  Many applications in vision require estimation of thin structures such as
boundary edges, surfaces, roads, blood vessels, neurons, etc. Unlike most
previous approaches, we simultaneously detect and delineate thin structures
with sub-pixel localization and real-valued orientation estimation. This is an
ill-posed problem that requires regularization. We propose an objective
function combining detection likelihoods with a prior minimizing curvature of
the center-lines or surfaces. Unlike simple block-coordinate descent, we
develop a novel algorithm that is able to perform joint optimization of
location and detection variables more effectively. Our lower bound optimization
algorithm applies to quadratic or absolute curvature. The proposed early vision
framework is sufficiently general and it can be used in many higher-level
applications. We illustrate the advantage of our approach on a range of 2D and
3D examples.
