Related papers: A fully data-driven method for estimating the shap…

Given noisy data, function estimation is considered when the unknown function is known apriori to consist of a small number of regions where the function is either convex or concave. When the regions are known apriori, the estimate is…

We propose a computationally efficient estimator, formulated as a convex program, for a broad class of non-linear regression problems that involve difference of convex (DC) non-linearities. The proposed method can be viewed as a significant…

A novel formulation of the clustering problem is introduced in which the task is expressed as an estimation problem, where the object to be estimated is a function which maps a point to its distribution of cluster membership. Unlike…

Existing learning-based point cloud upsampling methods often overlook the intrinsic data distribution charac?teristics of point clouds, leading to suboptimal results when handling sparse and non-uniform point clouds. We propose a novel…

Existing point cloud representation learning methods primarily rely on data-driven strategies to extract geometric information from large amounts of scattered data. However, most methods focus solely on the spatial distribution features of…

Point cloud analysis is very challenging, as the shape implied in irregular points is difficult to capture. In this paper, we propose RS-CNN, namely, Relation-Shape Convolutional Neural Network, which extends regular grid CNN to irregular…

Support points summarize a large dataset through a smaller set of representative points that can be used for data operations, such as Monte Carlo integration, without requiring access to the full dataset. In this sense, support points offer…

Object pose estimation is frequently achieved by first segmenting an RGB image and then, given depth data, registering the corresponding point cloud segment against the object's 3D model. Despite the progress due to CNNs, semantic…

The paper introduces a new estimation method for the standard linear regression model. The procedure is not driven by the optimisation of any objective function rather, it is a simple weighted average of slopes from observation pairs. The…

Most existing approaches for point cloud normal estimation aim to locally fit a geometric surface and calculate the normal from the fitted surface. Recently, learning-based methods have adopted a routine of predicting point-wise weights to…

Vehicle pose estimation with LiDAR is essential in the perception technology of autonomous driving. However, due to incomplete observation measurements and sparsity of the LiDAR point cloud, it is challenging to achieve satisfactory pose…

This article proposes a new discrete framework for approximating solutions to shape optimization problems under convexity constraints. The numerical method, based on the support function or the gauge function, is guaranteed to generate…

Over the past two decades, we have seen an exponentially increased amount of point clouds collected with irregular shapes in various areas. Motivated by the importance of solid modeling for point clouds, we develop a novel and efficient…

We study the sample complexity of stochastic convex optimization when problem parameters, e.g., the distance to optimality, are unknown. We pursue two strategies. First, we develop a reliable model selection method that avoids overfitting…

In circular plot sampling, trees within a given distance from the sample plot location constitute a sample, which is used to infer characteristics of interest for the forest area. If the sample is collected using a technical device located…

We propose a general analytical framework for single-facility continuous location problems under spatial demand uncertainty. In contrast to classical formulations based on discrete or regionally aggregated demands, the proposed model…

We propose a novel approach for density estimation called histogram trend filtering. Our estimator arises from looking at surrogate Poisson model for counts of observations in a partition of the support of the data. We begin by showing…

We consider a family of algorithms that successively sample and minimize simple stochastic models of the objective function. We show that under reasonable conditions on approximation quality and regularity of the models, any such algorithm…

Estimating probabilistic deformable template models is a new approach in the fields of computer vision and probabilistic atlases in computational anatomy. A first coherent statistical framework modelling the variability as a hidden random…

We introduce adaptive sampling methods for stochastic programs with deterministic constraints. First, we propose and analyze a variant of the stochastic projected gradient method where the sample size used to approximate the reduced…