Least-squares-based fitting of paraboloids

Dai, Min; Newman, Timothy S.; Cao, Chunguang

doi:10.1016/j.patcog.2006.01.016

Cited by 32 publications

(37 citation statements)

References 19 publications

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“…[7] Then, the parameters were refined using a custom-made iterative optimization algorithm, based on evolution strategies. [25] Residual fitting errors were measured for global and local HPs by computing the distance distributions of the surface points to the estimated models.…”

Section: Trochlear Surface Modeling Through Hyperbolic Paraboloidsmentioning

confidence: 99%

“…[4,5] From a surgical point of view, the extent of the morphologic variations is determinant for the selection of the optimal implant in trochleoplasty interventions. [6][7][8][9][10] Evaluating the morphologic deviations to normality is however complicated by the fact that the three-dimensional (3D) geometric profile of the trochlea is extremely complex and sensibly varies amongst individuals. [11][12][13] One of the most applied clinical approach to score the morphologic anomalies of the trochlear surface (TS) is based on the Dejour classification, which encompasses four different qualitative Grades (A, B, C, D) of increasing severity.…”

Section: Introductionmentioning

confidence: 99%

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Patient-specific modeling of the trochlear morphologic anomalies by means of hyperbolic paraboloids

Cerveri

Baroni

Confalonieri

et al. 2016

Computer Assisted Surgery

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Diagnostic and therapeutic purposes are issuing pressing demands to improve the evaluation of the dysplasia condition of the femoral trochlea. The traditional clinical assessment of the dysplasia, based on Dejour classification, recognized 4 increasing (A, B, C, D) levels of severity. It has been extensively questioned in the literature that this classification methodology can be defective suggesting that quantitative measures can ensure more reliable criteria for the dysplasia severity assessment. This study reports on a novel technique to model the trochlear surface (TS), digitally reconstructed by 3D volumetric imaging, using three hyperbolic paraboloids (HP), one to describe the global trochlear aspect, two to represent the local aspects of the medial and lateral compartments, respectively. Results on a cohort of 43 patients, affected by aspecific anterior knee pain, demonstrate the consistency of the estimated model parameters with the morphologic aspect of the TS. The obtained small fitting error (on average lower than 0.80 mm) demonstrated that the ventral aspect of the trochlear morphology can be modeled with high accuracy by HPs. We also showed that HP modeling provides a continuous representation of morphologic variations in shape parameter space while we found that similar morphologic anomalies of the trochlear aspect are actually attributed to different severity grades in the Dejour classification. This finding is in agreement with recent works in the literature reporting that morphometric parameters can only optimistically be used to discriminate between the Grade A and the remaining three grades. In conclusion, we can assert that the proposed methodology is a further step toward modeling of anatomical surfaces that can be used to quantify deviations to normality on a patient-specific basis.

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Section: Trochlear Surface Modeling Through Hyperbolic Paraboloidsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Patient-specific modeling of the trochlear morphologic anomalies by means of hyperbolic paraboloids

Cerveri

Baroni

Confalonieri

et al. 2016

Computer Assisted Surgery

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“…For curved surfaces quadrics are a natural option; Petitjean [2] surveyed quadric fitting, but there were few results that (a) quantified uncertainty, (b) recovered geometric parameterizations, and (c) fit bounded patches. In [5], Dai et al describe recovery of paraboloid geometric parameters 1 by linear least squares, without considering uncertainty. In [17] Wang et al studied quadric extraction in the context of range image segmentation, including quantified uncertainty in the algebraic (not geometric) patch parameters, but not on the input points.…”

Section: A Related Workmentioning

confidence: 99%

“…Geometric (vs. algebraic) parameterizations also support reasoning [5] about possible actions with patches, and allow some representation of spatial uncertainty with geometric error ellipsoids in task space. Minimality is desirable because redundant (non-minimal) parameterizations can slow the numerical optimizations used in surface fitting [6] and must be handled specially in uncertainty modeling [7].…”

