Tutorial Geometric Vision

Geometric Computer Vision Tutorial

The low level mathematics used to estimate the scene's structure and camera ego motion are contained in the Geometric Vision package in BoofCV. Most of the standard algorithms in this field are provided with numerious options for comptuing and refining constructs such as the Fundamental/Essential matrix, Trifocal Tensor, camera pose, and points/lines.

These algorithms are typically used in structure from motiom (SFM) and their correct usage is not trivial, see below for a list of books on the subject. The API is still being refined to help make this process easier. As is typical with BoofCV, most of the documentation on usage is provided in the form of examples and JavaDoc comments.

When reviewing the JavaDoc pay close attention to the type of inputs it takes (e.g. pixel or normalized image coordinates) and the direction of the reference frame transform. Pixels refers to coordinates in the image while normalized image coordinates are in Euclidean space and found by multiplying pixels by the inverse of the intrinsic camera calibration matirx.

To get started look at the following packages and classes:

• boofcv.abst.geo.*
• boofcv.alg.geo.*
• PerspectiveOps
• MultiViewOps
• FactoryMultiView
• FactoryTriangulate

Examples

• Compute Fundamental Matrix

Algorithm List

• Fundamental/Essential Matrix
  • Linear 8+ Points
  • Linear 7 Points
• Essential Matrix
  • Nister 5 Points
• Fundamental Matrix Optimization
  • Sampson Error
  • Epipolar Error
• Homography 4 Points (Linear)
• Homography Optimization
  • Sampson Error
  • Transfer Error
• Linear 6 Point Pose
• Linear Pixel Depth
• Perspective-N-Point (PnP)
  • Efficient PnP 4-Point (EPnP)
  • P3P Grunert
  • P3P Finsterwalder
• PnP Optimization
  • Euclidean Error
• Triangulation
  • Geometric
  • Linear
• Triangulation Optimization
  • Sampson Error
  • Euclidean Error
• Trifocal Tensor
  • Linear 7 point
• Decompose Essential
• Decompose Homography
• Bundle Adjustment
  • Dense (inefficient/slow)
• Stereo Rectification
  • Calibrated
  • Uncalibrated

Camera Model

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Recommend Reading

• Yi Ma, et. al., "An Invitation to 3-D Vision"
  • Algebraic approach to 3D vision.
  • Easy to use as a reference.
• R. Hartley, and A. Zisserman, "Multiple View Geometry in Computer Vision"
  • Geometric approach and the most popular book on this subject.
  • More content and good algorithms.
  • Mediocre index and tendency to not define terms in some chapters.