From active contours to active surfaces
Identifying the surfaces of three-dimensional static objects or of two-dimensional objects over time are key to a variety of applications throughout computer vision. Active surface techniques have been widely applied to such tasks, such that a deformable spline surface evolves by the influence of internal and external (typically opposing) energies until the model converges to the desired surface. Present deformable model surface extraction techniques are computationally expensive and are not able to reliably identify surfaces in the presence of noise, high curvature, or clutter. This paper proposes a novel active surface technique, decoupled active surfaces, with the specific objectives of robustness and computational efficiency. Motivated by recent results in two-dimensional object segmentation, the internal and external energies are treated separately, which leads to much faster convergence. A truncated maximum likelihood estimator is applied to generate a surface consistent with the measurements (external energy), and a Bayesian linear least squares estimator is asserted to enforce the prior (internal energy). To maintain tractability for typical three-dimensional problems, the density of vertices is dynamically resampled based on curvature, a novel quasi-random search is used as a substitute for the ML estimator, and sparse conjugate-gradient is used to execute the Bayesian estimator. The performance of the proposed method is presented using two natural and two synthetic image volumes.