Feature Preserving Point Set Surfaces based on Non-Linear Kernel regression

1. Briefly summarize the paper's contributions. Does it address a new problem? Does it present a new approach? Does it show new types of results?  [AS] This paper presents a new point set surface representation by combining implicit moving least squares (IMLS) with robust statistics. In particular, they explicitly derive IMLS in the local kernel regression (LKR) framework, forming the basis of a new robust moving least squares (MLS) surface representation that can handle sparse sampling, preserves details, and handles sharp features.  [DS] The paper presents a method that applies a robust statistics methods to MLS implicit surface. They use a robust kernel regression, which results in a representation that can handle sparse sampling, generates a continuous surface that preserves fine details better, and can handle sharp features with controllable sharpness. It can handle outliers and high frequency features, it is efficient and easy to implement, and it uses local computations so no preprocessing is needed. Improves representation of sharp features and details of any frequency, and can deal with high order corners and peaks.  [FP] The authors implicitly define the surface using a Robust Local Kernel Regression technique. The approach uses a first order estimation of the Local Kernel, which is reduced to a zero order estimation by approximating the gradient with the normal at each sample point. The obtained Local Kernel is equivalent to Kolluri's IMLS implicit function. The main contribution is the introduction of an efficient and robust technique which is resistant to both spatial and normal outliers. This robust approach allows the reconstruction of sharp features without needing to decompose or tag a local neighborhood.  [JD]  [LF]  [MK] The paper proposes interpreting the (implicit) moving least squares approach in the context of local kernel regression. This allows for designing a more robust algorithm that minimizes an energy that is less sensitive to outliers. Additionally, the authors show that by effectively incorporating a bilateral term that penalizes normal variation, their method can be made to better adapt to sharp features. 2. What is the key insight of the paper? (in 1-2 sentences)  [AS] The key insight of this paper is that MLS surfaces can be expressed in terms of LKR, which is a method in statistics to estimate the conditional expectation of a random variable.  [DS] The key insight is the fact that MLS surfaces can be expressed in …