ceres-solver/ceres-solver
Ceres Solver
Ceres Solver 是一个 C++ 数值优化库，专注于非线性最小二乘法和无约束优化问题。它作为一个自动微分和鲁棒曲线拟合框架，提供了求解大规模数学模型的工具。
该库以其光束法平差 (bundle adjustment) 能力而著称，利用稀疏矩阵结构来优化 3D 场景点和相机参数。它利用双数自动微分来计算代价函数的导数，无需手动推导雅可比矩阵。
该项目涵盖了广泛的优化功能，包括非欧几里得空间的流形约束、用于减轻异常值的鲁棒损失函数，以及稠密和稀疏线性系统求解。它还提供了用于旋转表示转换、表格数据插值和参数协方差估计的实用工具。
提供针对 Android 和 iOS 目标的构建配置，以支持移动硬件优化。
Features
- Bundle Adjustment Algorithms - Provides specialized algorithms for refining 3D coordinates and camera poses by exploiting sparse matrix structures via the Schur complement.
- Non-Linear Optimizers - Implements a high-performance solver for minimizing sums of squared non-linear functions in large-scale mathematical models.
- Automatic Differentiation - Provides a framework for computing exact derivatives of cost functions automatically using dual-number differentiation.
- Non-linear Problem Solvers - Provides a solver for large-scale non-linear least squares and unconstrained optimization problems using trust-region methods.
- Cost Functions - Computes residuals and Jacobian matrices for terms in an objective function using multiple differentiation schemes.
- Robust - Modifies the contribution of residuals using weight functions to prevent outliers from dominating the total cost.
- Pose Graph Optimizations - Provides techniques for optimizing pose graphs to align 3D point clouds and trajectory data while minimizing sensor drift.
- Local Parameterizations - Defines local parameterizations to constrain parameters to specific spaces such as quaternions or lines.
- Manifold Constraints - Restricts optimization variables to non-Euclidean spaces like spheres or quaternions to maintain geometric constraints.
- Sparse Linear Algebra Routines - Integrates high-performance sparse linear algebra routines to solve large systems of equations efficiently.
- Numerical Optimization Libraries - Provides a high-performance C++ toolkit for numerical optimization, linear algebra, and manifold parameterization.
- Numerical Computation Optimizers - Calculates the gradient of objective functions using analytic formulas, finite differences, or automatic differentiation.
- Problem Modeling - Implements a system for assembling optimization problems by connecting cost functions and loss functions to specific parameter blocks.
- Manifold Parameterization - Handles non-Euclidean variables by mapping them to a tangent space for updates and projecting them back to the manifold.
- Trust-Region Methods - Iteratively approximates the objective function with a quadratic model and restricts the step size to a safe region.
- Cost Function Composition - Allows wrapping cost functions into functors to mix analytic, numeric, and automatic differentiation within a single composition.
- Numerical Gradient Approximations - Approximates Jacobians using finite difference methods when analytic derivatives are unavailable.
- Iterative Refinement - Casts linear systems to single precision for speed and applies iterative refinement to maintain numerical accuracy.
- Sensor Calibration - Estimates intrinsic and extrinsic characteristics of cameras and IMUs to ensure accurate spatial measurements.
- Robust - Ships robust loss functions to prevent anomalous data points from biasing the curve fitting results.
- Bound Constraints - Enforces upper and lower limits on parameters during the trust region minimization process.
- Dense Linear System Solvers - Executes fast dense linear solves using QR, Cholesky, or Schur decompositions.
- Schur Decompositions - Employs Schur complement decomposition to exploit sparsity patterns and reduce the dimensionality of bundle adjustment linear systems.
- Numerical Derivative Estimations - Ceres Solver estimates Jacobians using finite differencing schemes for functions where analytic derivatives are not available.
- Preconditioned Iterative Solvers - Improves the convergence rate of iterative solvers using specialized preconditioning expansion techniques.
- Dynamic Sparsity Management - Optimizes memory and computation when the structural patterns of data change during the optimization process.
- Optimization Solvers - Large scale nonlinear optimization library.
- Numerical Optimization Solvers - Large-scale non-linear least squares optimization library.
- Optimization Libraries - C++ library for large-scale nonlinear optimization problems.
- Robotics Libraries - Library for modeling and solving complex optimization problems.
