From CT to NURBS: Contour Fitting with B-spline Curves

Grove, Olya; Rajab, Khairan; Piegl, Les A.; Lai-Yuen, Susana K.

doi:10.3722/cadaps.2011.3-21

Cited by 35 publications

(18 citation statements)

References 33 publications

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“…There exists some notable methods in the literature for the local fitting functions and the selection criterion. Grove et al [3] employed a Bezier curve to regress the local data and quantify the fitting error of the mean square error of the fitted curve to determine the knots. Rice [4, 5] used polynomial function to treat the local data and to quantify the fitting error by predetermined error tolerance based on a selectable norm and the method is intended for function approximation.…”

Section: State Of the Artmentioning

confidence: 99%

“…Unlike some existing methods in the literature that result in the knots without optimizing their locations [3], the knots are optimized to identify the locations and continuity levels. Multiple knots are simultaneously identified by using the optimization process.…”

Section: Local Algorithm For Free Knots Placement Based On Bisectimentioning

confidence: 99%

“…The bisecting method is also used as a tool for identifying a knot vector in [3–6, 10]. The proposed bisecting method in this paper has similar principle to that of the method in [3], except that in this process we use a single piece B-spline to fit the data.…”

Section: Local Algorithm For Free Knots Placement Based On Bisectimentioning

confidence: 99%

“…The proposed bisecting method in this paper has similar principle to that of the method in [3], except that in this process we use a single piece B-spline to fit the data. Fig 3 illustrates the working principle of the bisecting method in splitting the data for knot placement.…”

Section: Local Algorithm For Free Knots Placement Based On Bisectimentioning

confidence: 99%

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A direct method to solve optimal knots of B-spline curves: An application for non-uniform B-spline curves fitting

Dung

Tjahjowidodo

2017

PLoS ONE

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B-spline functions are widely used in many industrial applications such as computer graphic representations, computer aided design, computer aided manufacturing, computer numerical control, etc. Recently, there exist some demands, e.g. in reverse engineering (RE) area, to employ B-spline curves for non-trivial cases that include curves with discontinuous points, cusps or turning points from the sampled data. The most challenging task in these cases is in the identification of the number of knots and their respective locations in non-uniform space in the most efficient computational cost. This paper presents a new strategy for fitting any forms of curve by B-spline functions via local algorithm. A new two-step method for fast knot calculation is proposed. In the first step, the data is split using a bisecting method with predetermined allowable error to obtain coarse knots. Secondly, the knots are optimized, for both locations and continuity levels, by employing a non-linear least squares technique. The B-spline function is, therefore, obtained by solving the ordinary least squares problem. The performance of the proposed method is validated by using various numerical experimental data, with and without simulated noise, which were generated by a B-spline function and deterministic parametric functions. This paper also discusses the benchmarking of the proposed method to the existing methods in literature. The proposed method is shown to be able to reconstruct B-spline functions from sampled data within acceptable tolerance. It is also shown that, the proposed method can be applied for fitting any types of curves ranging from smooth ones to discontinuous ones. In addition, the method does not require excessive computational cost, which allows it to be used in automatic reverse engineering applications.

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Section: State Of the Artmentioning

confidence: 99%

Section: Local Algorithm For Free Knots Placement Based On Bisectimentioning

confidence: 99%

Section: Local Algorithm For Free Knots Placement Based On Bisectimentioning

confidence: 99%

Section: Local Algorithm For Free Knots Placement Based On Bisectimentioning

confidence: 99%

See 2 more Smart Citations

A direct method to solve optimal knots of B-spline curves: An application for non-uniform B-spline curves fitting

Dung

Tjahjowidodo

2017

PLoS ONE

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“…However, when it comes to practical engineering applications, the effectiveness of voxel-originated representations -regardless if surface or volume-based -that are omnipresent in medical imaging is at least questionable for at least two reasons [2,14]. On one hand, the accuracy of voxel-originated data is direct proportional with its overall size.…”

Section: Introductionmentioning

confidence: 99%

Determination of Elbow Flexion-Extension Axis Based on Planar and Closed B-Splines

Mostafavi¹,

Tutunea‐Fatan²,

Lalone³

et al. 2013

Computer-Aided Design and Applications

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Accurate determination of the flexion-extension axis of the elbow affects the outcome of implant replacement. The current study proposes an automated approach capable of determining the FE axis based on a stack of axial computer tomographic (CT) imaging slices of the distal humerus. The core of the algorithm consists of an original technique employing control polygon deformation used to approximate the segmented outer cortical bone points with closed B-Splines, followed by curvaturebased and least squares fitting methods for determination of the two relevant geometric centers. The new approach was validated against a conventional voxelbased FE axis determination procedure involving marching cubes algorithm.

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Methodologies for Development of Patient Specific Bone Models from Human Body CT Scans

Chougule¹,

Mulay²,

Ahuja

2016

J. Inst. Eng. India Ser. C

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This work deals with development of algorithm for physical replication of patient specific human bone and construction of corresponding implants/inserts RP models by using Reverse Engineering approach from non-invasive medical images for surgical purpose. In medical field, the volumetric data i.e. voxel and triangular facet based models are primarily used for bio-modelling and visualization, which requires huge memory space. On the other side, recent advances in Computer Aided Design (CAD) technology provides additional facilities/functions for design, prototyping and manufacturing of any object having freeform surfaces based on boundary representation techniques. This work presents a process to physical replication of 3D rapid prototyping (RP) physical models of human bone from various CAD modeling techniques developed by using 3D point cloud data which is obtained from noninvasive CT/MRI scans in DICOM 3.0 format. This point cloud data is used for construction of 3D CAD model by fitting B-spline curves through these points and then fitting surface between these curve networks by using swept blend techniques. This process also can be achieved by generating the triangular mesh directly from 3D point cloud data without developing any surface model using any commercial CAD software. The generated STL file from 3D point cloud data is used as a basic input for RP process. The Delaunay tetrahedralization approach is used to process the 3D point cloud data to obtain STL file. CT scan data of Metacarpus (human bone) is used as the case study for the generation of the 3D RP model. A 3D physical model of the human bone is generated on rapid prototyping machine and its virtual reality model is presented for visualization. The generated CAD model by different techniques is compared for the accuracy and reliability. The results of this research work are assessed for clinical reliability in replication of human bone in medical field.

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From CT to NURBS: Contour Fitting with B-spline Curves

Cited by 35 publications

References 33 publications

A direct method to solve optimal knots of B-spline curves: An application for non-uniform B-spline curves fitting

A direct method to solve optimal knots of B-spline curves: An application for non-uniform B-spline curves fitting

Determination of Elbow Flexion-Extension Axis Based on Planar and Closed B-Splines

Methodologies for Development of Patient Specific Bone Models from Human Body CT Scans

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