We present HexOpt , a novel software package designed to optimize hexahedral mesh quality through a Rectified Hybrid Quadratic Jacobian energy functional and geometry-aware mapping. HexOpt accepts a triangular surface mesh and a volumetric hexahedral mesh as inputs. To overcome critical challenges such as element size-dependent gradient biases, prolonged optimization times, and erroneous boundary projection, we formulate a constrained optimization problem. The Rectified Hybrid Quadratic Jacobian energy is set as the objective function, while equality constraints enforce precise alignment between the quadrilateral boundary and the input geometry. These constraints fix vertices at geometric corners, restrict edge points to edges, and map face points to triangular faces. The optimization is solved via the Augmented Lagrangian method, with the Limited-Broyden–Fletcher–Goldfarb–Shanno method and the Armijo line search method driving the iterative process. The geometry-aware mapping employs normal-guided closest-point projection and mean value Tutte embedding to ensure geometric fidelity. HexOpt demonstrates robust performance across diverse 3D models and hexahedral meshes generated by various methods. It achieves consistent quality improvements without requiring manual intervention or parameter tuning compared with the initial state. Experimental results validate its computational efficiency and robustness in complex geometries, underscoring its utility as a reliable post-processing tool for hexahedral mesh optimization. We provide the HexOpt source code, input/output meshes (around 100 examples), and statistical data in the repository: https://github.com/CMU-CBML/HexOpt .

Conforming hex meshes are widely regarded as an effective computational domain for simulation because of their nice numerical properties, yet automatically decomposing a general 3D volume into a conforming hex mesh remains a formidable challenge. Among existing approaches, methods that construct an adaptive Cartesian grid and subsequently convert it into a conforming mesh stand out for their robustness. However, topological conversion schemes require strict compatibility conditions that inevitably increase element count. State-of-the-art 2-refinement octree methods employ weakly-balanced and generalized pairing conditions to yield low element counts, but suffer from critical limitations: primal cell information is lost after dualization, and resulting dual cells often exhibit non-planar quad faces. Alternatively, 3-refinement 27-tree methods directly generate conforming hex meshes through template-based replacement, producing higher-quality elements with planar faces, but previous techniques impose far stricter conditions, severely over-refining grids by factors of ten to one hundred. This article introduces a novel 3-refinement approach using a moderately-balanced condition, slightly stronger than weakly-balanced but substantially more relaxed than prior 3-refinement requirements. The key insight is that recursively applying local refinements can isolate and reduce complex configurations to simpler cases covered by a fundamental template set. Two open-sourced variants are provided: one optimized for speed, and another trading some computational cost for marginally reduced element counts. Compared to previous 3-refinement methods, they significantly reduce final hex element counts while preserving min SJ values and guaranteeing convex polyhedral cells; relative to 2-refinement state-of-the-art, they also achieve a lower Hausdorff ratio using slightly fewer elements.

Accurate segmentation of anatomical substructures within 3D curvilinear structures in medical imaging remains challenging due to their complex geometry and the scarcity of diverse, large-scale datasets for algorithm development and evaluation. In this paper, we use dendritic spine segmentation as a case study and address these challenges by introducing a novel Frenet-Serret Frame-based Decomposition, which decomposes 3D curvilinear structures into a globally smooth continuous curve that captures the overall shape, and a cylindrical primitive that encodes local geometric properties. This approach leverages Frenet-Serret Frames and arc length parameterization to preserve essential geometric features while reducing representational complexity, facilitating data-efficient learning, improved segmentation accuracy, and generalization on 3D curvilinear structures. To rigorously evaluate our method, we introduce two datasets: CurviSeg, a synthetic dataset for 3D curvilinear structure segmentation that validates our method's key properties, and DenSpineEM, a benchmark for dendritic spine segmentation, which comprises 4,476 manually annotated spines from 70 dendrites across three public electron microscopy datasets, covering multiple brain regions and species. Our experiments on DenSpineEM demonstrate exceptional cross-region and cross-species generalization: models trained on the mouse somatosensory cortex subset achieve 94.43% Dice, maintaining strong performance in zero-shot segmentation on both mouse visual cortex (95.61% Dice) and human frontal lobe (86.63% Dice) subsets. Moreover, we test the generalizability of our method on the IntrA dataset, where it achieves 77.08% Dice (5.29% higher than prior arts) on intracranial aneurysm segmentation from entire artery models. These findings demonstrate the potential of our approach for accurately analyzing complex curvilinear structures across diverse medical imaging fields. Our dataset, code, and models are available at https://github.com/VCG/FFD4DenSpineEM to support future research.

