Related papers: Geometric Inference on Kernel Density Estimates
In the this paper, the authors propose to estimate the density of a targeted population with a weighted kernel density estimator (wKDE) based on a weighted sample. Bandwidth selection for wKDE is discussed. Three mean integrated squared…
With the emergence of passive and active optical sensors available for geospatial imaging, information fusion across sensors is becoming ever more important. An important aspect of single (or multiple) sensor geospatial image analysis is…
Most graph kernels are an instance of the class of $\mathcal{R}$-Convolution kernels, which measure the similarity of objects by comparing their substructures. Despite their empirical success, most graph kernels use a naive aggregation of…
Seismic noise cross correlations are used to image crustal structure and heterogeneity. Typically, seismic networks are only anisotropically illuminated by seismic noise, a consequence of the non-uniform distribution of sources. Here, we…
Graph-based methods pervade the inference toolkits of numerous disciplines including sociology, biology, neuroscience, physics, chemistry, and engineering. A challenging problem encountered in this context pertains to determining the…
Edges of an image are considered a crucial type of information. These can be extracted by applying edge detectors with different methodology. Edge detection is a vital step in computer vision tasks, because it is an essential issue for…
Diffusion models indirectly estimate the probability density over a data space, which can be used to study its structure. In this work, we show that geodesics can be computed in diffusion latent space, where the norm induced by the…
We address the problem of estimating topological features from data in high dimensional Euclidean spaces under the manifold assumption. Our approach is based on the computation of persistent homology of the space of data points endowed with…
In this work we: (1) review likelihood-based inference for parameter estimation and the construction of confidence regions; and, (2) explore the use of techniques from information geometry, including geodesic curves and Riemann scalar…
We present a new paradigm for rigid alignment between point clouds based on learnable weighted consensus which is robust to noise as well as the full spectrum of the rotation group. Current models, learnable or axiomatic, work well for…
How can we tell complex point clouds with different small scale characteristics apart, while disregarding global features? Can we find a suitable transformation of such data in a way that allows to discriminate between differences in this…
In this paper, we propose a random projection approach to estimate variance in kernel ridge regression. Our approach leads to a consistent estimator of the true variance, while being computationally more efficient. Our variance estimator is…
Most point cloud compression methods operate in the voxel or octree domain which is not the original representation of point clouds. Those representations either remove the geometric information or require high computational power for…
We propose GeoFusion, a SLAM-based scene estimation method for building an object-level semantic map in dense clutter. In dense clutter, objects are often in close contact and severe occlusions, which brings more false detections and noisy…
The reconstruction of smooth density fields from scattered data points is a procedure that has multiple applications in a variety of disciplines, including Lagrangian (particle-based) models of solute transport in fluids. In random walk…
Local polynomial density (LPD) estimators are widely used for inference on boundary features of the density function. Contrary to conventional wisdom, we show that kernel choice substantially affects efficiency. Theory, simulations, and…
Kernel matrices, as well as weighted graphs represented by them, are ubiquitous objects in machine learning, statistics and other related fields. The main drawback of using kernel methods (learning and inference using kernel matrices) is…
This paper addresses the problem of generating uniform dense point clouds to describe the underlying geometric structures from given sparse point clouds. Due to the irregular and unordered nature, point cloud densification as a generative…
Gaussian processes are powerful models for probabilistic machine learning, but are limited in application by their $O(N^3)$ inference complexity. We propose a method for deriving parametric families of kernel functions with compact spatial…
Key points, correspondences, projection matrices, point clouds and dense clouds are the skeletons in image-based 3D reconstruction, of which point clouds have the important role in generating a realistic and natural model for a 3D…