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Deformable BSolids and Implicit Snakes for 3D Localization and Tracking of SPAMM MRIData
"... To date, MRISPAMM data from different image slices have been analyzed independently. In this paper, we propose an approach for 3D tag localization and tracking of SPAMM data by a novel deformable Bsolid. The solid is defined in terms of a 3D tensor product Bspline. The isoparametric curves of th ..."
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Cited by 36 (9 self)
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To date, MRISPAMM data from different image slices have been analyzed independently. In this paper, we propose an approach for 3D tag localization and tracking of SPAMM data by a novel deformable Bsolid. The solid is defined in terms of a 3D tensor product Bspline. The isoparametric curves of the Bspline solid have special importance. These are termed implicit snakes as they deform under image forces from tag lines in different image slices. The localization and tracking of tag lines is performed under constraints of continuity and smoothness of the Bsolid. To track motion from boundaries and restrict image forces to the myocardium, a volumetric model is employed as a pair of coupled endocardial and epicardial Bspline surfaces. To recover deformations of the Left Ventricle (LV) an energyminimization problem is posed where both tag and LV boundary data are used. The framework has been implemented on tag data from Short Axis (SA) cardiac images, as well as SA LV boundaries, and i...
Heterogeneous Material Modeling with Distance Fields
 Computer Aided Geometric Design
, 2004
"... We propose a universal approach to the problem of computer modeling of shapes with continuously varying material properties satisfying prescribed material conditions on a finite collection of material features and global constraints. The central notion is a parameterization of space by distances f ..."
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Cited by 31 (1 self)
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We propose a universal approach to the problem of computer modeling of shapes with continuously varying material properties satisfying prescribed material conditions on a finite collection of material features and global constraints. The central notion is a parameterization of space by distances from the material features  either exactly or approximately. Functions of such distances provide a systematic and intuitive means for modeling of desired material distributions as they arise in design, manufacturing, analysis and optimization of components with varying material properties.
Representation of Heterogeneous Material Properties in the Core Product Model
"... The Core Product Model (CPM) was developed at NIST as a high level abstraction for representing product related information, to support data exchange, in a distributive and a collaborative environment. In this paper, we extend the CPM to components with continuously varying material properties. Such ..."
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The Core Product Model (CPM) was developed at NIST as a high level abstraction for representing product related information, to support data exchange, in a distributive and a collaborative environment. In this paper, we extend the CPM to components with continuously varying material properties. Such components are becoming increasing important and popular due to progress in design, analysis and manufacturing techniques. The key enabling concept for modeling continuously varying material properties is that of distance fields associated with a set of material features, where values and rates of material properties are specified. Material fields, representing distribution of material properties within a component, are usually expressed as functions of distances to material features, and are controlled with a variety of differential, integral or algebraic constraints. Our formulation is independent of any particular platform or representation, and applies to most proposed techniques for representing continuously varying material properties. The proposed model is described using system independent Unified Modeling Language (UML) and is illustrated through a number of specific examples.
Algebraic Representation of CSG Solids Built from FreeForm Primitives
"... A mathematical model for freeform solid modelling was presented in previous published works. The key aspects of this model are the decomposition of the volume occupied by the solid into nondisjoint cells, and the representation of the solid as an algebraic sum of these cells. Here we apply this sc ..."
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A mathematical model for freeform solid modelling was presented in previous published works. The key aspects of this model are the decomposition of the volume occupied by the solid into nondisjoint cells, and the representation of the solid as an algebraic sum of these cells. Here we apply this scheme to represent CSG solids built by combining freeform solids in boolean operations. As a proof of the validity of this scheme, we present an algorithm that allows us to visualize the nonevaluated result of the operations. We have worked with freeform solids whose surfaces are bounded by a set of low degree triangular parametric patches.
Contour Detection and Color Influence in Defocused Environtments
"... this article, we propose a new technique to measure the displacement of contours in color images. Applying the facet model to detect edge points has the advantage to detect thin and almost connected edges with subpixel localization accuracy. Optimizing the snakes on the edge map allows to approximat ..."
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this article, we propose a new technique to measure the displacement of contours in color images. Applying the facet model to detect edge points has the advantage to detect thin and almost connected edges with subpixel localization accuracy. Optimizing the snakes on the edge map allows to approximate the contours disregarding edge points due to noise and filling the gaps among the edges. When using snakes to detect contours we are able to appreciate different behaviour of color contours as a function of the defocusing rate. At the same time, the snake technique provides a technique to measure the displacement between two contours since the potential energy of a snake placed on a potential field gives an average distance to the valleys of the potential that we determine to coincide with the other snake. The advantage consists in the fact that discontinuity does not affect the measurement precision since distance is measured between two continous curves. Also, the discretization of both contours does not influence the measurements; the mean distance is an integral of the distance of the first curve to the nearest point from the second curve.