  Shape modeling is a challenging task with many potential applications in
computer vision and medical imaging. There are many shape modeling methods in
the literature, each with its advantages and applications. However, many shape
modeling methods have difficulties handling shapes that have missing pieces or
outliers. In this regard, this paper introduces shape denoising, a fundamental
problem in shape modeling that lies at the core of many computer vision and
medical imaging applications and has not received enough attention in the
literature. The paper introduces six types of noise that can be used to perturb
shapes as well as an objective measure for the noise level and for comparing
methods on their shape denoising capabilities. Finally, the paper evaluates
seven methods capable of accomplishing this task, of which six are based on
deep learning, including some generative models.
