Wei Lian

Wei Lian, Fei Ma, Hang Pan et al.

Achieving globally optimal point cloud registration under partial overlaps and large misalignments remains a fundamental challenge. While simultaneous transformation ($\boldsymbolθ$) and correspondence ($\mathbf{P}$) estimation has the advantage of being robust to nonrigid deformation, its non-convex coupled objective often leads to local minima for heuristic methods and prohibitive convergence times for existing global solvers due to loose lower bounds. To address this, we propose DC-Reg, a robust globally optimal framework that significantly tightens the Branch-and-Bound (BnB) search. Our core innovation is the derivation of a holistic concave underestimator for the coupled transformation-assignment objective, grounded in the Difference of Convex (DC) programming paradigm. Unlike prior works that rely on term-wise relaxations (e.g., McCormick envelopes) which neglect variable interplay, our holistic DC decomposition captures the joint structural interaction between $\boldsymbolθ$ and $\mathbf{P}$. This formulation enables the computation of remarkably tight lower bounds via efficient Linear Assignment Problems (LAP) evaluated at the vertices of the search boxes. We validate our framework on 2D similarity and 3D rigid registration, utilizing rotation-invariant features for the latter to achieve high efficiency without sacrificing optimality. Experimental results on synthetic data and the 3DMatch benchmark demonstrate that DC-Reg achieves significantly faster convergence and superior robustness to extreme noise and outliers compared to state-of-the-art global techniques.

Dongmei Shan, Wei Lian, Chongxia Wang

Backdoor attacks pose a critical threat to deep learning, especially in safety-sensitive 3D domains such as autonomous driving and robotics. Despite their potency, existing attacks on 3D point clouds are limited to a static one-to-one paradigm, leaving the more flexible one-to-N backdoor threat largely unexplored and without a theoretical or practical foundation. We address this by introducing STONE (Spherical Trigger One-to-N Backdoor Enabling), the first framework that instantiates this threat through a configurable spherical trigger. Its parameterizable spatial properties create a dynamic key space, enabling a single trigger to control multiple output labels. Theoretically, we ground STONE through Neural Tangent Kernel (NTK) analysis, providing the first formal basis for one-to-N mappings in 3D models. Empirically, extensive evaluations show high attack success rate (up to 100\%) with no loss in clean-data accuracy. This work establishes a foundational benchmark for multi-target threats in 3D vision, crucial for securing future intelligent systems.

Wei Lian, Zhesen Cui, Fei Ma et al.

Numerous applications require algorithms that can align partially overlapping point sets while maintaining invariance to geometric transformations (e.g., similarity, affine, rigid). This paper introduces a novel global optimization method for this task by minimizing the objective function of the Robust Point Matching (RPM) algorithm. We first reveal that the original RPM objective is a cubic polynomial. Through a concise variable substitution, we transform this objective into a quadratic function. By leveraging the convex envelope of bilinear monomials, we derive a tight lower bound for this quadratic function. This lower bound problem conveniently and efficiently decomposes into two parts: a standard linear assignment problem (solvable in polynomial time) and a low-dimensional convex quadratic program. Furthermore, we devise a specialized Branch-and-Bound (BnB) algorithm that branches exclusively on the transformation parameters, which significantly accelerates convergence by confining the search space. Experiments on 2D and 3D synthetic and real-world data demonstrate that our method, compared to state-of-the-art approaches, exhibits superior robustness to non-rigid deformations, positional noise, and outliers, particularly in scenarios where outliers are distinct from inliers.

Wei Lian, Wangmeng Zuo

In many applications, we need algorithms which can align partially overlapping point sets and are invariant to the corresponding transformations. In this work, a method possessing such properties is realized by minimizing the objective of the robust point matching (RPM) algorithm. We first show that the RPM objective is a cubic polynomial. We then utilize the convex envelopes of trilinear and bilinear monomials to derive its lower bound function. The resulting lower bound problem has the merit that it can be efficiently solved via linear assignment and low dimensional convex quadratic programming. We next develop a branch-and-bound (BnB) algorithm which only branches over the transformation variables and runs efficiently. Experimental results demonstrated better robustness of the proposed method against non-rigid deformation, positional noise and outliers in case that outliers are not mixed with inliers when compared with the state-of-the-art approaches. They also showed that it has competitive efficiency and scales well with problem size.

Wei Lian, WangMeng Zuo, Lei Zhang

Aligning partially overlapping point sets where there is no prior information about the value of the transformation is a challenging problem in computer vision. To achieve this goal, we first reduce the objective of the robust point matching algorithm to a function of a low dimensional variable. The resulting function, however, is only concave over a finite region including the feasible region. To cope with this issue, we employ the inner approximation optimization algorithm which only operates within the region where the objective function is concave. Our algorithm does not need regularization on transformation, and thus can handle the situation where there is no prior information about the values of the transformations. Our method is also $ε-$globally optimal and thus is guaranteed to be robust. Moreover, its most computationally expensive subroutine is a linear assignment problem which can be efficiently solved. Experimental results demonstrate the better robustness of the proposed method over state-of-the-art algorithms. Our method is also efficient when the number of transformation parameters is small.

Pengju Liu, Hongzhi Zhang, Wei Lian et al.

In computer vision, convolutional networks (CNNs) often adopts pooling to enlarge receptive field which has the advantage of low computational complexity. However, pooling can cause information loss and thus is detrimental to further operations such as features extraction and analysis. Recently, dilated filter has been proposed to trade off between receptive field size and efficiency. But the accompanying gridding effect can cause a sparse sampling of input images with checkerboard patterns. To address this problem, in this paper, we propose a novel multi-level wavelet CNN (MWCNN) model to achieve better trade-off between receptive field size and computational efficiency. The core idea is to embed wavelet transform into CNN architecture to reduce the resolution of feature maps while at the same time, increasing receptive field. Specifically, MWCNN for image restoration is based on U-Net architecture, and inverse wavelet transform (IWT) is deployed to reconstruct the high resolution (HR) feature maps. The proposed MWCNN can also be viewed as an improvement of dilated filter and a generalization of average pooling, and can be applied to not only image restoration tasks, but also any CNNs requiring a pooling operation. The experimental results demonstrate effectiveness of the proposed MWCNN for tasks such as image denoising, single image super-resolution, JPEG image artifacts removal and object classification.

Wei Lian

To address the problem of 3D point matching where the poses of two point sets are unknown, we adapt a recently proposed path following based method to use similarity transformation instead of the original affine transformation. The reduced number of transformation parameters leads to more constrained and desirable matching results. Experimental results demonstrate better robustness of the proposed method over state-of-the-art methods.

Wei Lian, Lei Zhang

Point matching refers to the process of finding spatial transformation and correspondences between two sets of points. In this paper, we focus on the case that there is only partial overlap between two point sets. Following the approach of the robust point matching method, we model point matching as a mixed linear assignment-least square problem and show that after eliminating the transformation variable, the resulting problem of minimization with respect to point correspondence is a concave optimization problem. Furthermore, this problem has the property that the objective function can be converted into a form with few nonlinear terms via a linear transformation. Based on these properties, we employ the branch-and-bound (BnB) algorithm to optimize the resulting problem where the dimension of the search space is small. To further improve efficiency of the BnB algorithm where computation of the lower bound is the bottleneck, we propose a new lower bounding scheme which has a k-cardinality linear assignment formulation and can be efficiently solved. Experimental results show that the proposed algorithm outperforms state-of-the-art methods in terms of robustness to disturbances and point matching accuracy.