Camera Calibration & Geometry
Mathematical Foundations for Precision Vision
Transform image data into precise measurements through geometric mathematics
sub-pixel accuracy
rotation precision
calibration success
Camera Models & Parameters
I Intrinsic Parameters
Camera Matrix (K)
[ 0 fy cy]
[ 0 0 1]
Distortion Models
E Extrinsic Parameters
Pose Matrix [R|t]
[r₂₁ r₂₂ r₂₃ | ty]
[r₃₁ r₃₂ r₃₃ | tz]
Rotation (R)
- • Euler angles
- • Quaternions
- • Axis-angle
Translation (t)
- • tx: X-axis translation
- • ty: Y-axis translation
- • tz: Z-axis translation
Calibration Techniques
Zhang's Method
Standard method using checkerboard patterns for calibration
- Easy to implement
- High accuracy
- Handles distortion
Bundle Adjustment
Non-linear optimization for maximum accuracy
- Maximum accuracy
- Multi-view support
- Joint optimization
Self-Supervised
Automatic calibration using deep learning
- No calibration pattern
- Automatic process
- Adaptive learning
Stereo Calibration
Dual camera calibration for 3D measurements
- Epipolar geometry
- Depth measurement
- 3D reconstruction
Multi-Camera
Multiple camera networks for comprehensive inspection
- Complete coverage
- Time synchronization
- Global optimization
Real-time Calibration
Dynamic calibration for changing environments
- Auto-adaptation
- Change detection
- Instant correction
Industrial Applications
Precision Measurement
3D Dimensional Measurement
Measure size, volume, and shape of components
Assembly Verification
Verify component positions and assembly
Distance/Angle Measurement
High-precision distance and angle measurements
Robotics & Automation
Robot Vision Guidance
Provide position and orientation data to robots
Pick & Place Systems
Precise part picking and placement systems
Welding & Cutting
Precise welding and cutting path control
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