In this paper , we prove that given n images captured by a pinhole camera with varying parameters and under general motion , the number of independent kruppa constraints is 5n - 9 , and it is less than that of independent constraints from the absolute quadric by only one 本文首次從代數上嚴格證明了,攝像機在通常運動下當攝像機的內參數變化時,從n n 3幅圖像得到的所有kruppa方程中,只有5n - 9個是獨立的
This one - constraint - less property of the kruppa equations is their inherent deficiency and is independent of camera motion . this deficiency is due to their failure of automatic enforcement of the rank - three - ness on the absolute quadric 從而, kruppa方程的獨立個數比基于絕對二次曲面或基于無窮遠平面的自標定方程的獨立個數少1 ,這是源于kruppa方程不能保證絕對二次曲面的秩為3 ,是由kruppa方程自身的特性決定的,而與攝像機的運動無關。