Doo-Sabin Subdivision Surfaces Research Articles

Automated Segmentation of the Right Ventricle in 3D Echocardiography: A Kalman Filter State Estimation Approach.

As the right ventricle's (RV) role in cardiovascular diseases is being more widely recognized, interest in RV imaging, function and quantification is growing. However, there are currently few RV quantification methods for 3D echocardiography presented in the literature or commercially available. In this paper we propose an automated RV segmentation method for 3D echocardiographic images. We represent the RV geometry by a Doo-Sabin subdivision surface with deformation modes derived from a training set of manual segmentations. The segmentation is then represented as a state estimation problem and solved with an extended Kalman filter by combining the RV geometry with a motion model and edge detection. Validation was performed by comparing surface-surface distances, volumes and ejection fractions in 17 patients with aortic insufficiency between the proposed method, magnetic resonance imaging (MRI), and a manual echocardiographic reference. The algorithm was efficient with a mean computation time of 2.0 s. The mean absolute distances between the proposed and manual segmentations were 3.6 ± 0.7 mm. Good agreements of end diastolic volume, end systolic volume and ejection fraction with respect to MRI ( -26±24 mL , -16±26 mL and 0 ± 10%, respectively) and a manual echocardiographic reference (7 ± 30 mL, 13 ± 17 mL and -5±7% , respectively) were observed.

EVALUATION OF NON-UNIFORM DOO-SABIN SURFACES

Parameterization approaches for non-uniform Doo-Sabin subdivision surfaces are developed in this paper using the eigenstructure of Doo-Sabin subdivision. New methods for evaluation of values and derivatives of Doo-Sabin surfaces at arbitrary parameters by means of non-iterative approaches are presented. Furthermore, generalized basis functions for non-uniform Doo-Sabin surfaces are derived. Thus, many algorithms and analysis techniques developed for parametric surfaces can be extended to Doo-Sabin surfaces.

Making Doo-Sabin surface interpolation always work over irregular meshes

This paper presents a reliable method for constructing a control mesh whose Doo-Sabin subdivision surface interpolates the vertices of a given mesh with arbitrary topology. The method improves on existing techniques in two respects: (1) it is guaranteed to always work for meshes of arbitrary topological type; (2) there is no need to solve a system of linear equations to obtain the control points. Extensions to include normal vector interpolation and/or shape adjustment are also discussed.

Adaptive Subdivision of Catmull-Clark Subdivision Surfaces

AbstractCatmull-Clark subdivision scheme provides a powerful method for building smooth and complex surfaces. But the number of faces in the uniformly refined meshes increases sharply with respect to subdivision depth. This paper presents an adaptive subdivision technique as a solution to this problem. Instead of subdivision depths of mesh faces, the adaptive subdivision process is driven by labels of mesh vertices, which can be viewed as subdivision depths of the surface in the vicinity of the mesh vertices. Smooth transition between faces with different subdivision depths is provided by an unbalanced-subdivision process. The resulting meshes are crack-free, and all the faces are quadrilaterals. Limit surface of the resulting meshes is the same as the original limit surface. Test results show that the number of faces generated in the adaptively refined meshes is one order less than the uniform approach. The proposed technique works for cubic Doo-Sabin subdivision surfaces, non-uniform cubic subdivision s...

Precise evaluation of uniform Doo-Sabin surfaces*

Abstract Using eigenanalysis of uniform Doo-Sabin subdivision surfaces, parameterization approaches for two types of Doo-Sabin subdivision surfaces are developed, and evaluation methods for values and derivatives of Doo-Sabin surfaces at arbitrary parameters are presented by means of non-iterative approaches. Generalized basis functions for Doo-Sabin surfaces are also derived. Thus, the prejudice is disproved further that subdivision surfaces cannot be evaluated precisely.