skip to main content


Title: Computing Medial Axis Transform with Feature Preservation via Restricted Power Diagram
We propose a novel framework for computing the medial axis transform of 3D shapes while preserving their medial features via restricted power diagram (RPD). Medial features, including external features such as the sharp edges and corners of the input mesh surface and internal features such as the seams and junctions of medial axis, are important shape descriptors both topologically and geometrically. However, existing medial axis approximation methods fail to capture and preserve them due to the fundamentally under-sampling in the vicinity of medial features, and the difficulty to build their correct connections. In this paper we use the RPD of medial spheres and its affiliated structures to help solve these challenges. The dual structure of RPD provides the connectivity of medial spheres. The surfacic restricted power cell (RPC) of each medial sphere provides the tangential surface regions that these spheres have contact with. The connected components (CC) of surfacic RPC give us the classification of each sphere, to be on a medial sheet, a seam, or a junction. They allow us to detect insufficient sphere sampling around medial features and develop necessary conditions to preserve them. Using this RPD-based framework, we are able to construct high quality medial meshes with features preserved. Compared with existing sampling-based or voxel-based methods, our method is the first one that can preserve not only external features but also internal features of medial axes.  more » « less
Award ID(s):
2007661
NSF-PAR ID:
10424870
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
ACM Transactions on Graphics
Volume:
41
Issue:
6
ISSN:
0730-0301
Page Range / eLocation ID:
1 to 18
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. null (Ed.)
    Learning pose invariant representation is a fundamental problem in shape analysis. Most existing deep learning algorithms for 3D shape analysis are not robust to rotations and are often trained on synthetic datasets consisting of pre-aligned shapes, yielding poor generalization to unseen poses. This observation motivates a growing interest in rotation invariant and equivariant methods. The field of rotation equivariant deep learning is developing in recent years thanks to a well established theory of Lie group representations and convolutions. A fundamental problem in equivariant deep learning is to design activation functions which are both informative and preserve equivariance. The recently introduced Tensor Field Network (TFN) framework provides a rotation equivariant network design for point cloud analysis. TFN features undergo a rotation in feature space given a rotation of the input pointcloud. TFN and similar designs consider nonlinearities which operate only over rotation invariant features such as the norm of equivariant features to preserve equivariance, making them unable to capture the directional information. In a recent work entitled "Gauge Equivariant Mesh CNNs: Anisotropic Convolutions on Geometric Graphs" Hann et al. interpret 2D rotation equivariant features as Fourier coefficients of functions on the circle. In this work we transpose the idea of Hann et al. to 3D by interpreting TFN features as spherical harmonics coefficients of functions on the sphere. We introduce a new equivariant nonlinearity and pooling for TFN. We show improvments over the original TFN design and other equivariant nonlinearities in classification and segmentation tasks. Furthermore our method is competitive with state of the art rotation invariant methods in some instances. 
    more » « less
  2. We introduce FINCH, a Julia-based domain specific language (DSL) for solving partial differential equations in a discretization agnostic way, currently including finite element and finite volume methods. A key focus is code generation for various internal or external software targets. Internal targets use a modular set of tools in Julia providing a direct solution within the framework. In contrast, external code generation produces a set of code files to be compiled and run with external libraries or frameworks. Examples include a matlab target, for smaller problems or prototyping, or C++/MPI based targets for larger problems needing scalability. This allows us to take advantage of their capabilities without needlessly duplicating them, and provides options tailored to the needs of the domain scientist. The modular design of FINCH allows ongoing development of these target modules resulting in a more extensible framework and a broader set of applications. The support for multiple discretizations, including finite element and finite volume methods, also contributes to this goal. Another focus of this project is complex systems containing a large set of coupled PDEs that could be challenging to efficiently code and optimize by hand, but that are relatively simple to specify using the DSL. In this paper we present the key features of FINCH that set it apart from many other DSL options, and demonstrate the basic usage and current capabilities through examples. 
    more » « less
  3. null (Ed.)
