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.

通过一种新方法，我们提出了一种改进 3D 对象表示的方法，保证其表面遵循拓扑先验性，以确保对象之间的拓扑相互作用。我们的关键观察是，可以通过随机逼近方法观察到对象之间的相互作用：大量随机点到对象表面的符号距离的统计数据反映了它们之间的相互作用。因此，可以通过选择一组点作为锚点以改进对象表面，间接操纵对象之间的相互作用。特别地，我们展示了我们的方法可以在两个对象之间强制实现特定的接触比例而没有表面交叉。进行的实验证明了我们的方法可以准确重建人类心脏，保证组件之间的正确拓扑连接。此外，我们展示了我们的方法可以用于模拟手与任意对象互动的各种方式。

通过均匀采样强制隐式表面之间的拓扑相互作用

Enforcing Topological Interaction between Implicit Surfaces via Uniform  Sampling

The g-and-k and (generalised) g-and-h distributions are flexible univariate
distributions which can model highly skewed or heavy tailed data through only
four parameters: location and scale, and two shape parameters influencing the
skewness and kurtosis. These distributions have the unusual property that they
are defined through their quantile function (inverse cumulative distribution
function) and their density is unavailable in closed form, which makes
parameter inference complicated. This paper presents the gk R package to work
with these distributions. It provides the usual distribution functions and
several algorithms for inference of independent identically distributed data,
including the finite difference stochastic approximation method, which has not
been used before for this problem.

介绍了 gk R 包，可以用于高度偏斜或重尾数据的建模和参数推断，其中使用了 g-and-k 和（generalised）g-and-h 分布，主要关注于其分布函数和推断算法。