Elasticity is one of therepresentative parameters that reflect the mechanical properties of soft materials. Detecting the underneath elasticity distribution called elastography is a key step for understanding and interacting with objects. Existing solutions for capturing the interior elasticity distribution typically rely on expensive apparatus. In this work, the dense tactile signal captured by the high-resolution vision-based tactile sensor is introduced as a new modality for reconstructing 3D elasticity distribution. We propose a model-based method, which exploits the tactile maps from active pressing trials for the elastography task. The interior elasticity distribution for non-rigid objects is reconstructed from an inverse physics model. We analyze the credibility of the estimated elasticity distribution obtained from our method. Varying design factors are also discussed. We experiment our method on a set of synthesized 3D models and physical models in robot-assisted scenes. Various experimental results have been gathered, demonstrating the efficacy of our approach in perceiving elasticity distribution.

Automatic rib labeling and anatomical centerline extraction are common prerequisites for various clinical applications. Prior studies either use in-house datasets that are inaccessible to communities, or focus on rib segmentation that neglects the clinical significance of rib labeling. To address these issues, we extend our prior dataset (RibSeg) on the binary rib segmentation task to a comprehensive benchmark, named RibSeg v2, with 660 CT scans (15,466 individual ribs in total) and annotations manually inspected by experts for rib labeling and anatomical centerline extraction. Based on the RibSeg v2, we develop a pipeline including deep learning-based methods for rib labeling, and a skeletonization-based method for centerline extraction. To improve computational efficiency, we propose a sparse point cloud representation of CT scans and compare it with standard dense voxel grids. Moreover, we design and analyze evaluation metrics to address the key challenges of each task. Our dataset, code, and model are available online to facilitate open research at https://github.com/M3DV/RibSeg.

Mesh-based image warping techniques typically represent image deformation using linear functions on triangular meshes or bilinear functions on rectangular meshes. This enables simple and efficient implementation, but in turn, restricts the representation capability of the deformation, often leading to unsatisfactory warping results. We present a novel, flexible polygonal finite element (poly-FEM) method for content-aware image warping. Image deformation is represented by high-order poly-FEMs on a content-aware polygonal mesh with a cell distribution adapted to saliency information in the source image. This allows highly adaptive meshes and smoother warping with fewer degrees of freedom, thus significantly extending the flexibility and capability of the warping representation. Benefiting from the continuous formulation of image deformation, our poly-FEM warping method is able to compute the optimal image deformation by minimizing existing or even newly designed warping energies consisting of penalty terms for specific transformations. We demonstrate the versatility of the proposed poly-FEM warping method in representing different deformations and its superiority by comparing it to other existing state-of-the-art methods.

Vector image representation methods that can faithfully reconstruct objects and color variations in a raster image are desired in many practical applications. This article presents triangular configuration B-spline (referred to as TCB-spline)-based vector graphics for raster image vectorization. Based on this new representation, an automatic raster image vectorization paradigm is proposed. The proposed framework first detects sharp curvilinear features in the image and constructs knot meshes based on the detected feature lines. It iteratively optimizes color and position of control points and updates the knot meshes. By using collinear knots at feature lines, both smooth and discontinuous color variations can be efficiently modeled by the same set of quadratic TCB-splines. A variational knot mesh generation method is designed to adaptively introduce knots and update their connectivity to satisfy the local reconstruction quality. Experiments and comparisons show that our framework outperforms the existing state-of-the-art methods in providing more faithful reconstruction results. In particular, our method is able to model undetected features and subtle or complicated color variations in-between features, which the previous methods cannot handle efficiently. Our vectorization representation also facilitates a variety of editing operations performed directly over vector images.

