Pareto gamuts

Makatura, Liane; Guo, Minghao; Schulz, Adriana; Solomon, Justin; Matusik, Wojciech

doi:10.1145/3450626.3459750

Cited by 3 publications

(1 citation statement)

References 51 publications

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“…Considering multiple configurations can greatly expand the applicability of a particular method [11]. In the case of multi-objective optimization, a Pareto set exists, where progress on any one objective regresses performance on another objective.…”

Section: Introductionmentioning

confidence: 99%

Direct Fitting of Gaussian Mixture Models

Keselman

Hebert

2019

2019 16th Conference on Computer and Robot Vision (CRV)

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When fitting Gaussian Mixture Models to 3D geometry, the model is typically fit to point clouds, even when the shapes were obtained as 3D meshes. Here we present a formulation for fitting Gaussian Mixture Models (GMMs) directly to a triangular mesh instead of using points sampled from its surface. Part of this work analyzes a general formulation for evaluating likelihood of geometric objects. This modification enables fitting higher-quality GMMs under a wider range of initialization conditions. Additionally, models obtained from this fitting method are shown to produce an improvement in 3D registration for both meshes and RGB-D frames. This result is general and applicable to arbitrary geometric objects, including representing uncertainty from sensor measurements.

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Section: Introductionmentioning

confidence: 99%

Direct Fitting of Gaussian Mixture Models

Keselman

Hebert

2019

2019 16th Conference on Computer and Robot Vision (CRV)

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Discovering Multiple Algorithm Configurations

Keselman

Hebert

2023

2023 IEEE International Conference on Robotics and Automation (ICRA)

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TinyAD: Automatic Differentiation in Geometry Processing Made Simple

Schmidt

Born

Bommes

et al. 2022

Computer Graphics Forum

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Non‐linear optimization is essential to many areas of geometry processing research. However, when experimenting with different problem formulations or when prototyping new algorithms, a major practical obstacle is the need to figure out derivatives of objective functions, especially when second‐order derivatives are required. Deriving and manually implementing gradients and Hessians is both time‐consuming and error‐prone. Automatic differentiation techniques address this problem, but can introduce a diverse set of obstacles themselves, e.g. limiting the set of supported language features, imposing restrictions on a program's control flow, incurring a significant run time overhead, or making it hard to exploit sparsity patterns common in geometry processing. We show that for many geometric problems, in particular on meshes, the simplest form of forward‐mode automatic differentiation is not only the most flexible, but also actually the most efficient choice. We introduce TinyAD: a lightweight C++ library that automatically computes gradients and Hessians, in particular of sparse problems, by differentiating small (tiny) sub‐problems. Its simplicity enables easy integration; no restrictions on, e.g., looping and branching are imposed. TinyAD provides the basic ingredients to quickly implement first and second order Newton‐style solvers, allowing for flexible adjustment of both problem formulations and solver details. By showcasing compact implementations of methods from parametrization, deformation, and direction field design, we demonstrate how TinyAD lowers the barrier to exploring non‐linear optimization techniques. This enables not only fast prototyping of new research ideas, but also improves replicability of existing algorithms in geometry processing. TinyAD is available to the community as an open source library.

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Pareto gamuts

Cited by 3 publications

References 51 publications

Direct Fitting of Gaussian Mixture Models

Direct Fitting of Gaussian Mixture Models

Discovering Multiple Algorithm Configurations

TinyAD: Automatic Differentiation in Geometry Processing Made Simple

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