arXiv subjects

Paul Zhang

Publications and source records attributed to Paul Zhang.

13 recordsLinked to original sources

arXiv2026

World Tracing: Generative Pixel-Aligned Geometry Beyond the Visible

Image-to-3D methods often trade off faithfulness and completeness: depth estimators are anchored to input pixels but stop at the visible surface, while image-to-3D models generate complete shapes that are often misaligned with the input. We introduce World Tracing, a generative pixel-aligned geometry representation that predicts 3D points aligned with observed pixels while completing geometry beyond the visible surface. For each input pixel, World Tracing predicts an ordered stack of camera-space 3D points, where the first layer represents the visible surface and subsequent layers represent front-to-back intersections with occluded surfaces. We instantiate this representation with a world-tracing diffusion transformer, WT-DiT, which treats multiple geometry layers as separate denoising tokens coupled through factorized and global attention. WT-DiT is trained with pixel-space flow matching and a mixed noise schedule that balances visible-surface reconstruction with occluded-geometry generation. World Tracing achieves strong performance on visible-surface reconstruction and complete geometry generation across object, scene, and dynamic benchmarks, outperforming both depth predictors and image-to-3D generators. It also preserves 2D-to-3D correspondence, enabling text-driven 3D scene editing, geometry-conditioned novel-view video synthesis, and training-free integration with textured-mesh generators.

cs.CV↗

arXiv2024

Symmetry-Robust 3D Orientation Estimation

Orientation estimation is a fundamental task in 3D shape analysis which consists of estimating a shape's orientation axes: its side-, up-, and front-axes. Using this data, one can rotate a shape into canonical orientation, where its orientation axes are aligned with the coordinate axes. Developing an orientation algorithm that reliably estimates complete orientations of general shapes remains an open problem. We introduce a two-stage orientation pipeline that achieves state of the art performance on up-axis estimation and further demonstrate its efficacy on full-orientation estimation, where one seeks all three orientation axes. Unlike previous work, we train and evaluate our method on all of Shapenet rather than a subset of classes. We motivate our engineering contributions by theory describing fundamental obstacles to orientation estimation for rotationally-symmetric shapes, and show how our method avoids these obstacles.

cs.CV↗

arXiv2024

Segment Any Mesh

We propose Segment Any Mesh, a novel zero-shot mesh part segmentation method that overcomes the limitations of shape analysis-based, learning-based, and contemporary approaches. Our approach operates in two phases: multimodal rendering and 2D-to-3D lifting. In the first phase, multiview renders of the mesh are individually processed through Segment Anything to generate 2D masks. These masks are then lifted into a mesh part segmentation by associating masks that refer to the same mesh part across the multiview renders. We find that applying Segment Anything to multimodal feature renders of normals and shape diameter scalars achieves better results than using only untextured renders of meshes. By building our method on top of Segment Anything, we seamlessly inherit any future improvements made to 2D segmentation. We compare our method with a robust, well-evaluated shape analysis method, Shape Diameter Function, and show that our method is comparable to or exceeds its performance. Since current benchmarks contain limited object diversity, we also curate and release a dataset of generated meshes and use it to demonstrate our method's improved generalization over Shape Diameter Function via human evaluation. We release the code and dataset at https://github.com/gtangg12/samesh

cs.CV↗

arXiv2024

Decomposed Prompting to Answer Questions on a Course Discussion Board

We propose and evaluate a question-answering system that uses decomposed prompting to classify and answer student questions on a course discussion board. Our system uses a large language model (LLM) to classify questions into one of four types: conceptual, homework, logistics, and not answerable. This enables us to employ a different strategy for answering questions that fall under different types. Using a variant of GPT-3, we achieve $81\%$ classification accuracy. We discuss our system's performance on answering conceptual questions from a machine learning course and various failure modes.

cs.CL↗

arXiv2024

Multi-modality Regional Alignment Network for Covid X-Ray Survival Prediction and Report Generation

