A Derivation of the junction point motion of two lines

  In this appendix the expression for the motion of a junction point from the angles of two lines will be derived using the projective line representation. A junction point is represented as the intersection of two straight lines. This is a more general representation than was used by Malik [9], as it does not rely on rectified cameras. The following proof shows that this new representation can be used to derive Malik's two component disparity .

  
Figure 9: Occlusion junction (as defined by Malik)

These two lines in the left and right images intersect at (0;0) and (see figure 9).

This equation has related the angle of the lines forming the occlusion junction to the horizontal disparity, and is the same result as obtained by Malik [9].

• 1 Introduction
• 2 Review
• 3 Describing Occlusion Junctions
• 4 Detecting occlusion junctions using three views
  • 4.1 Algorithm
  • 4.2 Results and discussion
• 5 Planarity constraint of two lines
  • 5.1 The occlusion pseudo-junction
  • 5.2 The planarity constraint
  • 5.3 Method
  • 5.4 Results
  • 5.5 Discussion
• 6 Conclusion
• References
• A Derivation of the junction point motion of two lines
• B Alternate proof of planarity constraint.
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