An implicit evolution scheme for active contours and surfaces based on IIR filtering

Abstract In this work, we present an approach for implementing an implicit scheme for the numerical solution of the partial differential equation of the evolution of an active contour/surface. The proposed scheme is applicable to any variant of the traditional active contour (AC), irrespectively of...

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Bibliographic Details
Published in:Computers in biology and medicine 2014-05, Vol.48, p.42-54
Main Authors: Delibasis, Konstantinos K, Asvestas, Pantelis A, Kechriniotis, Aristides I, Matsopoulos, George K
Format: Article
Language:English
Subjects:
3D segmentation
Active contour
Active surface
Algorithms
Coronary vessels
Diagnostic Imaging - methods
Humans
Imaging, Three-Dimensional - methods
Implicit evolution
Internal Medicine
Linear algebra
Medical Informatics Applications
Other
Partial differential equations
Three dimensional imaging
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Summary:Abstract In this work, we present an approach for implementing an implicit scheme for the numerical solution of the partial differential equation of the evolution of an active contour/surface. The proposed scheme is applicable to any variant of the traditional active contour (AC), irrespectively of the calculation of the image-based force field and it is readily applicable to explicitly parameterized active surfaces (AS). The proposed approach is formulated as an infinite impulse response (IIR) filtering of the coordinates of the contour/surface points. The poles of the filter are determined by the parameters controlling the shape of the active contour/surface. We show that the proposed IIR-based implicit evolution scheme has very low complexity. Furthermore, the proposed scheme is numerically stable, thus it allows the convergence of the AC/AS with significantly fewer iterations than the explicit evolution scheme. It also possesses the separability property along the two parameters of the AS, thus it may be applied to deformable surfaces, without the need to store and invert large sparse matrices. We implemented the proposed IIR-based implicit evolution scheme in the Vector Field Convolution (VFC) AC/AS using synthetic and clinical volumetric data. We compared the segmentation results with those of the explicit AC/AS evolution, in terms of accuracy and efficiency. Results show that the VFC AC/AS with the proposed IIR-based implicit evolution scheme achieves the same segmentation results with the explicit scheme, with considerably less computation time.
ISSN:0010-4825
1879-0534
DOI:10.1016/j.compbiomed.2014.02.007