3D reconstruction is a key problem in computer vision and many algorithms based on multiple view geometry have been proposed for the 3D point or 3D line reconstruction in projective space. In these existing algorithms, some of them are more sensitive to noise due to not fully taking into account the measurement errors of image point and image line; others are of high computational complexity although the impacts of measurement error are taken into account. This study is focused on 3D point and 3D line reconstruction in projective space. The main work is summarized as follows: 1. Point Triangulation from Two Views: Based on the fundamental cone, a new optimal triangulation framework is proposed, in which the nearest point on fundamental cone to the measure point is searched. Although this triangulation needs finding out the root of 6-degree polynomial, the Euclidean transformation in it doesn’t depend on the measured point and the degree of the polynomial doesn’t depend on the order of images. To reduce the computational load, three efficient suboptimal algorithms based on generating cone, generating line and Sampson sequence are proposed. Our proposed three suboptimal al-gorithms can achieve comparable estimation accuracy compared with the optimal trian-gulation, but with much less computational load. 2. Point Triangulation from Multiple Views: A L2-norm distance optimality criterion is proposed. Based on this criterion, a simple Sampson approximation iterative algorithm is introduced for the point triangulation from multiple views. In addition a fast iterative algorithm based on conjugate gradient is also proposed to speedup the iteration. Compared with the Gold Standard algorithm, our proposed two iterative algorithms can achieve comparable estimation accuracy, but with lower computational complexity. 3. Line triangulation from Three Views: Two new algorithms are proposed. Based on Plucker coordinates, the first algorithm minimizes the algebraic distance under Klein qu-adric constraint to obtain a suboptimal solution. The algebraic distance of the suboptimal solution is less than double of the optimal solution. Via a new line representation in image, the second algorithm minimizes the normal distance from the measured endpoint to the estimated line under point-line-line tensor constraint using an iterative method. This algorithm can achieve comparable estimation accuracy compared with the Gold Standard algorithm, but with much less computational load.
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