Related papers: Density-based Isometric Mapping
We introduce a 3D Mueller Matrix (MM) image reconstruction technique using digital holographic approach for the layer-by-layer profiling thin films with polycrystalline structures, like dehydrated blood smears. The proposed method…
Recent years have witnessed a tremendous growth using topological summaries, especially the persistence diagrams (encoding the so-called persistent homology) for analyzing complex shapes. Intuitively, persistent homology maps a potentially…
Dimension reduction plays an essential role when decreasing the complexity of solving large-scale problems. The well-known Johnson-Lindenstrauss (JL) Lemma and Restricted Isometry Property (RIP) admit the use of random projection to reduce…
Discrete biomarkers derived as cell densities or counts from tissue microarrays and immunostaining are widely used to study immune signatures in relation to survival outcomes in cancer. Although routinely collected, these signatures are not…
Classical multidimensional scaling only works well when the noisy distances observed in a high dimensional space can be faithfully represented by Euclidean distances in a low dimensional space. Advanced models such as Maximum Variance…
In the context of 3D mapping, larger and larger point clouds are acquired with LIDAR sensors. The Iterative Closest Point (ICP) algorithm is used to align these point clouds. However, its complexity is directly dependent of the number of…
In many robot motion planning problems, task objectives and physical constraints induce non-Euclidean geometry on the configuration space, yet many planners operate using Euclidean distances that ignore this structure. We address the…
This paper studies the effect of discretizing the parametrization of a dictionary used for Matching Pursuit decompositions of signals. Our approach relies on viewing the continuously parametrized dictionary as an embedded manifold in the…
Sufficient dimension reduction (SDR) is continuing an active research field nowadays for high dimensional data. It aims to estimate the central subspace (CS) without making distributional assumption. To overcome the large-$p$-small-$n$…
In this paper we are interested in a version of the All-pairs Shortest Paths problem (APSP) that fits neither in the exact nor in the approximate case. We define a measure of centrality of a shortest path, related to the ``importance'' of…
Computational difficulty of quadratic matching and the Gromov-Wasserstein distance has led to various approximation and relaxation schemes. One of such methods, relying on the notion of distance profiles, has been widely used in practice,…
We tackle the problem of high-dimensional nonparametric density estimation by taking the class of log-concave densities on $\mathbb{R}^p$ and incorporating within it symmetry assumptions, which facilitate scalable estimation algorithms and…
Breast cancer is one of the leading causes of death globally, and thus there is an urgent need for early and accurate diagnostic techniques. Although ultrasound imaging is a widely used technique for breast cancer screening, it faces…
This work proposes a novel SLAM framework for stereo and visual inertial odometry estimation. It builds an efficient and robust parametrization of co-planar points and lines which leverages specific geometric constraints to improve camera…
The Isomap is a well-known nonlinear dimensionality reduction method that highly suffers from computational complexity. Its computational complexity mainly arises from two stages; a) embedding a full graph on the data in the ambient space,…
Purpose: Deformable image registration (DIR) is critical in adaptive radiation therapy (ART) to account for anatomical changes. Conventional intensity-based DIR methods often fail when image intensities differ. This study evaluates a hybrid…
Computing globally optimal motion plans for a robot is challenging in part because it requires analyzing a robot's configuration space simultaneously from both a macroscopic viewpoint (i.e., considering paths in multiple homotopic classes)…
We introduce stronger notions for approximate single-source shortest-path distances, show how to efficiently compute them from weaker standard notions, and demonstrate the algorithmic power of these new notions and transformations. One…
Neuroimaging provides essential tools for characterizing brain activity by quantifying connectivity strength between remote regions, using different modalities that capture different aspects of connectivity. Yet, decoding meaningful neural…
Analyzing high-dimensional data with manifold learning algorithms often requires searching for the nearest neighbors of all observations. This presents a computational bottleneck in statistical manifold learning when observations of…