NBGVF: Normally Biased Gradient Vector Flow External Force for Active Contours

Gradient vector flow (GVF) has been one effective external force for active contours, but it is based on isotropic diffusion. The recently proposed NGVF external force just took into account the diffusion along normal direction of the level line, so it is sensitive to noise and could smear the weak boundaries. In this article, we present a novel one called normally biased gradient vector flow (NBGVF) which keeps the diffusion along the tangential direction of the level line and biases that along the normal direction. The biasing weight of the diffusion along the normal direction approaches zero at boundaries and is 1, even larger, in homogeneous regions. Consequently, the NBGVF can preserve weak edges and smooth out noise while maintaining other desirable properties of GVF and NGVF such as enlarged capture range, insensitivity to initialization and convergence to u-shape concavity. These properties are evaluated on synthetic and real images.