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This paper deals with projective shape analysis, which is a study of finite configurations of points modulo projective transformations. The topic has various applications in machine vision. We introduce a convenient projective shape space,…
Classical extragradient schemes and their stochastic counterpart represent a cornerstone for resolving monotone variational inequality problems. Yet, such schemes have a per-iteration complexity of two projections onto a convex set and…
We consider the convex geometry of the cone of nonnegative quadratics over Stanley-Reisner varieties. Stanley-Reisner varieties (which are unions of coordinate planes) are amongst the simplest real projective varieties, so this is…
Point cloud analysis has drawn broader attentions due to its increasing demands in various fields. Despite the impressive performance has been achieved on several databases, researchers neglect the fact that the orientation of those point…
In this article, for the first time, one develops a nonparametric methodology for an analysis of shapes of configurations of landmarks on real 3D objects from regular camera photographs, thus making 3D shape analysis very accessible. A…
In this paper, we address the problem of 6-DoF object pose estimation from a single RGB image. Indirect methods that typically predict intermediate 2D keypoints, followed by a Perspective-n-Point solver, have shown great performance. Direct…
Many man-made objects are characterised by a shape that is symmetric along one or more planar directions. Estimating the location and orientation of such symmetry planes can aid many tasks such as estimating the overall orientation of an…
Category-level object pose estimation aims to determine the pose and size of novel objects in specific categories. Existing correspondence-based approaches typically adopt point-based representations to establish the correspondences between…
We present a novel inverse rendering-based framework to estimate the 3D shape (per-pixel surface normals and depth) of objects and scenes from single-view polarization images, the problem popularly known as Shape from Polarization (SfP).…
In geometry processing, symmetry is a universal type of high-level structural information of 3D models and benefits many geometry processing tasks including shape segmentation, alignment, matching, and completion. Thus it is an important…
Symmetry detection, especially partial and extrinsic symmetry, is essential for various downstream tasks, like 3D geometry completion, segmentation, compression and structure-aware shape encoding or generation. In order to detect partial…
Point cloud analysis without pose priors is very challenging in real applications, as the orientations of point clouds are often unknown. In this paper, we propose a brand new point-set learning framework PRIN, namely, Point-wise Rotation…
Probabilistic state-estimation approaches offer a principled foundation for designing localization systems, because they naturally integrate sequences of imperfect motion and exteroceptive sensor data. Recently, probabilistic localization…
The vast majority of Shape-from-Polarization (SfP) methods work under the oversimplified assumption of using orthographic cameras. Indeed, it is still not well understood how to project the Stokes vectors when the incoming rays are not…
We would like to estimate the pose and full shape of an object from a single observation, without assuming known 3D model or category. In this work, we propose OmniShape, the first method of its kind to enable probabilistic pose and shape…
Perspective distortion (PD) causes unprecedented changes in shape, size, orientation, angles, and other spatial relationships of visual concepts in images. Precisely estimating camera intrinsic and extrinsic parameters is a challenging task…
For a tall $n\times d$ matrix $A$ and a random $m\times n$ sketching matrix $S$, the sketched estimate of the inverse covariance matrix $(A^\top A)^{-1}$ is typically biased: $E[(\tilde A^\top\tilde A)^{-1}]\ne(A^\top A)^{-1}$, where…
The aim of the present paper is to provide an intrinsic investigation of projective changes in Finlser geometry, following the pullback formalism. Various known local results are generalized and other new intrinsic results are obtained.…
Learning model-free object pose estimation for unseen instances remains a fundamental challenge in 3D vision. Existing methods typically fall into two disjoint paradigms: category-level approaches predict absolute poses in a canonical space…
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…