📐

Camera Calibration & Geometry

Mathematical Foundations for Precision Vision

Transform image data into precise measurements through geometric mathematics

🎯
0.01px

sub-pixel accuracy

📏
±0.02°

rotation precision

🔄
99.9%

calibration success

Camera Models & Parameters

I Intrinsic Parameters

Camera Matrix (K)

K = [fx s cx]
    [ 0 fy cy]
    [ 0 0 1]
fx, fy: Focal lengths
cx, cy: Principal point
s: Skew parameter

Distortion Models

Radial: k₁r² + k₂r⁴ + k₃r⁶
Tangential: p₁(r² + 2x²) + p₂(2xy)

E Extrinsic Parameters

Pose Matrix [R|t]

[R|t] = [r₁₁ r₁₂ r₁₃ | tx]
        [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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Extrinsic Parameters

Calibration Techniques

Traditional Methods

Modern Deep Learning Approaches

Multi-Camera Systems

Stereo Vision

Multi-view Geometry

Geometric Transformations

2D Transformations

3D Transformations

Feature Detection & Matching

Classical Features

Learning-based Features

Structure from Motion (SfM)

Sequential SfM

Global SfM

Visual SLAM

Monocular SLAM

Stereo & RGB-D SLAM

การประยุกต์ใช้งาน

Industrial Applications

Automotive & Transportation

Entertainment & Media

เทคนิคขั้นสูง

Optimization Techniques

Robust Methods

การประเมินและเมตริก