Lei Sun

Lei Sun, Xinchen Wang, Youdi Li

Large Language Models (LLMs) possess impressive reasoning abilities but are prone to generating incorrect information, often referred to as hallucinations. While incorporating external Knowledge Graphs (KGs) can partially mitigate this issue, existing methods primarily treat KGs as static knowledge repositories, overlooking the critical disparity between KG and LLM knowledge, and failing to fully exploit the reasoning capabilities inherent in KGs. To address these limitations, we propose Pyramid-Driven Alignment (PDA), a novel framework for seamlessly integrating LLMs with KGs. PDA utilizes Pyramid Principle analysis to construct a hierarchical pyramid structure. This structure is designed to reflect the input question and generate more validated deductive knowledge, thereby enhancing the alignment of LLMs and KGs and ensuring more cohesive integration. Furthermore, PDA employs a recursive mechanism to harness the underlying reasoning abilities of KGs, resulting in more accurate knowledge retrieval for question-answering tasks. Our experimental results reveal a substantial performance advantage of PDA over state-of-the-art baselines, with improvements reaching 26.70% and 26.78%.

Lei Sun

Correspondence-based point cloud registration is a cornerstone in geometric computer vision, robotics perception, photogrammetry and remote sensing, which seeks to estimate the best rigid transformation between two point clouds from the correspondences established over 3D keypoints. However, due to limited robustness and accuracy, current 3D keypoint matching techniques are very prone to yield outliers, probably even in very large numbers, making robust estimation for point cloud registration of great importance. Unfortunately, existing robust methods may suffer from high computational cost or insufficient robustness when encountering high (or even extreme) outlier ratios, hardly ideal enough for practical use. In this paper, we present a novel time-efficient RANSAC-type consensus maximization solver, named DANIEL (Double-layered sAmpliNg with consensus maximization based on stratIfied Element-wise compatibiLity), for robust registration. DANIEL is designed with two layers of random sampling, in order to find inlier subsets with the lowest computational cost possible. Specifically, we: (i) apply the rigidity constraint to prune raw outliers in the first layer of one-point sampling, (ii) introduce a series of stratified element-wise compatibility tests to conduct rapid compatibility checking between minimal models so as to realize more efficient consensus maximization in the second layer of two-point sampling, and (iii) probabilistic termination conditions are employed to ensure the timely return of the final inlier set. Based on a variety of experiments over multiple real datasets, we show that DANIEL is robust against over 99% outliers and also significantly faster than existing state-of-the-art robust solvers (e.g. RANSAC, FGR, GORE).

Lei Sun

Rotation search and point cloud registration are two fundamental problems in robotics and computer vision, which aim to estimate the rotation and the transformation between the 3D vector sets and point clouds, respectively. Due to the presence of outliers, probably in very large numbers, among the putative vector or point correspondences in real-world applications, robust estimation is of great importance. In this paper, we present ICOS (Inlier searching using COmpatible Structures), a novel, efficient and highly robust solver for both the correspondence-based rotation search and point cloud registration problems. Specifically, we (i) propose and construct a series of compatible structures for the two problems where various invariants can be established, and (ii) design three time-efficient frameworks, the first for rotation search, the second for known-scale registration and the third for unknown-scale registration, to filter out outliers and seek inliers from the invariant-constrained random sampling based on the compatible structures proposed. In this manner, even with extreme outlier ratios, inliers can be sifted out and collected for solving the optimal rotation and transformation effectively, leading to our robust solver ICOS. Through plentiful experiments over standard datasets, we demonstrate that: (i) our solver ICOS is fast, accurate, robust against over 95% outliers with nearly 100% recall ratio of inliers for rotation search and both known-scale and unknown-scale registration, outperforming other state-of-the-art methods, and (ii) ICOS is practical for use in multiple real-world applications.

Lei Sun

Correspondence-based rotation search and point cloud registration are two fundamental problems in robotics and computer vision. However, the presence of outliers, sometimes even occupying the great majority of the putative correspondences, can make many existing algorithms either fail or have very high computational cost. In this paper, we present RANSIC (RANdom Sampling with Invariant Compatibility), a fast and highly robust method applicable to both problems based on a new paradigm combining random sampling with invariance and compatibility. Generally, RANSIC starts with randomly selecting small subsets from the correspondence set, then seeks potential inliers as graph vertices from the random subsets through the compatibility tests of invariants established in each problem, and eventually returns the eligible inliers when there exists at least one K-degree vertex (K is automatically updated depending on the problem) and the residual errors satisfy a certain termination condition at the same time. In multiple synthetic and real experiments, we demonstrate that RANSIC is fast for use, robust against over 95% outliers, and also able to recall approximately 100% inliers, outperforming other state-of-the-art solvers for both the rotation search and the point cloud registration problems.

Lei Sun

In this paper, we present IRON (Invariant-based global Robust estimation and OptimizatioN), a non-minimal and highly robust solution for point cloud registration with a great number of outliers among the correspondences. To realize this, we decouple the registration problem into the estimation of scale, rotation and translation, respectively. Our first contribution is to propose RANSIC (RANdom Samples with Invariant Compatibility), which employs the invariant compatibility to seek inliers from random samples and robustly estimates the scale between two sets of point clouds in the meantime. Once the scale is estimated, our second contribution is to relax the non-convex global registration problem into a convex Semi-Definite Program (SDP) in a certifiable way using Sum-of-Squares (SOS) Relaxation and show that the relaxation is tight. For robust estimation, we further propose RT-GNC (Rough Trimming and Graduated Non-Convexity), a global outlier rejection heuristic having better robustness and time-efficiency than traditional GNC, as our third contribution. With these contributions, we can render our registration algorithm, IRON. Through experiments over real datasets, we show that IRON is efficient, highly accurate and robust against as many as 99% outliers whether the scale is known or unknown, outperforming the existing state-of-the-art algorithms.