Triangle meshes are used in many important shape-related applications including geometric modeling, animation production, system simulation, and visualization. However, these meshes are typically generated in raw form with several defects and poor-quality elements, obstructing them from practical application. Over the past decades, different surface remeshing techniques have been presented to improve these poor-quality meshes prior to the downstream utilization. A typical surface remeshing algorithm converts an input mesh into a higher quality mesh with consideration of given quality requirements as well as an acceptable approximation to the input mesh. In recent years, surface remeshing has gained significant attention from researchers and engineers, and several remeshing algorithms have been proposed. However, there has been no survey article on remeshing methods in general with a defined search strategy and article selection mechanism covering the recent approaches in surface remeshing domain with a good connection to classical approaches. In this article, we present a survey on surface remeshing techniques, classifying all collected articles in different categories and analyzing specific methods with their advantages, disadvantages, and possible future improvements. Following the systematic literature review methodology, we define step-by-step guidelines throughout the review process, including search strategy, literature inclusion/exclusion criteria, article quality assessment, and data extraction. With the aim of literature collection and classification based on data extraction, we summarized collected articles, considering the key remeshing objectives, the way the mesh quality is defined and improved, and the way their techniques are compared with other previous methods. Remeshing objectives are described by angle range control, feature preservation, error control, valence optimization, and remeshing compatibility. The metrics used in the literature for the evaluation of surface remeshing algorithms are discussed. Meshing techniques are compared with other related methods via a comprehensive table with indices of the method name, the remeshing challenge met and solved, the category the method belongs to, and the year of publication. We expect this survey to be a practical reference for surface remeshing in terms of literature classification, method analysis, and future prospects.

Morphing materials allow us to create new modalities of interaction and fabrication by leveraging the materials? dynamic behaviors. Yet, despite the ongoing rapid growth of computational tools within this realm, current developments are bottlenecked by the lack of an effective simulation method. As a result, existing design tools must trade-off between speed and accuracy to support a real-time interactive design scenario. In response, we introduce SimuLearn, a data-driven method that combines finite element analysis and machine learning to create real-time (0.61 seconds) and truthful (97% accuracy) morphing material simulators. We use mesh-like 4D printed structures to contextualize this method and prototype design tools to exemplify the design workflows and spaces enabled by a fast and accurate simulation method. Situating this work among existing literature, we believe SimuLearn is a timely addition to the HCI CAD toolbox that can enable the proliferation of morphing materials.

Four-dimensional (4D) printing, a new technology emerged from additive manufacturing (3D printing), is widely known for its capability of programming post-fabrication shape-changing into artifacts. Fused deposition modeling (FDM)-based 4D printing, in particular, uses thermoplastics to produce artifacts and requires computational analysis to assist the design processes of complex geometries. However, these artifacts are weak against structural loads, and the design quality can be limited by less accurate material models and numerical simulations. To address these issues, this paper propounds a composite structure design made of two materials – polylactic acid (PLA) and carbon fiber reinforced PLA (CFPLA) – to increase the structural strength of 4D printed artifacts and a workflow composed of several physical experiments and series of dynamic mechanical analysis (DMA) to characterize materials. We apply this workflow to 3D printed samples fabricated with different printed parameters to accurately characterize the materials and implement a sequential finite element analysis (FEA) to achieve accurate simulations. The accuracy of deformation induced by the triggering process is both computationally and experimentally verified with several creative design examples and is measured to be at least 95%, with a confidence interval of (0.972,0.985). We believe the presented workflow is essential to the combination of geometry, material mechanism and design, and has various potential applications.

Prediction of the likely evolution of traffic scenes is a challenging task because of high uncertainties from sensing technology and the dynamic environment. It leads to failure of motion planning for intelligent agents like autonomous vehicles. In this paper, we propose a fluid-inspired model to estimate collision risk in road scenes. Multi-object states are detected and tracked, and then a stable fluid model is adopted to construct the risk field. Objects’ state spaces are used as the boundary conditions in the simulation of advection and diffusion processes. We have evaluated our approach on the public KITTI dataset; our model can provide predictions in the cases of misdetection and tracking error caused by occlusion. It proves a promising approach for collision risk assessment in road scenes.

