Constraints for Closest Point Finding

The traditional closest point criterion has been widely used for 3D free form shape matching, object recognition, internet search, computer graphics and medical imaging. However, the rationale of this criterion has not yet been well understood and exploited. In this paper, we apply vector operations and the triangle inequality to carefully analyse this criterion and reveal that this criterion can guarantee that the found point matches satisfy the orientation, rigidity and matching error constraints and thus, are of high relative quality. Such properties not only shed light on and deepen our understanding of this criterion about its generality and practicality and improve our awareness about whether the established point matches are consistent with each other, but also provide us with a possibility to develop novel algorithms for the reliability evaluation of existing point matches and an efficient establishment of more accurate point matches. The experimental results based on real images show that the possible point matches established through extracting and matching spin images often violate these constraints and these constraints can often be successfully applied to reject (probably part of) the unlikely point matches for more accurate free form shape matching results.