arXiv subjects

Dong Ye

Publications and source records attributed to Dong Ye.

At least 37 records · Page 2Linked to original sources

arXiv2023

Rethinking Class Activation Maps for Segmentation: Revealing Semantic Information in Shallow Layers by Reducing Noise

Class activation maps are widely used for explaining deep neural networks. Due to its ability to highlight regions of interest, it has evolved in recent years as a key step in weakly supervised learning. A major limitation to the performance of the class activation maps is the small spatial resolution of the feature maps in the last layer of the convolutional neural network. Therefore, we expect to generate high-resolution feature maps that result in high-quality semantic information. In this paper, we rethink the properties of semantic information in shallow feature maps. We find that the shallow feature maps still have fine-grained non-discriminative features while mixing considerable non-target noise. Furthermore, we propose a simple gradient-based denoising method to filter the noise by truncating the positive gradient. Our proposed scheme can be easily deployed in other CAM-related methods, facilitating these methods to obtain higher-quality class activation maps. We evaluate the proposed approach through a weakly-supervised semantic segmentation task, and a large number of experiments demonstrate the effectiveness of our approach.

cs.CV↗

arXiv2023

A Systematic Approach for Inertial Sensor Calibration of Gravity Recovery Satellites and Its Application to Taiji-1 Mission

High-precision inertial sensors or accelerometers can provide us references of free-falling motions in gravitational field in space. They serve as the key payloads for gravity recovery missions such as the CHAMP, the GRACE-type missions, and the planned Next Generation Gravity Missions. In this work, a systematic method of electrostatic inertial sensor calibrations for gravity recovery satellites is suggested, which is applied to and verified with the Taiji-1 mission. With this method, the complete operating parameters including the scale factors, the center of mass offset vector and the intrinsic biased acceleration can be precisely calibrated with only two sets of short-term in-orbit experiments. Taiji-1 is the first technology demonstration satellite of the "Taiji Program in Space", which, in its final extended phase in 2022, could be viewed as operating in the mode of a high-low satellite-to-satellite tracking gravity mission. Based on the calibration principles, swing maneuvers with time span about 200 s and rolling maneuvers for 19 days were conducted by Taiji-1 in 2022. The inertial sensor's operating parameters are precisely re-calibrated with Kalman filters and are updated to the Taiji-1 science team. Data from one of the sensitive axis is re-processed with the updated operating parameters, and the performance is found to be slightly improved compared with former results. This approach could be of high reference value for the accelerometer or inertial sensor calibrations of the GFO, the Chinese GRACE-type mission, and the Next Generation Gravity Missions. This could also shed some light on the in-orbit calibrations of the ultra-precision inertial sensors for future GW space antennas because of the technological inheritance between these two generations of inertial sensors.

physics.ins-det↗

arXiv2023

On Sign-Invertible Graphs

Let $G$ be a graph and $A$ be its adjacency matrix. A graph $G$ is invertible if its adjacency matrix $A$ is invertible and the inverse of $G$ is a weighted graph with adjacency matrix $A^{-1}$. A signed graph $(G,σ)$ is a weighted graph with a special weight function $σ: E(G)\to \{-1,1\}$. A graph is sign-invertible (or sign-invertible) if its inverse is a signed graph. A sign-invertible graph is always unimodular. The inverses of graphs have interesting combinatorial interests. In this paper, we study inverses of graphs and provide a combinatorial description for sign-invertible graphs, which provides a tool to characterize sign-invertible graphs. As applications, we complete characterize sign-invertible bipartite graphs with a unique perfect matching, and sign-invertible graphs with cycle rank at most two. As corollaries of these characterizations, some early results on trees (Buckley, Doty and Harary in 1982) and unicyclic graphs with a unique perfect matching (Kalita and Sarma in 2022) follow directly.

math.CO↗

arXiv2023

Infinitely many solutions with simultaneous synchronized and segregated components for nonlinear Schrödinger systems

