  A fundamental problem in computer vision is boundary estimation, where the
goal is to delineate the boundary of objects in an image. In this paper, we
propose a method which jointly incorporates geometric and topological
information within an image to simultaneously estimate boundaries for objects
within images with more complex topologies. We use a topological
clustering-based method to assist initialization of the Bayesian active contour
model. This combines pixel clustering, boundary smoothness, and potential prior
shape information to produce an estimated object boundary. Active contour
methods are knownto be extremely sensitive to algorithm initialization, relying
on the user to provide a reasonable starting curve to the algorithm. In the
presence of images featuring objects with complex topological structures, such
as objects with holes or multiple objects, the user must initialize separate
curves for each boundary of interest. Our proposed topologically-guided method
can provide an interpretable, smart initialization in these settings, freeing
up the user from potential pitfalls associated with objects of complex
topological structure. We provide a detailed simulation study comparing our
initialization to boundary estimates obtained from standard segmentation
algorithms. The method is demonstrated on artificial image datasets from
computer vision, as well as real-world applications to skin lesion and neural
cellular images, for which multiple topological features can be identified.
