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Abstract:
This study develops a new deformable model, the charged fluid model (CFM), that uses the simulation of a charged fluid for medical image segmentation. The CFM algorithm is based upon the theory of electrostatics and the properties of electrostatic equilibrium. Conceptually, the CFM consists of charged elements, each of which exerts a repelling electric force upon the others, on a propagating interface. Two alternate procedures are developed to guide the evolution of the CFM in such a way that the charged fluid behaves like a liquid flowing through and around different obstacles. The first step, charge distribution , distributes the elements of the charged fluid along a 2-pixel-wide propagating interface until an electrostatic equilibrium is achieved. A pure electrostatic system governed by Poisson's equation is used to achieve equilibrium. The electric potential of the simulated system is rapidly calculated using the finite-size particle (FSP) method implemented via the fast Fourier transform (FFT) algorithm. The second step, front deformation, advances the 1-pixel-wide propagating front of the CFM so that it deforms into a new shape based upon an effective field. This field is defined as the vector sum of the gradients of the equilibrium electric potential and an image potential, which is defined as the normalized gradient map of an image. The procedure is repeated until the propagating front resides on the boundaries of objects being segmented. The front of the CFM resides on the lattice during curve evolution, from which we can obtain the area and length of the segmented region with subpixel precision. Some important characteristics of the CFM algorithm for medical image segmentation are that it requires no computation of curvature or normal direction, no calculation of velocity and acceleration, no time interval setting, and it uses only one effective parameter. The CFM can automatically handle topological changes, capture sharp corners and cusps, and is straightforward to extend to 3-D segmentation. In addition, it does not require any prior knowledge of the underlying structure of the object being segmented. The CFM is validated in segmenting a wide variety of anatomic structures, including the ventricle, brain, lung, and brain tumors. The performance of the 3-D CFM is validated in the segmentation of a large number of 3-D brain vasculature trees. The results indicate that the CFM algorithm is of potential value in a broad range of challenging medical image segmentation applications.
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