In response to the worldwide COVID-19 pandemic, advanced automated technologies have emerged as valuable tools to aid healthcare professionals in managing an increased workload by improving radiology report generation and prognostic analysis. This study proposes Multi-modality Regional Alignment Network (MRANet), an explainable model for radiology report generation and survival prediction that focuses on high-risk regions. By learning spatial correlation in the detector, MRANet visually grounds region-specific descriptions, providing robust anatomical regions with a completion strategy. The visual features of each region are embedded using a novel survival attention mechanism, offering spatially and risk-aware features for sentence encoding while maintaining global coherence across tasks. A cross LLMs alignment is employed to enhance the image-to-text transfer process, resulting in sentences rich with clinical detail and improved explainability for radiologist. Multi-center experiments validate both MRANet's overall performance and each module's composition within the model, encouraging further advancements in radiology report generation research emphasizing clinical interpretation and trustworthiness in AI models applied to medical studies. The code is available at https://github.com/zzs95/MRANet.

eess.IV↗

arXiv2024

Region-specific Risk Quantification for Interpretable Prognosis of COVID-19

The COVID-19 pandemic has strained global public health, necessitating accurate diagnosis and intervention to control disease spread and reduce mortality rates. This paper introduces an interpretable deep survival prediction model designed specifically for improved understanding and trust in COVID-19 prognosis using chest X-ray (CXR) images. By integrating a large-scale pretrained image encoder, Risk-specific Grad-CAM, and anatomical region detection techniques, our approach produces regional interpretable outcomes that effectively capture essential disease features while focusing on rare but critical abnormal regions. Our model's predictive results provide enhanced clarity and transparency through risk area localization, enabling clinicians to make informed decisions regarding COVID-19 diagnosis with better understanding of prognostic insights. We evaluate the proposed method on a multi-center survival dataset and demonstrate its effectiveness via quantitative and qualitative assessments, achieving superior C-indexes (0.764 and 0.727) and time-dependent AUCs (0.799 and 0.691). These results suggest that our explainable deep survival prediction model surpasses traditional survival analysis methods in risk prediction, improving interpretability for clinical decision making and enhancing AI system trustworthiness.

cs.CV↗

arXiv2022

Wassersplines for Neural Vector Field--Controlled Animation

Much of computer-generated animation is created by manipulating meshes with rigs. While this approach works well for animating articulated objects like animals, it has limited flexibility for animating less structured free-form objects. We introduce Wassersplines, a novel trajectory inference method for animating unstructured densities based on recent advances in continuous normalizing flows and optimal transport. The key idea is to train a neurally-parameterized velocity field that represents the motion between keyframes. Trajectories are then computed by advecting keyframes through the velocity field. We solve an additional Wasserstein barycenter interpolation problem to guarantee strict adherence to keyframes. Our tool can stylize trajectories through a variety of PDE-based regularizers to create different visual effects. We demonstrate our tool on various keyframe interpolation problems to produce temporally-coherent animations without meshing or rigging.

cs.GR↗

arXiv2022

Local Decomposition of Hexahedral Singular Nodes into Singular Curves

Hexahedral (hex) meshing is a long studied topic in geometry processing with many fascinating and challenging associated problems. Hex meshes vary in complexity from structured to unstructured depending on application or domain of interest. Fully structured meshes require that all interior mesh edges are adjacent to exactly four hexes. Edges not satisfying this criteria are considered singular and indicate an unstructured hex mesh. Singular edges join together into singular curves that either form closed cycles, end on the mesh boundary, or end at a singular node, a complex junction of more than two singular curves. While all hex meshes with singularities are unstructured, those with more complex singular nodes tend to have more distorted elements and smaller scaled Jacobian values. In this work, we study the topology of singular nodes. We show that all eight of the most common singular nodes are decomposable into just singular curves. We further show that all singular nodes, regardless of edge valence, are locally decomposable. Finally we demonstrate these decompositions on hex meshes, thereby decreasing their distortion and converting all singular nodes into singular curves. With this decomposition, the enigmatic complexity of 3D singular nodes becomes effectively 2D.