Section: Introductionmentioning

confidence: 99%

Curved surface contact patches with quantified uncertainty

Vona

Kanoulas

2011

2011 IEEE/RSJ International Conference on Intelligent Robots and Systems

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Abstract-We introduce a set of 10 bounded curved-surface patch types suitable for modeling local contact regions both in the environment and on a robot. We present minimal geometric parameterizations using the exponential map for spatial pose both in the usual 6DoF case and also for patches with revolute symmetry that have only 5DoF. We then give an algorithm to fit any patch type to point samples of a surface, with quantified uncertainty both in the input points (including nonuniform variance, common in data from range sensors) and in the output patch. Finally, we outline how such patches can be composed into a spatial patch map of the available contact surfaces both on and around a robot.

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“…A random sample consensus paradigm (Fischler and Bolles 1981) integrated with the least-square-based quadric surface fitting algorithm (Dai et al 2007) was applied to estimate geometric parameters of this hyperboloid model and, simultaneously, to handle a large portion of outliers in the relatively large number of sample points at the femoral neck.…”

Section: Automatic 3d Reference Coordinate System Constructionmentioning

confidence: 99%

Automated segmentation and quantitative analysis of the hip joint from magnetic resonance images

Xia¹

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The aim of this thesis is to develop a novel computer-aided system with advanced medical image processing approaches. This will allow automatic segmentation and quantification of the osteochondral elements (i.e. the articulating bones and cartilages) from high-resolution three-dimensional (3D) magnetic resonance (MR) images of the hip joint.This research is motivated by the importance of early detection of structural changes and degeneration of the bones and articular cartilages for good patient outcomes, particularly for early and pre-osteoarthritic conditions such as cam-type femoroacetabular impingement (FAI). MR imaging provides an optimal tool for in vivo assessment of the hip joint structure, including the bones and cartilages. This has generated extensive interest in the development of MR technologies to analyse cartilage morphology and assess biochemical compositions of the hyaline cartilage to facilitate early diagnostic and treatment for hip osteoarthritis (OA) and FAI.Quantitative analyses can provide useful morphometric data from complex MR data. In the hip joint, the segmentation of bones and cartilages is an essential prerequisite, which must be accurate, reliable and reproducible, for quantitative measurements. However, this is difficult and is traditionally performed using time-and expert-intensive manual or semi-automatic methods.The hypothesis behind this research is that accurate and reproducible quantitative data can be automatically obtained from high-resolution 3D MR images of the hip joint, through the use of advanced image processing techniques. To this end, this research focuses on two specific aims: Aim 1 -to develop and evaluate a fully automated segmentation approach to deliver accurate and reproducible bone and cartilage segmentations from high-resolution 3D MR images of the hip joint and Aim 2 -to automatically extract reliable and reproducible morphometric data based on the segmented subchondral bones and articular cartilages.The development of an automatic segmentation scheme for the bones and cartilages with high precision and reproducibility is firstly needed in order to provide a basis for subsequent quantitative measurements, which deliver reliable morphometric data of the segmented bones and cartilages for the use in early OA and FAI studies. To attain these aims, images were acquired using different MR sequences from a mixed demographic (male or female and young adult to elderly) of participants with a variety of femoral head-neck junction presentations but no apparent hip OA. Different sequence scans were used to image the same participant for the associated reproducibility experiments.Two state-of-the-art methods (multi-atlas-based and active shape model (ASM) based algorithms) i were developed and evaluated for automatic segmentation of proximal femurs and innominate bones from large field of view (FOV) MR images (water-excitation dual echo steady state (DESS) and multi echo data image combination (MEDIC)). The validation results have indicated accurate and robust...

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Least-squares-based fitting of paraboloids

Cited by 32 publications

References 19 publications

Patient-specific modeling of the trochlear morphologic anomalies by means of hyperbolic paraboloids

Patient-specific modeling of the trochlear morphologic anomalies by means of hyperbolic paraboloids

Curved surface contact patches with quantified uncertainty

Automated segmentation and quantitative analysis of the hip joint from magnetic resonance images

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