ceres-solver/ceres-solver
Ceres Solver
Ceres Solver is a C++ library for numerical optimization, specializing in non-linear least squares and unconstrained optimization problems. It serves as a framework for automatic differentiation and robust curve fitting, providing tools to solve large-scale mathematical models.
The library is distinguished by its bundle adjustment capabilities, which exploit sparse matrix structures to refine 3D scene points and camera parameters. It utilizes dual-number automatic differentiation to compute derivatives of cost functions, removing the need for manual Jacobian derivation.
The project covers a broad range of optimization capabilities, including manifold constraints for non-Euclidean spaces, robust loss functions to mitigate outliers, and both dense and sparse linear system solving. It also provides utilities for rotation representation conversion, tabulated data interpolation, and parameter covariance estimation.
Build configurations are available for Android and iOS targets to support mobile hardware optimization.
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.
