Curve/Surface Representation and Evolution Using Vector Level Sets with Application to the Shape-Based Segmentation Problem

• Published in: IEEE transactions on pattern analysis and machine intelligence Vol. 29; no. 6; pp. 945 - 958
• Main Authors: Abd El Munim, H.E., Farag, A.A.
• Format: Journal Article
• Language: English
• Published: Los Alamitos, CA IEEE 01.06.2007; IEEE Computer Society; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied sciences; Artificial Intelligence; Biomedical imaging; Cluster Analysis; Computer science; control theory; systems; Control theory. Systems; Deformable models; Evolution; Exact sciences and technology; Image Enhancement - methods; Image Interpretation, Computer-Assisted - methods; Image segmentation; Imaging, Three-Dimensional - methods; Information Storage and Retrieval - methods; Level set; level sets; Mathematical analysis; Mathematical models; Multidimensional systems; Partial differential equations; Pattern Recognition, Automated - methods; Pattern recognition. Digital image processing. Computational geometry; Process control; Process control. Computer integrated manufacturing; Representations; Reproducibility of Results; Segmentation; Sensitivity and Specificity; Shape control; Shape measurement; Shape representation; shape-based segmentation; Studies; Three dimensional; Topology; Vectors (mathematics); Prior information; Image registration; Information system; Image processing; Process control; Contour line; Set computation; Minimization; Correspondence principle; deformable models; Modeling; Partial differential equation; Shape representation; Image segmentation; level sets; shape-based segmentation; Multidimensional database; Active system; Variational calculus; Tridimensional image; Strain control; Pattern analysis; Artificial intelligence; Vector equation
• ISSN: 0162-8828; 1939-3539; 2160-9292
• DOI: 10.1109/TPAMI.2007.1100

In this paper, we revisit the implicit front representation and evolution using the vector level set function (VLSF) proposed in (H. E. Abd El Munim, et al., Oct. 2005). Unlike conventional scalar level sets, this function is designed to have a vector form. The distance from any point to the nearest point on the front has components (projections) in the coordinate directions included in the vector function. This kind of representation is used to evolve closed planar curves and 3D surfaces as well. Maintaining the VLSF property as the distance projections through evolution will be considered together with a detailed derivation of the vector partial differential equation (PDE) for such evolution. A shape-based segmentation framework will be demonstrated as an application of the given implicit representation. The proposed level set function system will be used to represent shapes to give a dissimilarity measure in a variational object registration process. This kind of formulation permits us to better control the process of shape registration, which is an important part in the shape-based segmentation framework. The method depends on a set of training shapes used to build a parametric shape model. The color is taken into consideration besides the shape prior information. The shape model is fitted to the image volume by registration through an energy minimization problem. The approach overcomes the conventional methods problems like point correspondences and weighing coefficients tuning of the evolution (PDEs). It is also suitable for multidimensional data and computationally efficient. Results in 2D and 3D of real and synthetic data will demonstrate the efficiency of the framework