In this paper, we consider the following nonlinear Schrödinger system in $R^3$: \begin{align*} -Δu_j +P_j(x) u=μ_j u_j^3+\sum\limits_{i=1,i\neq j}^Nβ_{ij}u_i^2u_j, \end{align*} where $N\geq3$, $P_j$ are nonnegative radial potentials, $μ_j>0$ and $β_{ij}=β_{ji}$ are coupling constants. This type of systems have been widely studied in the last decade, many purely synchronized or segregated solutions are constructed, but few considerations for simultaneous synchronized and segregated positive solutions exist. Using Lyapunov-Schmidt reduction method, we construct new type of solutions with simultaneous synchronization and segregation. Comparing to known results in the literature, the novelties are threefold. We prove the existence of infinitely many non-radial positive and also sign-changing vector solutions, where some components are synchronized but segregated with other components; the energy level can be arbitrarily large; and our approach works for any $N \geq 3$.

math.AP↗

arXiv2021

First order Hardy inequalities revisited

In this paper, we consider the first order Hardy inequalities using simple equalities. This basic setting not only permits to derive quickly many well-known Hardy inequalities with optimal constants, but also supplies improved or new estimates in miscellaneous situations, such as multipolar potential, the exponential weight, hyperbolic space, Heisenberg group, the edge Laplacian, or the Grushin type operator.

math.AP↗

arXiv2021

The number of cliques in graphs covered by long cycles

Let $G$ be a 2-connected $n$-vertex graph and $N_s(G)$ be the total number of $s$-cliques in $G$. Let $k\ge 4$ and $s\ge 2$ be integers. In this paper, we show that if $G$ has an edge $e$ which is not on any cycle of length at least $k$, then $N_s(G)\le r{k-1\choose s}+{t+2\choose s}$, where $n-2=r(k-3)+t$ and $0\le t\le k-4$. This result settles a conjecture of Ma and Yuan and provides a clique version of a theorem of Fan, Wang and Lv. As a direct corollary, if $N_s(G)> r{k-1\choose s}+{t+2\choose s}$, every edge of $G$ is covered by a cycle of length at least $k$.

math.CO↗

arXiv2021

How to Explain Neural Networks: an Approximation Perspective

The lack of interpretability has hindered the large-scale adoption of AI technologies. However, the fundamental idea of interpretability, as well as how to put it into practice, remains unclear. We provide notions of interpretability based on approximation theory in this study. We first implement this approximation interpretation on a specific model (fully connected neural network) and then propose to use MLP as a universal interpreter to explain arbitrary black-box models. Extensive experiments demonstrate the effectiveness of our approach.

cs.LG↗

arXiv2021

Complex Convolutional Neural Networks for Ultrafast Ultrasound Image Reconstruction from In-Phase/Quadrature Signal

Ultrafast ultrasound imaging remains an active area of interest in the ultrasound community due to its ultra-high frame rates. Recently, a wide variety of studies based on deep learning have sought to improve ultrafast ultrasound imaging. Most of these approaches have been performed on radio frequency (RF) signals. However, inphase/quadrature (I/Q) digital beamformers are now widely used as low-cost strategies. In this work, we used complex convolutional neural networks for reconstruction of ultrasound images from I/Q signals. We recently described a convolutional neural network architecture called ID-Net, which exploited an inception layer designed for reconstruction of RF diverging-wave ultrasound images. In the present study, we derive the complex equivalent of this network; i.e., the Complex-valued Inception for Diverging-wave Network (CID-Net) that operates on I/Q data. We provide experimental evidence that CID-Net provides the same image quality as that obtained from RF-trained convolutional neural networks; i.e., using only three I/Q images, the CID-Net produces high-quality images that can compete with those obtained by coherently compounding 31 RF images. Moreover, we show that CID-Net outperforms the straightforward architecture that consists of processing the real and imaginary parts of the I/Q signal separately, which thereby indicates the importance of consistently processing the I/Q signals using a network that exploits the complex nature of such signals.

eess.IV↗

arXiv2021

Training Neural Networks for Solving 1-D Optimal Piecewise Linear Approximation

Recently, the interpretability of deep learning has attracted a lot of attention. A plethora of methods have attempted to explain neural networks by feature visualization, saliency maps, model distillation, and so on. However, it is hard for these methods to reveal the intrinsic properties of neural networks. In this work, we studied the 1-D optimal piecewise linear approximation (PWLA) problem, and associated it with a designed neural network, named lattice neural network (LNN). We asked four essential questions as following: (1) What are the characters of the optimal solution of the PWLA problem? (2) Can an LNN converge to the global optimum? (3) Can an LNN converge to the local optimum? (4) Can an LNN solve the PWLA problem? Our main contributions are that we propose the theorems to characterize the optimal solution of the PWLA problem and present the LNN method for solving it. We evaluated the proposed LNNs on approximation tasks, forged an empirical method to improve the performance of LNNs. The experiments verified that our LNN method is competitive with the start-of-the-art method.

