Deterministic and stochastic state model of right generalized cylinder (RGC-sm): application in computer phantoms synthesis

Authors:
Jacques Azencot;Maciej Orkisz
Affiliations:
CREATIS, INSA de Lyon, Bât. Blaise Pascal, 7, rue J. Capelle, 69621 Villeurbanne Cedex, France;Creatis, CNRS Research Unit (UMR 5515), affiliated with INSERM, Lyon, France
Venue:
Graphical Models
Year:
2003

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Abstract

RGC-sm is a state model proposed to describe complex-shaped objects within the family of right generalized cylinders (RGCs). A continuous deformation of a planar curve (contour) along the object's axis describes its surface. The contour, locally orthogonal to the axis, is modeled by a finite Fourier series (FS). The zero-order FS harmonics (contour centers) define the axis. The object is divided into sections of variable length where the variation rule of the shape remains unchanged. Very concise description of a RGC family having the same statistical properties is obtained by applying an auto-regressive stochastic model to state variables. RGC-sm gives access to morphological parameters such as curvature and torsion of the axis, area of cross-sections, and volume of a cylinder segment. Its usefulness is illustrated in synthesis of vascular phantoms and in segmentation/quantification of real vascular images. It can also be used in other fields such as classification and pattern recognition.