cs.CG↗

arXiv2021

Sum-of-Squares Geometry Processing

Geometry processing presents a variety of difficult numerical problems, each seeming to require its own tailored solution. This breadth is largely due to the expansive list of geometric primitives, e.g., splines, triangles, and hexahedra, joined with an ever-expanding variety of objectives one might want to achieve with them. With the recent increase in attention toward higher-order surfaces, we can expect a variety of challenges porting existing solutions that work on triangle meshes to work on these more complex geometry types. In this paper, we present a framework for solving many core geometry processing problems on higher-order surfaces. We achieve this goal through sum-of-squares optimization, which transforms nonlinear polynomial optimization problems into sequences of convex problems whose complexity is captured by a single degree parameter. This allows us to solve a suite of problems on higher-order surfaces, such as continuous collision detection and closest point queries on curved patches, with only minor changes between formulations and geometries.

cs.CG↗

arXiv2021

Interactive All-Hex Meshing via Cuboid Decomposition

Standard PolyCube-based hexahedral (hex) meshing methods aim to deform the input domain into an axis-aligned PolyCube volume with integer corners; if this deformation is bijective, then applying the inverse map to the voxelized PolyCube yields a valid hex mesh. A key challenge in these methods is to maintain the bijectivity of the PolyCube deformation, thus reducing the robustness of these algorithms. In this work, we present an interactive pipeline for hex meshing that sidesteps this challenge by using a new representation of PolyCubes as unions of cuboids. We begin by deforming the input tetrahedral mesh into a near-PolyCube domain whose faces are close but not perfectly aligned to the major axis directions. We then build a PolyCube by optimizing the layout of a set of cuboids with user guidance to closely fit the deformed domain. Finally, we construct an inversion-free pullback map from the voxelized PolyCube to the input domain while optimizing for mesh quality metrics. We allow extensive user control over each stage, such as editing the voxelized PolyCube, positioning surface vertices, and exploring the trade-off among competing quality metrics, while also providing automatic alternatives. We validate our method on over one hundred shapes, including models that are challenging for past PolyCube-based and frame-field-based methods. Our pipeline reliably produces hex meshes with quality on par with or better than state-of-the-art. We additionally conduct a user study with 20 participants in which the majority prefer hex meshes they make using our tool to the ones from automatic state-of-the-art methods. This demonstrates the need for intuitive interactive hex meshing tools where the user can dictate the priorities of their mesh.

cs.GR↗

arXiv2020

Octahedral Frames for Feature-Aligned Cross-Fields

We present a method for designing smooth cross fields on surfaces that automatically align to sharp features of an underlying geometry. Our approach introduces a novel class of energies based on a representation of cross fields in the spherical harmonic basis. We provide theoretical analysis of these energies in the smooth setting, showing that they penalize deviations from surface creases while otherwise promoting intrinsically smooth fields. We demonstrate the applicability of our method to quad-meshing and include an extensive benchmark comparing our fields to other automatic approaches for generating feature-aligned cross fields on triangle meshes.

cs.GR↗

arXiv2020

Medial Axis Isoperimetric Profiles

Recently proposed as a stable means of evaluating geometric compactness, the isoperimetric profile of a planar domain measures the minimum perimeter needed to inscribe a shape with prescribed area varying from 0 to the area of the domain. While this profile has proven valuable for evaluating properties of geographic partitions, existing algorithms for its computation rely on aggressive approximations and are still computationally expensive. In this paper, we propose a practical means of approximating the isoperimetric profile and show that for domains satisfying a "thick neck" condition, our approximation is exact. For more general domains, we show that our bound is still exact within a conservative regime and is otherwise an upper bound. Our method is based on a traversal of the medial axis which produces efficient and robust results. We compare our technique with the state-of-the-art approximation to the isoperimetric profile on a variety of domains and show significantly tighter bounds than were previously achievable.

cs.CG↗

arXiv2014

Quantum Strongly Secure Ramp Secret Sharing

Quantum secret sharing is a scheme for encoding a quantum state (the secret) into multiple shares and distributing them among several participants. If a sufficient number of shares are put together, then the secret can be fully reconstructed. If an insufficient number of shares are put together however, no information about the secret can be revealed. In quantum ramp secret sharing, partial information about the secret is allowed to leak to a set of participants, called an unqualified set, that cannot fully reconstruct the secret. By allowing this, the size of a share can be drastically reduced. This paper introduces a quantum analog of classical strong security in ramp secret sharing schemes. While the ramp secret sharing scheme still leaks partial information about the secret to unqualified sets of participants, the strong security condition ensures that qudits with critical information can no longer be leaked.

quant-ph↗