cs.LG↗

arXiv2021

Quadrangular embeddings of complete graphs and the Even Map Color Theorem (with details)

Hartsfield and Ringel constructed orientable quadrangular embeddings of the complete graph $K_n$ for $n\equiv 5 \pmod 8$, and nonorientable ones for $n \ge 9$ and $n\equiv 1 \pmod 4$. These provide minimal quadrangulations of their underlying surfaces. We extend these results to determine, for every complete graph $K_n$, $n \ge 4$, the minimum genus, both orientable and nonorientable, for the surface in which $K_n$ has an embedding with all faces of degree at least $4$, and also for the surface in which $K_n$ has an embedding with all faces of even degree. These last embeddings provide sharpness examples for a result of Hutchinson bounding the chromatic number of graphs embedded with all faces of even degree, completing the proof of the Even Map Color Theorem. We also show that if a connected simple graph $G$ has a perfect matching and a cycle then the lexicographic product $G[K_4]$ has orientable and nonorientable quadrangular embeddings; this provides new examples of minimal quadrangulations.

math.CO↗

arXiv2021

Minimal quadrangulations of surfaces

A quadrangular embedding of a graph in a surface $Σ$, also known as a quadrangulation of $Σ$, is a cellular embedding in which every face is bounded by a $4$-cycle. A quadrangulation of $Σ$ is minimal if there is no quadrangular embedding of a (simple) graph of smaller order in $Σ$. In this paper we determine $n(Σ)$, the order of a minimal quadrangulation of a surface $Σ$, for all surfaces, both orientable and nonorientable. Letting $S_0$ denote the sphere and $N_2$ the Klein bottle, we prove that $n(S_0)=4, n(N_2)=6$, and $n(Σ)=\lceil (5+\sqrt{25-16χ(Σ)})/2\rceil$ for all other surfaces $Σ$, where $χ(Σ)$ is the Euler characteristic. Our proofs use a `diagonal technique', introduced by Hartsfield in 1994. We explain the general features of this method.

math.CO↗

arXiv2021

LCCNet: LiDAR and Camera Self-Calibration using Cost Volume Network

In this paper, we propose a novel online self-calibration approach for Light Detection and Ranging (LiDAR) and camera sensors. Compared to the previous CNN-based methods that concatenate the feature maps of the RGB image and decalibrated depth image, we exploit the cost volume inspired by the PWC-Net for feature matching. Besides the smooth L1-Loss of the predicted extrinsic calibration parameters, an additional point cloud loss is applied. Instead of regress the extrinsic parameters between LiDAR and camera directly, we predict the decalibrated deviation from initial calibration to the ground truth. During inference, the calibration error decreases further with the usage of iterative refinement and the temporal filtering approach. The evaluation results on the KITTI dataset illustrate that our approach outperforms CNN-based state-of-the-art methods in terms of a mean absolute calibration error of 0.297cm in translation and 0.017° in rotation with miscalibration magnitudes of up to 1.5m and 20°.

cs.CV↗

arXiv2021

CFNet: LiDAR-Camera Registration Using Calibration Flow Network

As an essential procedure of data fusion, LiDAR-camera calibration is critical for autonomous vehicles and robot navigation. Most calibration methods rely on hand-crafted features and require significant amounts of extracted features or specific calibration targets. With the development of deep learning (DL) techniques, some attempts take advantage of convolutional neural networks (CNNs) to regress the 6 degrees of freedom (DOF) extrinsic parameters. Nevertheless, the performance of these DL-based methods is reported to be worse than the non-DL methods. This paper proposed an online LiDAR-camera extrinsic calibration algorithm that combines the DL and the geometry methods. We define a two-channel image named calibration flow to illustrate the deviation from the initial projection to the ground truth. EPnP algorithm within the RANdom SAmple Consensus (RANSAC) scheme is applied to estimate the extrinsic parameters with 2D-3D correspondences constructed by the calibration flow. Experiments on KITTI datasets demonstrate that our proposed method is superior to the state-of-the-art methods. Furthermore, we propose a semantic initialization algorithm with the introduction of instance centroids (ICs). The code will be publicly available at https://github.com/LvXudong-HIT/CFNet.

