A Fourier-based implicit evolution scheme for active surfaces, for object segmentation in volumetric images

In this work we present an approach for implementing the implicit scheme for the numerical solution of the partial differential equation of the evolution of an active contour / surface. The proposed approach is formulated as a deconvolution of the current contour/surface points with a one-dimensional mask that is performed using the Discrete Fourier Transform (DFT). The proposed scheme possesses the separability property along different dimensions and allows us to apply it to deformable surfaces and implement implicit evolution, without the need to store and invert large sparse matrices. Initial results from the application of the proposed scheme to synthetic and clinical volumetric data, demonstrate the correctness and applicability of the method. The computational complexity of the proposed scheme is also derived.