Related papers: Approximate computation of projection depths

In ordinary Dimensionality Reduction (DR), each data instance in a high dimensional space (original space), or on a distance matrix denoting original space distances, is mapped to (projected onto) one point in a low dimensional space…

Multidimensional Projection is a fundamental tool for high-dimensional data analytics and visualization. With very few exceptions, projection techniques are designed to map data from a high-dimensional space to a visual space so as to…

The real-life data have a complex and non-linear structure due to their nature. These non-linearities and the large number of features can usually cause problems such as the empty-space phenomenon and the well-known curse of dimensionality.…

In this paper we propose a method for estimating depth from a single image using a coarse to fine approach. We argue that modeling the fine depth details is easier after a coarse depth map has been computed. We express a global (coarse)…

The convex hull of a set of points, $C$, serves to expose extremal properties of $C$ and can help identify elements in $C$ of high interest. For many problems, particularly in the presence of noise, the true vertex set (and facets) may be…

Depth estimation features are helpful for 3D recognition. Commodity-grade depth cameras are able to capture depth and color image in real-time. However, glossy, transparent or distant surface cannot be scanned properly by the sensor. As a…

Predicting depth is an essential component in understanding the 3D geometry of a scene. While for stereo images local correspondence suffices for estimation, finding depth relations from a single image is less straightforward, requiring…

Data depth is a statistical function that generalizes order and quantiles to the multivariate setting and beyond, with applications spanning over descriptive and visual statistics, anomaly detection, testing, etc. The celebrated halfspace…

With the ubiquity of sensors in the IoT era, statistical observations are becoming increasingly available in the form of massive (multivariate) time-series. Formulated as unsupervised anomaly detection tasks, an abundance of applications…

We present a method for depth estimation with monocular images, which can predict high-quality depth on diverse scenes up to an affine transformation, thus preserving accurate shapes of a scene. Previous methods that predict metric depth…

The statistical rank tests play important roles in univariate non-parametric data analysis. If one attempts to generalize the rank tests to a multivariate case, the problem of defining a multivariate order will occur. It is not clear how to…

Centrality descriptors are widely used to rank nodes according to specific concept(s) of importance. Despite the large number of centrality measures available nowadays, it is still poorly understood how to identify the node which can be…

The Tukey (or halfspace) depth extends nonparametric methods toward multivariate data. The multivariate analogues of the quantiles are the central regions of the Tukey depth, defined as sets of points in the $d$-dimensional space whose…

We propose a general approach to construct weighted likelihood estimating equations with the aim of obtain robust estimates. The weight, attached to each score contribution, is evaluated by comparing the statistical data depth at the model…

Constructing a differentially private (DP) estimator requires deriving the maximum influence of an observation, which can be difficult in the absence of exogenous bounds on the input data or the estimator, especially in high dimensional…

Due to the abundance of 2D product images from the Internet, developing efficient and scalable algorithms to recover the missing depth information is central to many applications. Recent works have addressed the single-view depth estimation…

The intrinsic dimensionality refers to the ``true'' dimensionality of the data, as opposed to the dimensionality of the data representation. For example, when attributes are highly correlated, the intrinsic dimensionality can be much lower…

Depth estimation is a cornerstone of a vast number of applications requiring 3D assessment of the environment, such as robotics, augmented reality, and autonomous driving to name a few. One prominent technique for depth estimation is stereo…

Depth imaging has largely focused on sensor and intrinsics properties. However, the accuracy of acquire pixel is largely dependent on the capture. We propose a new depth estimation and approximation algorithm which takes an arbitrary 3D…

Ground-truth depth, when combined with color data, helps improve object detection accuracy over baseline models that only use color. However, estimated depth does not always yield improvements. Many factors affect the performance of object…