cs.RO↗

arXiv2021

High-quality Low-dose CT Reconstruction Using Convolutional Neural Networks with Spatial and Channel Squeeze and Excitation

Low-dose computed tomography (CT) allows the reduction of radiation risk in clinical applications at the expense of image quality, which deteriorates the diagnosis accuracy of radiologists. In this work, we present a High-Quality Imaging network (HQINet) for the CT image reconstruction from Low-dose computed tomography (CT) acquisitions. HQINet was a convolutional encoder-decoder architecture, where the encoder was used to extract spatial and temporal information from three contiguous slices while the decoder was used to recover the spacial information of the middle slice. We provide experimental results on the real projection data from low-dose CT Image and Projection Data (LDCT-and-Projection-data), demonstrating that the proposed approach yielded a notable improvement of the performance in terms of image quality, with a rise of 5.5dB in terms of peak signal-to-noise ratio (PSNR) and 0.29 in terms of mutual information (MI).

eess.IV↗

arXiv2020

Qualitative properties of Hénon type equations with exponential nonlinearity

We are interested in the qualitative properties of solutions of the Hénon type equations with exponential nonlinearity. First, we classify the stable at infinity solutions of $Δu +|x|^αe^u=0$ in $\mathbb{R}^N$, which gives a complete answer to the problem considered in [Wang-Ye]. Secondly, existence and precise asymptotic behaviors of entire radial solutions to $Δ^2 u=|x|^α e^u$ are obtained. Then we classify the stable and stable at infinity radial solutions to $Δ^2 u=|x|^α e^u$ in any dimension.

math.AP↗

arXiv2020

Semantic Flow-guided Motion Removal Method for Robust Mapping

Moving objects in scenes are still a severe challenge for the SLAM system. Many efforts have tried to remove the motion regions in the images by detecting moving objects. In this way, the keypoints belonging to motion regions will be ignored in the later calculations. In this paper, we proposed a novel motion removal method, leveraging semantic information and optical flow to extract motion regions. Different from previous works, we don't predict moving objects or motion regions directly from image sequences. We computed rigid optical flow, synthesized by the depth and pose, and compared it against the estimated optical flow to obtain initial motion regions. Then, we utilized K-means to finetune the motion region masks with instance segmentation masks. The ORB-SLAM2 integrated with the proposed motion removal method achieved the best performance in both indoor and outdoor dynamic environments.

cs.CV↗

arXiv2020

Existence and non-existence results for the higher order Hardy-Hénon equation revisited

This paper is devoted to studies of non-negative, non-trivial (classical, punctured, or distributional) solutions to the higher order Hardy-Hénon equations \[ (-Δ)^m u = |x|^σu^p \] in $\mathbf R^n$ with $p > 1$. We show that the condition \[ n - 2m - \frac{2m+σ}{p-1} >0 \] is necessary for the existence of distributional solutions. For $n \geq 2m$ and $σ> -2m$, we prove that any distributional solution satisfies an integral equation and a weak super polyharmonic property. We establish some sufficient conditions for punctured or classical solution to be a distributional solution. As application, we show that if $n \geq 2m$ and $σ> -2m$, there is no non-negative, non-trivial, classical solution to the equation if \[ 1 < p < \frac{n+2m+2σ}{n-2m}. \] At last, we prove that for for $n > 2m$, $σ> -2m$ and $$p \geq \frac{n+2m+2σ}{n-2m},$$ there exist positive, radially symmetric, classical solutions to the equation.

math.AP↗

arXiv2020

Existence and nonexistence results for a weighted elliptic equation in exterior domains

We consider positive solution to the weighted elliptic problem \begin{equation*} \left \{ \begin{array}{ll} -{\rm div} (|x|^θ\nabla u)=|x|^\ell u^p \;\;\; \mbox{in $\mathbb{R}^N \backslash {\overline B}$},\\ u=0 \;\;\; \mbox{on $\partial B$}, \end{array} \right. \end{equation*} where $B$ is the standard unit ball of $\mathbb{R}^N$. We give a complete answer for the existence question when $N':=N+θ>2$. In particular, for $N' > 2$ and $τ:=\ell-θ>-2$, it is shown that the problem admits a unique positive radial solution for $p>p_s:=\frac{N'+2+2τ}{N'-2}$, while for any $ 0<p \leq p_s$, the only nonnegative solution is $u \equiv 0$.

math.AP↗