Related papers: Elliptical Ordinal Embedding
A common representation of a three dimensional object in computer applications, such as graphics and design, is in the form of a triangular mesh. In many instances, individual or groups of triangles in such representation need to satisfy…
The recent success of 3D Gaussian Splatting (3DGS) has reshaped novel view synthesis by enabling fast optimization and real-time rendering of high-quality radiance fields. However, it relies on simplified, order-dependent alpha blending and…
We introduce a rotation-invariant representation of planar shapes. In particular, this representation encodes shapes as vectors such that the Euclidean distance between them serves as a valid shape distance. For standardized, star-shaped…
We propose a new embedding method for a single vector and for a pair of vectors. This embedding method enables: a) efficient classification and regression of functions of single vectors; b) efficient approximation of distance functions; and…
This work presents a novel and effective method for fitting multidimensional ellipsoids to scattered data in the contamination of noise and outliers. We approach the problem as a Bayesian parameter estimate process and maximize the…
To fully understand the 3D context of a single image, a visual system must be able to segment both the visible and occluded regions of objects, while discerning their occlusion order. Ideally, the system should be able to handle any object…
Word embedding maps words into a low-dimensional continuous embedding space by exploiting the local word collocation patterns in a small context window. On the other hand, topic modeling maps documents onto a low-dimensional topic space, by…
Most previous bounding-box-based segmentation methods assume the bounding box tightly covers the object of interest. However it is common that a rectangle input could be too large or too small. In this paper, we propose a novel segmentation…
Learning representation from relative similarity comparisons, often called ordinal embedding, gains rising attention in recent years. Most of the existing methods are based on semi-definite programming (\textit{SDP}), which is generally…
Dense embedding models are commonly deployed in commercial search engines, wherein all the document vectors are pre-computed, and near-neighbor search (NNS) is performed with the query vector to find relevant documents. However, the…
We present an approach for aggregating a sparse set of views of an object in order to compute a semi-implicit 3D representation in the form of a volumetric feature grid. Key to our approach is an object-centric canonical 3D coordinate…
We present an optical mapping near-eye (OMNI) three-dimensional display method for wearable devices. By dividing a display screen into different sub-panels and optically mapping them to various depths, we create a multiplane volumetric…
This paper studies the minimal dimension required to embed subset memberships ($m$ elements and ${m\choose k}$ subsets of at most $k$ elements) into vector spaces, denoted as Minimal Embeddable Dimension (MED). The tight bounds of MED are…
Most object detection methods use bounding boxes to encode and represent the object shape and location. In this work, we explore a fuzzy representation of object regions using Gaussian distributions, which provides an implicit binary…
This paper investigates theoretical properties of subsampling and hashing as tools for approximate Euclidean norm-preserving embeddings for vectors with (unknown) additive Gaussian noises. Such embeddings are sometimes called…
An "elephant in the room" for most current object detection and localization methods is the lack of explicit modelling of partial visibility due to occlusion by other objects or truncation by the image boundary. Based on a sliding window…
Autonomous systems need to understand the semantics and geometry of their surroundings in order to comprehend and safely execute object-level task specifications. This paper proposes an expressive yet compact model for joint object pose and…
This work lists and describes the main recent strategies for building fixed-length, dense and distributed representations for words, based on the distributional hypothesis. These representations are now commonly called word embeddings and,…
Automatic instance segmentation is a problem that occurs in many biomedical applications. State-of-the-art approaches either perform semantic segmentation or refine object bounding boxes obtained from detection methods. Both suffer from…
Multidimensional scaling (MDS) is a family of methods that embed a given set of points into a simple, usually flat, domain. The points are assumed to be sampled from some metric space, and the mapping attempts to preserve the distances…