Ellipsoid-Constrained Robust Fitting of Quadrics with Application to the 3D Morphological Characterization of Articular Surfaces

Allaire, S.; Jacq, Jean-José; Burdin, Valérie; Roux, C.

doi:10.1109/iembs.2007.4353484

Cited by 8 publications

(12 citation statements)

References 8 publications

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“…Fisher made in the mid-nineties to guarantee an ellipse at fitting conic curves to any input 2D data [7]. To our knowledge, so far only the ellipsoid type has been addressed in this way [12,13].…”

Section: Context Of Characterization With Priormentioning

confidence: 99%

“…Griffiths [12] as a robustly enforceable ellipsoid-guarantee [13]. To this end, we have exploited the bi-dimensional diagram called the Quadric Shape Map (QSM) which we had previously introduced with the distinct purpose of analyzing and comparing the output primitives of a fitting procedure [2].…”

Section: Context Of Characterization With Priormentioning

confidence: 99%

“…Note that the model through the intermediary of which we extract features is simple. Consequently, the expectable local discrepancies, potentially exaggerated by the added constraining, must be handled during the fitting process by robust methods which possibly reject some outliers [2,8,13]. Furthermore, as regards data, usual errors are to occur while they are acquired, preprocessed and segmented.…”

Section: Context Of Characterization With Priormentioning

confidence: 99%

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Type-Constrained Robust Fitting of Quadrics with Application to the 3D Morphological Characterization of Saddle-Shaped Articular Surfaces

Allaire

Jacq

Burdin

et al. 2007

2007 IEEE 11th International Conference on Computer Vision

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The scope of this paper is the guaranteed fitting of specified types of quadratic surfaces to scattered 3D point clouds. Since we chose quadrics to account for articular surfaces of various shapes in medical images, the models thus estimated usefully extract global symmetry-related intrinsic features in human joints: centers, axes, extremal curvatures. The unified type-enforcing method is based on a constrained weighted least-squares minimization of algebraic residuals which uses a robust and biascorrected metric. Provided that at most one quadratic constraint is involved, every step produces closed-form eigenvector solutions. In this framework, guaranteeing the occurrence of 3D primitives of certain types among this eigendecomposition is not a straightforward transcription of the priorly handled 2D case. To explore possibilities, we re-exploit a mapping to a 2D space called the Quadric Shape Map (QSM) where the influence of any constraint on shape and type can in fact be studied visually. As a result, we provide a new enforceable quadratic constraint that practically ensures types such as hyperboloids, which helps characterize saddle-like articular surfaces. Application to a database shows how this guarantee is needed to coherently extract the center and axes of the ankle joint.

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Section: Context Of Characterization With Priormentioning

confidence: 99%

Section: Context Of Characterization With Priormentioning

confidence: 99%

Section: Context Of Characterization With Priormentioning

confidence: 99%

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Type-Constrained Robust Fitting of Quadrics with Application to the 3D Morphological Characterization of Saddle-Shaped Articular Surfaces

Allaire

Jacq

Burdin

et al. 2007

2007 IEEE 11th International Conference on Computer Vision

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“…Information registration in the biomechanical model 3. Contact definition between the tibia and the femur In the first step a quadric robust-fitting approach [2] was used to model the condyles. The fitting methods resulted in two ellipsoids, one for each condyle (see fig.…”

Section: Geometry-based Knee Jointmentioning

confidence: 99%

Evaluation of a geometry-based knee joint compared to a planar knee joint

et al. 2011

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Today neuromuscular simulations are used in several fields, such as diagnostics and planing of surgery, to get a deeper understanding of the musculoskeletal system. During the last year new models and datasets have been presented which can provide us with more in-depth simulations and results. The same kind of development has occurred in the field of studying the human knee joint using complex three dimensional finite element models and simulations. In the field of musculoskeletal simulations, no such knee joints can be used. Instead the most common knee joint description is an idealized knee joint with limited accuracy or a planar knee joint which only describes the knee motion in a plan. In this paper, a new knee joint based on both equations and geometry is introduced and compared to a common clinical planar knee joint. The two kinematical models are analyzed using a gait motion, and are evaluated using the muscle activation and joint reaction forces which are compared to in-vivo measured forces. We show that we are able to predict the lateral, anterior and longitudinal moments, and that we are able to prediction better knee and hip joint reaction forces.

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“…While these metrics provide important information on the overall curvature of a surface, they may not discriminate between differently shaped surfaces because they do not preserve spatial information. An alternative method for describing joint shape is based on fitting circles or ellipsoids to the articular surfaces [18], but this method is not extendable to joints with concave and convex portions (e.g., saddle joints). Statistical shape models (SSMs) have also been used to describe whole bone shape [19][20][21] and to identify drastic changes in bony morphology that occur with severe pathology [21,22].…”

Section: Introductionmentioning

confidence: 99%

Polar Histograms of Curvature for Quantifying Skeletal Joint Shape and Congruence

Halilaj

Laidlaw

Moore

et al. 2014

Journal of Biomechanical Engineering

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The effect of articular joint shape and congruence on kinematics, contact stress, and the natural progression of joint disease continues to be a topic of interest in the orthopedic biomechanics literature. Currently, the most widely used metrics of assessing skeletal joint shape and congruence are based on average principal curvatures across the articular surfaces. Here we propose a method for comparing articular joint shape and quantifying joint congruence based on three-dimensional (3D) histograms of curvature—shape descriptors that preserve spatial information. Illustrated by experimental results from the trapeziometacarpal joint, this method could help unveil the interrelations between joint shape and function and provide much needed insight for the high incidence of osteoarthritis (OA)—a mechanically mediated disease whose onset has been hypothesized to be precipitated by joint incongruity.

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Ellipsoid-Constrained Robust Fitting of Quadrics with Application to the 3D Morphological Characterization of Articular Surfaces

Cited by 8 publications

References 8 publications

Type-Constrained Robust Fitting of Quadrics with Application to the 3D Morphological Characterization of Saddle-Shaped Articular Surfaces

Type-Constrained Robust Fitting of Quadrics with Application to the 3D Morphological Characterization of Saddle-Shaped Articular Surfaces

Evaluation of a geometry-based knee joint compared to a planar knee joint

Polar Histograms of Curvature for Quantifying Skeletal Joint Shape and Congruence

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