Thermoplastic and Fused Deposition Modeling (FDM) based 4D printing are rapidly expanding to allow for space- and material-saving 2D printed sheets morphing into 3D shapes when heated. However, to our knowledge, all the known examples are either origami-based models with obvious folding hinges, or beam-based models with holes on the morphing surfaces. Morphing continuous double-curvature surfaces remains a challenge, both in terms of a tailored toolpath-planning strategy and a computational model that simulates it. Additionally, neither approach takes surface texture as a design parameter in its computational pipeline. To extend the design space of FDM-based 4D printing, in Geodesy, we focus on the morphing of continuous double-curvature surfaces or surface textures. We suggest a unique tool path - printing thermoplastics along 2D closed geodesic paths to form a surface with one raised continuous double-curvature tiles when exposed to heat. The design space is further extended to more complex geometries composed of a network of rising tiles (i.e., surface textures). Both design components and the computational pipeline are explained in the paper, followed by several printed geometric examples.

Sensing and presenting on-road information of moving vehicles is essential for fully and semi-automated driving. It is challenging to track vehicles from affordable on-board cameras in crowded scenes. The mismatch or missing data are unavoidable and it is ineffective to directly present uncertain cues to support the decision-making. In this paper, we propose a physical model based on incompressible fluid dynamics to represent the vehicle’s motion, which provides hints of possible collision as a continuous scalar riskmap. We estimate the position and velocity of other vehicles from a monocular on-board camera located in front of the ego-vehicle. The noisy trajectories are then modeled as the boundary conditions in the simulation of advection and diffusion process. We then interactively display the animating distribution of substances, and show that the continuous scalar riskmap well matches the perception of vehicles even in presence of the tracking failures. We test our method on real-world scenes and discuss about its application for driving assistance and autonomous vehicle in the future.

Neurons depend critically on active transport of cargoes throughout their complex neurite networks for their survival and function. Defects in this process have been strongly associated with many human neurodevelopmental and neurodegenerative diseases. To understand related neuronal physiology and disease mechanisms, it is essential to measure the traffic flow within the neurite networks. Currently, however, image analysis methods required for this measurement are lacking. To address this deficiency, we developed a method that could measure the flow rates of cargo traffic at any specified locations along individual branches of the neurite networks. Our method is based on detecting and counting cargo trajectories passing through the specified locations of measurement in kymographs, which are spatiotemporal maps of cargo movement within one-dimensional neurites. A main focus of our method development is robust performance, which ensures that our method works reliably and accurately under low signal-to-noise ratios. We validated and benchmarked our method using both synthetic and actual image data and found its accuracy to be >85% on average under normal conditions. Our method can be used to measure traffic flow in not just neurite networks but also other intracellular networks such as cytoskeletal filament networks.

MOTIVATION: Quantitative shape analysis is required by a wide range of biological studies across diverse scales, ranging from molecules to cells and organisms. In particular, high-throughput and systems-level studies of biological structures and functions have started to produce large volumes of complex high-dimensional shape data. Analysis and understanding of high-dimensional biological shape data require dimension-reduction techniques. RESULTS: We have developed a technique for non-linear dimension reduction of 2D and 3D biological shape representations on their Riemannian spaces. A key feature of this technique is that it preserves distances between different shapes in an embedded low-dimensional shape space. We demonstrate an application of this technique by combining it with non-linear mean-shift clustering on the Riemannian spaces for unsupervised clustering of shapes of cellular organelles and proteins. AVAILABILITY AND IMPLEMENTATION: Source code and data for reproducing results of this article are freely available at https://github.com/ccdlcmu/shape_component_analysis_Matlab The implementation was made in MATLAB and supported on MS Windows, Linux and Mac OS. CONTACT: [email protected].