    Context. Over the past decades, several interplanetary missions have studied small bodies in situ, leading to major advances in our understanding of their geological and geophysical properties. These missions, however, have had a limited number of targets. Among them, the NASA Dawn mission has characterised in detail the topography and albedo variegation across the surface of asteroid (4) Vesta down to a spatial resolution of ~20 m pixel −1 scale. Aims. Here our aim was to determine how much topographic and albedo information can be retrieved from the ground with VLT/SPHERE in the case of Vesta, having a former space mission (Dawn) providing us with the ground truth that can be used as a benchmark. Methods. We observed Vesta with VLT/SPHERE/ZIMPOL as part of our ESO large programme (ID 199.C-0074) at six different epochs, and deconvolved the collected images with a parametric point spread function (PSF). We then compared our images with synthetic views of Vesta generated from the 3D shape model of the Dawn mission, on which we projected Vesta’s albedo information. Results. We show that the deconvolution of the VLT/SPHERE images with a parametric PSF allows the retrieval of the main topographic and albedo features present across the surface of Vesta down to a spatial resolution of ~20–30 km. Contour extraction shows an accuracy of ~1 pixel (3.6 mas). The present study provides the very first quantitative estimate of the accuracy of ground-based adaptive-optics imaging observations of asteroid surfaces. Conclusions. In the case of Vesta, the upcoming generation of 30–40 m telescopes (ELT, TMT, GMT) should in principle be able to resolve all of the main features present across its surface, including the troughs and the north–south crater dichotomy, provided that they operate at the diffraction limit. 
    more » « less
  4. The growing adoption of hardware accelerators driven by their intelligent compiler and runtime system counterparts has democratized ML services and precipitously reduced their execution times. This motivates us to shift our attention to efficiently serve these ML services under distributed settings and characterize the overheads imposed by the RPC mechanism (‘RPC tax’) when serving them on accelerators. The RPC implementations designed over the years implicitly assume the host CPU services the requests, and we focus on expanding such works towards accelerator-based services. While recent proposals calling for SmartNICs to take on this task are reasonable for simple kernels, serving complex ML models requires a more nuanced view to optimize both the data-path and the control/orchestration of these accelerators. We program today’s commodity network interface cards (NICs) to split the control and data paths for effective transfer of control while efficiently transferring the payload to the accelerator. As opposed to unified approaches that bundle these paths together, limiting the flexibility in each of these paths, we design and implement SplitRPC - a {control + data} path optimizing RPC mechanism for ML inference serving. SplitRPC allows us to optimize the datapath to the accelerator while simultaneously allowing the CPU to maintain full orchestration capabilities. We implement SplitRPC on both commodity NICs and SmartNICs and demonstrate how GPU-based ML services running different compiler/runtime systems can benefit. For a variety of ML models served using different inference runtimes, we demonstrate that SplitRPC is effective in minimizing the RPC tax while providing significant gains in throughput and latency over existing kernel by-pass approaches, without requiring expensive SmartNIC devices. 
    more » « less
  5. The growing adoption of hardware accelerators driven by their intelligent compiler and runtime system counterparts has democratized ML services and precipitously reduced their execution times. This motivates us to shift our attention to efficiently serve these ML services under distributed settings and characterize the overheads imposed by the RPC mechanism ('RPC tax') when serving them on accelerators. The RPC implementations designed over the years implicitly assume the host CPU services the requests, and we focus on expanding such works towards accelerator-based services. While recent proposals calling for SmartNICs to take on this task are reasonable for simple kernels, serving complex ML models requires a more nuanced view to optimize both the data-path and the control/orchestration of these accelerators. We program today's commodity network interface cards (NICs) to split the control and data paths for effective transfer of control while efficiently transferring the payload to the accelerator. As opposed to unified approaches that bundle these paths together, limiting the flexibility in each of these paths, we design and implement SplitRPC - a control + data path optimizing RPC mechanism for ML inference serving. SplitRPC allows us to optimize the datapath to the accelerator while simultaneously allowing the CPU to maintain full orchestration capabilities. We implement SplitRPC on both commodity NICs and SmartNICs and demonstrate how GPU-based ML services running different compiler/runtime systems can benefit. For a variety of ML models served using different inference runtimes, we demonstrate that SplitRPC is effective in minimizing the RPC tax while providing significant gains in throughput and latency over existing kernel by-pass approaches, without requiring expensive SmartNIC devices. 
    more » « less