Reconstruction of 3D objects from 2D cross-sections with the 4-point subdivision scheme adapted to sets

Kels, Shay; Dyn, Nira

doi:10.1016/j.cag.2011.03.007

Cited by 20 publications

(11 citation statements)

References 15 publications

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“…18 However, such landmark points cannot be identified in infarct image slices, as the shape and topology of myocardial infarct regions are not uniform. Implicit methods, on the other hand, rely on functions, such as characteristic functions, 19 signed distance maps, [20][21][22] and radial basis functions, 23,24 to implicitly define the organ shape in 2D slices, which are then interpolated on a voxelwise or global basis. While effective implicit methods have been reported for the reconstruction of certain organs, e.g., the cardiac ventricles, 25,26 there is a lack of such a methodology that is specifically developed and tested for infarct reconstruction.…”

Section: Introductionmentioning

confidence: 99%

Image‐based reconstruction of three‐dimensional myocardial infarct geometry for patient‐specific modeling of cardiac electrophysiology

et al. 2015

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Section: Introductionmentioning

confidence: 99%

Image‐based reconstruction of three‐dimensional myocardial infarct geometry for patient‐specific modeling of cardiac electrophysiology

et al. 2015

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“…We used 300 points to represent each curve. Then, we used the method proposed by Kels et al [47] to reconstruct a 3D surface from a set of 2D MR contours. For all experiments, the maximum number of iterations was set to be 50 and was empirically chosen, and was altered between 0.6 and 0.01, with 0.012 as a step size.…”

Section: Methodsmentioning

confidence: 99%

“…To generate semisynthetic data, the boundary of soft tissue organs such as the bladder, uterus, ovary, and rectum are segmented from five MR slices. Then, we use [47] to reconstruct 3D surfaces from the 2D segmented contours. The reconstructed 3D surfaces are deformed using an advection method [50].…”

Section: Generating Semi-synthetic Datamentioning

confidence: 99%

Mapping and characterizing endometrial implants by registering 2D transvaginal ultrasound to 3D pelvic magnetic resonance images

Yavariabdi¹,

Bartoli²,

Samir³

et al. 2015

Computerized Medical Imaging and Graphics

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We propose a new deformable slice-to-volume registration method to register a 2D Transvaginal Ultrasound (TVUS) to a 3D Magnetic Resonance (MR) volume. Our main goal is to find a cross-section of the MR volume such that the endometrial implants and their depth of infiltration can be mapped from TVUS to MR. The proposed TVUS-MR registration method uses contour to surface correspondences through a novel variational one-step deformable Iterative Closest Point (ICP) method. Specifically, we find a smooth deformation field while establishing point correspondences automatically. We demonstrate the accuracy of the proposed method by quantitative and qualitative tests on both semi-synthetic and clinical data. To generate semi-synthetic data sets, 3D surfaces are deformed with 4-40% degrees of deformation and then various intersection curves are obtained at 0-20° cutting angles. Results show an average mean square error of 5.7934±0.4615mm, average Hausdorff distance of 2.493±0.14mm, and average Dice similarity coefficient of 0.9750±0.0030.

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“…The basement surface was assumed constant. We constructed the data of surfaces in time interval [0,5] by constructing the data of each surface (A, B, C) in each time interval, [0, 1], [1,2], [3,4] and [4,5]. For the purpose of brevity, we only describe the procedure to construct data of surface B in time interval [1,2].…”

Section: Software and Experimentsmentioning

confidence: 99%

“…Some studies exist regarding morphological interpolation based on mathematical morphology [2][3][4][5]. These methods were restricted to images (binary/grayscale and color) and were used to generate intermediate 2D sections and to reconstruct 3D objects from their initial 2D sections.…”

Section: Introductionmentioning

confidence: 99%

Spatio-Temporal Data Construction

2013

IJGI

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Abstract:On the route to a spatio-temporal geoscience information system, an appropriate data model for geo-objects in space and time has been developed. In this model, geo-objects are represented as sequences of geometries and properties with continuous evolution in each time interval. Because geomodeling software systems usually model objects at specific time instances, we want to interpolate the geometry and properties from two models of an object with only geometrical constraints (no physical or mechanical constraints). This process is called spatio-temporal data construction or morphological interpolation of intermediate geometries. This paper is strictly related to shape morphing, shape deformation, cross-parameterization and compatible remeshing and is only concerned with geological surfaces. In this study, two main sub-solutions construct compatible meshes and find trajectories in which vertices of the mesh evolve. This research aims to find an algorithm to construct spatio-temporal data with some constraints from the geosciences, such as cutting surfaces by faulting or fracturing phenomena and evolving boundaries attached to other surfaces. Another goal of this research is the implementation of the algorithm in a software product, namely a gOcad plug-in. The four main procedures of the algorithm are cutting the surfaces, setting up constraints, partitioning and calculating the parameterizations and trajectories. The software has been tested to construct data for a salt dome and other surfaces in regard to the geological processes of faulting, deposition and erosion. The result of this research is an algorithm and software for the construction of spatio-temporal data.

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Reconstruction of 3D objects from 2D cross-sections with the 4-point subdivision scheme adapted to sets

Cited by 20 publications

References 15 publications

Image‐based reconstruction of three‐dimensional myocardial infarct geometry for patient‐specific modeling of cardiac electrophysiology

Image‐based reconstruction of three‐dimensional myocardial infarct geometry for patient‐specific modeling of cardiac electrophysiology

Mapping and characterizing endometrial implants by registering 2D transvaginal ultrasound to 3D pelvic magnetic resonance images

Spatio-Temporal Data Construction

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