBF, can be characterized as vector fields having a specific smoothness, making the native space quite small. In this paper we develop Sobolevtype error estimates when the target function is less smooth than functions in the native space. 1. Introduction and