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3D object-level mapping is a fundamental problem in robotics, which is especially challenging when object CAD models are unavailable during inference. In this work, we propose a framework that can reconstruct high-quality object-level maps…
As we collect additional samples from a data population for which a known density function estimate may have been previously obtained by a black box method, the increased complexity of the data set may result in the true density being…
Regular measurement of carbon stock in the world's forests is critical for carbon accounting and reporting under national and international climate initiatives, and for scientific research, but has been largely limited in scalability and…
Dice similarity coefficient (DSC) and Hausdorff distance (HD) are widely used for evaluating medical image segmentation. They have also been criticised, when reported alone, for their unclear or even misleading clinical interpretation. DSCs…
In this paper, we develop a method of performing the one-point statistics of a perturbed density field with a multiresolutional decomposition based on the discrete wavelet transform (DWT). We establish the algorithm of the one-point…
Let $\{x\_n\}\_{n\geq 0}$ be a sequence of $[0,1]^d$, $\{\lambda\_n\} \_{n\geq 0}$ a sequence of positive real numbers converging to 0, and $\delta>1$. Let $\mu$ be a positive Borel measure on $[0,1]^d$, $\rho\in (0,1]$ and $\alpha>0$.…
We propose a neural network component, the regional aggregation layer, that makes it possible to train a pixel-level density estimator using only coarse-grained density aggregates, which reflect the number of objects in an image region. Our…
The prediction of cross sections for nuclei far off stability is crucial in the field of nuclear astrophysics. In recent calculations the nuclear level density -- as an important ingredient to the statistical model (Hauser-Feshbach) -- has…
Datasets such as images, text, or movies are embedded in high-dimensional spaces. However, in important cases such as images of objects, the statistical structure in the data constrains samples to a manifold of dramatically lower…
Statistical inference from high-dimensional data with low-dimensional structures has recently attracted lots of attention. In machine learning, deep generative modeling approaches implicitly estimate distributions of complex objects by…
A new tuning-free subgrid-scale model, termed `locally-averaged scale-dependent dynamic' (LASDD) model, is developed and implemented in large-eddy simulations (LESs) of stable boundary layers. The new model dynamically computes the…
The local density of states \rho(x,E) is calculated for a Bloch electron in an electric field. Depending on the system size, we can see one or more sequences of Wannier-Stark ladders in \rho(x,E), with Lorentz type level widths and apparent…
This paper considers the problem of estimating an unknown high dimensional signal from noisy linear measurements, {when} the signal is assumed to possess a \emph{group-sparse} structure in a {known,} fixed dictionary. We consider signals…
Recently, dense pseudo-label, which directly selects pseudo labels from the original output of the teacher model without any complicated post-processing steps, has received considerable attention in semi-supervised object detection (SSOD).…
In the manifold learning problem one seeks to discover a smooth low dimensional surface, i.e., a manifold embedded in a higher dimensional linear vector space, based on a set of measured sample points on the surface. In this paper we…
Anomaly detection in medical imaging is essential for identifying rare pathological conditions, particularly when annotated abnormal samples are limited. We propose a hybrid anomaly detection framework that integrates self-supervised…
We consider digits-deleted sets or Cantor-type sets with $\beta$-expansions. We calculate the Hausdorff dimension $d$ of these sets and show that $d$ is continuous with respect to $\beta$. The $d$-dimentional Hausdorff measure of these sets…
Fix $k \in \mathbb{N}$ and $0 < \delta < 1$. We study how large $N$ must be so that every $\delta$-dense subset $\mathcal{D} \subset \{0,1\}^N$ (meaning $|\mathcal{D}| \geq \delta 2^N$) contains the image of a metric embedding $f: \{0,1\}^k…
Object pose estimation enables a variety of tasks in computer vision and robotics, including scene understanding and robotic grasping. The complexity of a pose estimation task depends on the unknown variables related to the target object.…
We introduce a new approach for estimating the invariant density of a multidimensional diffusion when dealing with high-frequency observations blurred by independent noises. We consider the intermediate regime, where observations occur at…