Enforcing Topological Interaction between Implicit Surfaces via Uniform
  Sampling
Hieu Le Nicolas Talabot Jiancheng Yang Pascal Fua
Objects interact with each other in various ways, including containment,
contact, or maintaining fixed distances. Ensuring these topological
interactions is crucial for accurate modeling in many scenarios. In this paper,
we propose a novel method to refine 3D object representations, ensuring that
their surfaces adhere to a topological prior. Our key observation is that the
object interaction can be observed via a stochastic approximation method: the
statistic of signed distances between a large number of random points to the
object surfaces reflect the interaction between them. Thus, the object
interaction can be indirectly manipulated by using choosing a set of points as
anchors to refine the object surfaces. In particular, we show that our method
can be used to enforce two objects to have a specific contact ratio while
having no surface intersection. The conducted experiments show that our
proposed method enables accurate 3D reconstruction of human hearts, ensuring
proper topological connectivity between components. Further, we show that our
proposed method can be used to simulate various ways a hand can interact with
an arbitrary object.