arXiv subjects

Zixiang Zhou

Publications and source records attributed to Zixiang Zhou.

46 records · Page 3Linked to original sources

arXiv2021

Panoptic-PolarNet: Proposal-free LiDAR Point Cloud Panoptic Segmentation

Panoptic segmentation presents a new challenge in exploiting the merits of both detection and segmentation, with the aim of unifying instance segmentation and semantic segmentation in a single framework. However, an efficient solution for panoptic segmentation in the emerging domain of LiDAR point cloud is still an open research problem and is very much under-explored. In this paper, we present a fast and robust LiDAR point cloud panoptic segmentation framework, referred to as Panoptic-PolarNet. We learn both semantic segmentation and class-agnostic instance clustering in a single inference network using a polar Bird's Eye View (BEV) representation, enabling us to circumvent the issue of occlusion among instances in urban street scenes. To improve our network's learnability, we also propose an adapted instance augmentation technique and a novel adversarial point cloud pruning method. Our experiments show that Panoptic-PolarNet outperforms the baseline methods on SemanticKITTI and nuScenes datasets with an almost real-time inference speed. Panoptic-PolarNet achieved 54.1% PQ in the public SemanticKITTI panoptic segmentation leaderboard and leading performance for the validation set of nuScenes.

cs.CV↗

arXiv2020

PolarNet: An Improved Grid Representation for Online LiDAR Point Clouds Semantic Segmentation

The need for fine-grained perception in autonomous driving systems has resulted in recently increased research on online semantic segmentation of single-scan LiDAR. Despite the emerging datasets and technological advancements, it remains challenging due to three reasons: (1) the need for near-real-time latency with limited hardware; (2) uneven or even long-tailed distribution of LiDAR points across space; and (3) an increasing number of extremely fine-grained semantic classes. In an attempt to jointly tackle all the aforementioned challenges, we propose a new LiDAR-specific, nearest-neighbor-free segmentation algorithm - PolarNet. Instead of using common spherical or bird's-eye-view projection, our polar bird's-eye-view representation balances the points across grid cells in a polar coordinate system, indirectly aligning a segmentation network's attention with the long-tailed distribution of the points along the radial axis. We find that our encoding scheme greatly increases the mIoU in three drastically different segmentation datasets of real urban LiDAR single scans while retaining near real-time throughput.

cs.CV↗

arXiv2002

Liouville integrability of the finite dimensional Hamiltonian systems derived from principal chiral field

For finite dimensional Hamiltonian systems derived from 1+1 dimensional integrable systems, if they have Lax representations, then the Lax operator creates a set of conserved integrals. When these conserved integrals are in involution, it is believed quite popularly that there will be enough functionally independent ones among them to guarantee the Liouville integrability of the Hamiltonian systems, at least for those derived from physical problems. In this paper, we give a counterexample based on the U(2) principal chiral field. It is proved that the finite dimensional Hamiltonian systems derived from the U(2) principal chiral field are Liouville integrable. Moreover, their Lax operator gives a set of involutive conserved integrals, but they are not enough to guarantee the integrability of the Hamiltonian systems.

nlin.SI↗

arXiv2001

Relation between the solitons of Yang-Mills-Higgs fields in 2+1 dimensional Minkowski space-time and anti-de Sitter space-time

The Yang-Mills-Higgs-Bogomolny equations in both 2+1 dimensional Minkowski space-time and 2+1 dimensional anti-de Sitter space-time are known to be integrable and their soliton solutions have already been obtained. In this paper we show that there is a natural relation between the Lax pairs and soliton solutions in these two space-times when the curvature changes from 0 to -1. The change of the asymptotic behaviors of the solitons are also discussed.

nlin.SI↗

arXiv2001

Binary Symmetry Constraints of N-wave Interaction Equations in 1+1 and 2+1 Dimensions

Binary symmetry constraints of the N-wave interaction equations in 1+1 and 2+1 dimensions are proposed to reduce the N-wave interaction equations into finite-dimensional Liouville integrable systems. A new involutive and functionally independent system of polynomial functions is generated from an arbitrary order square matrix Lax operator and used to show the Liouville integrability of the constrained flows of the N-wave interaction equations. The constraints on the potentials resulting from the symmetry constraints give rise to involutive solutions to the N-wave interaction equations, and thus the integrability by quadratures are shown for the N-wave interaction equations by the constrained flows.

nlin.SI↗

arXiv2001

Finite-dimensional integrable systems associated with Davey-Stewartson I equation

For the Davey-Stewartson I equation, which is an integrable equation in 1+2 dimensions, we have already found its Lax pair in 1+1 dimensional form by nonlinear constraints. This paper deals with the second nonlinearization of this 1+1 dimensional system to get three 1+0 dimensional Hamiltonian systems with a constraint of Neumann type. The full set of involutive conserved integrals is obtained and their functional independence is proved. Therefore, the Hamiltonian systems are completely integrable in Liouville sense. A periodic solution of the Davey-Stewartson I equation is obtained by solving these classical Hamiltonian systems as an example.

nlin.SI↗

arXiv2001

Finite dimensional integrable Hamiltonian systems associated with DSI equation by Bargmann constraints

The Davey-Stewartson I equation is a typical integrable equation in 2+1 dimensions. Its Lax system being essentially in 1+1 dimensional form has been found through nonlinearization from 2+1 dimensions to 1+1 dimensions. In the present paper, this essentially 1+1 dimensional Lax system is further nonlinearized into 1+0 dimensional Hamiltonian systems by taking the Bargmann constraints. It is shown that the resulting 1+0 dimensional Hamiltonian systems are completely integrable in Liouville sense by finding a full set of integrals of motion and proving their functional independence.

nlin.SI↗

arXiv2000

Solutions of the Yang-Mills-Higgs equations in 2+1 dimensional anti-de Sitter space-time

The solutions of the Bogomolny equation in anti-de Sitter space-time are obtained by using Darboux transformations with both constant spectral parameters and variable "spectral parameters". These solutions give the Yang-Mills-Higgs fields in anti-de Sitter space-time. Some examples in SU(2) case are considered and qualitative asymptotic behaviors of the solutions as t tends to infinity are discussed in detail.

nlin.SI↗

arXiv1998

Localized solitons of hyperbolic su(N) AKNS system

Using the nonlinear constraint and Darboux transformation methods, the (m_1,...,m_N) localized solitons of the hyperbolic su(N) AKNS system are constructed. Here "hyperbolic su(N)" means that the first part of the Lax pair is F_y=JF_x+U(x,y,t)F where J is constant real diagonal and U^*=-U. When different solitons move in different velocities, each component U_{ij} of the solution U has at most m_i m_j peaks as t tends to infinity. This corresponds to the (M,N) solitons for the DSI equation. When all the solitons move in the same velocity, U_{ij} still has at most m_i m_j peaks if the phase differences are large enough.

solv-int↗

arXiv1998

Darboux transformations for twisted so(p,q) system and local isometric immersion of space forms

For the n-dimensional integrable system with a twisted so(p,q) reduction, Darboux transformations given by Darboux matrices of degree 2 are constructed explicitly. These Darboux transformations are applied to the local isometric immersion of space forms with flat normal bundle and linearly independent curvature normals to give the explicit expression of the position vector. Some examples are given from the trivial solutions and standard imbedding T^n\to R^{2n}.

solv-int↗