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Nonlinear embedding manifold learning methods provide invaluable visual insights into the structure of high-dimensional data. However, due to a complicated nonconvex objective function, these methods can easily get stuck in local minima and…

Reconstructing geometry and topology structures from raw unstructured data has always been an important research topic in indoor mapping research. In this paper, we aim to reconstruct the floorplan with a vectorized representation from…

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…

Manifold alignment (MA) involves a set of techniques for learning shared representations across domains, yet many traditional MA methods are incapable of performing out-of-sample extension, limiting their real-world applicability. We…

High-dimensional data are ubiquitous in contemporary science and finding methods to compress them is one of the primary goals of machine learning. Given a dataset lying in a high-dimensional space (in principle hundreds to several thousands…

Face inpainting requires the model to have a precise global understanding of the facial position structure. Benefiting from the powerful capabilities of deep learning backbones, recent works in face inpainting have achieved decent…

We propose a deep-learning based method for obtaining standardized data coordinates from scientific measurements.Data observations are modeled as samples from an unknown, non-linear deformation of an underlying Riemannian manifold, which is…

Although people spend most of their time indoors, outdoor tracking systems, such as the Global Positioning System (GPS), are predominantly used for location-based services. These systems are accurate outdoors, easy to use, and operate…

6D object pose estimation is widely applied in robotic tasks such as grasping and manipulation. Prior methods using RGB-only images are vulnerable to heavy occlusion and poor illumination, so it is important to complement them with depth…

With the growth of location-based services, indoor localization is attracting great interests as it facilitates further ubiquitous environments. Specifically, device free localization using wireless signals is getting increased attention as…

We propose a novel architecture that learns an end-to-end mapping function to improve the spatial resolution of the input natural images. The model is unique in forming a nonlinear combination of three traditional interpolation techniques…

We propose a differential geometric construction for families of low-rank covariance matrices, via interpolation on low-rank matrix manifolds. In contrast with standard parametric covariance classes, these families offer significant…

As the medical usage of computed tomography (CT) continues to grow, the radiation dose should remain at a low level to reduce the health risks. Therefore, there is an increasing need for algorithms that can reconstruct high-quality images…

We present precise anisotropic interpolation error estimates for smooth functions using a new geometric parameter and derive inverse inequalities on anisotropic meshes. In our theory, the interpolation error is bounded in terms of the…

This article presents a leak localization methodology based on state estimation and learning. The first is handled by an interpolation scheme, whereas dictionary learning is considered for the second stage. The novel proposed interpolation…

This paper presents a robust and accurate positioning system that adapts its behavior to the surrounding environment, mimicking the capability of the visual brain to filtering out clutter and focusing attention on activity and relevant…

Geometric knowledge has been shown to be beneficial for the stereo matching task. However, prior attempts to integrate geometric insights into stereo matching algorithms have largely focused on geometric knowledge from single images while…

Due to large variations in shape, appearance, and viewing conditions, object recognition is a key precursory challenge in the fields of object manipulation and robotic/AI visual reasoning in general. Recognizing object categories,…

Real world data often lie on low-dimensional Riemannian manifolds embedded in high-dimensional spaces. This motivates learning degenerate normalizing flows that map between the ambient space and a low-dimensional latent space. However, if…

We study the bias-variance tradeoff within a multiscale approximation framework. Our approach uses a given quasi-interpolation operator, which is repeatedly applied within an error-correction scheme over a hierarchical data structure. We…