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Dongping Li

Dongping Li contributes to research discovery and scholarly infrastructure.

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Published work

3 published item(s)

preprint2026arXiv

Mix3R: Mixing Feed-forward Reconstruction and Generative 3D Priors for Joint Multi-view Aligned 3D Reconstruction and Pose Estimation

Recent trends in sparse-view 3D reconstruction have taken two different paths: feed-forward reconstruction that predicts pixel-aligned point maps without a complete geometry, and generative 3D reconstruction that generates complete geometry but often with poor input-alignment. We present Mix3R, a novel generative 3D reconstruction method which mixes feed-forward reconstruction and 3D generation into a single framework in an aligned manner. Mix3R generates a 3D shape in two stages: a sparse voxel generation stage and a textured geometry generation stage. Unlike pure generative methods, our first-stage generation jointly produces a coarse 3D structure (sparse voxels), per-view point maps and camera parameters aligned to that 3D structure. This is made possible by introducing a Mixture-of-Transformers architecture that inserts global self-attentions to a feed-forward reconstruction model and a 3D generative model, both pretrained on large-scale data. This design effectively retains the pretrained priors but enables better 2D-3D alignment. Based on the initial aligned generations of sparse 3D voxels and point maps, we compute an overlap-based attention bias that is directly added to another pretrained textured geometry generation model, enabling it to correctly place input textures onto generated shapes in a training-free manner. Our design brings mutual benefits to both feed-forward reconstruction and 3D generation: The feed-forward branch learns to ground its predictions to a generative 3D prior, and conversely, the 3D generation branch is conditioned on geometrically informative features from the feed-forward branch. As a result, our method produces 3D shapes with better input alignment compared with pure 3D generative methods, together with camera pose estimations more accurate than previous feed-forward reconstruction methods. Our project page is at https://jsnln.github.io/mix3r/

preprint2022arXiv

Computing the Lyapunov operator φ-functions, with an application to matrix-valued exponential integrators

In this paper, we develop efficient and accurate evaluation for the Lyapunov operator function $φ_l(\mathcal{L}_A)[Q],$ where $φ_l(\cdot)$ is the function related to the exponential, $\mathcal{L}_A$ is a Lyapunov operator and $Q$ is a symmetric and full-rank matrix. An important application of the algorithm is to the matrix-valued exponential integrators for matrix differential equations such as differential Lyapunov equations and differential Riccati equations. The method is exploited by using the modified scaling and squaring procedure combined with the truncated Taylor series. A quasi-backward error analysis is presented to determine the value of the scaling parameter and the degree of the Taylor approximation. Numerical experiments show that the algorithm performs well in both accuracy and efficiency.

preprint2021arXiv

Efficient and accurate computation to the $φ$-function and its action on a vector

In this paper, we develop efficient and accurate algorithms for evaluating $φ(A)$ and $φ(A)b$, where $A$ is an $N\times N$ matrix, $b$ is an $N$ dimensional vector and $φ$ is the function defined by $φ(x)\equiv\sum\limits^{\infty}_{k=0}\frac{z^k}{(1+k)!}$. Such matrix function (the so-called $φ$-function) plays a key role in a class of numerical methods well-known as exponential integrators. The algorithms use the scaling and modified squaring procedure combined with truncated Taylor series. The backward error analysis is presented to find the optimal value of the scaling and the degree of the Taylor approximation. Some useful techniques are employed for reducing the computational cost. Numerical comparisons with state-of-the-art algorithms show that the algorithms perform well in both accuracy and efficiency.