Euclidean reconstruction: From paraperspective to perspective

Abstract

Abstract. In this paper we describe a method to perform Euclidean reconstruction with a perspective camera model. It incrementally performs reconstruction with a paraperspective camera in order to converge towards a perspective model. With respect to other methods that compute shape and motion from a sequence of images with a calibrated perspective camera, this method converges in a few iterations, is computationally efficient, and does not suffer from the non linear nature of the problem. Moreover, the behaviour of the algorithm may be simply explained and analysed, which is an advantage over classical non linear optimization approaches. With respect to 3-D reconstruction using an approximated camera model, our method solves for the sign (reversal) ambiguity in a very simple way and provides much more accurate reconstruction results.

Estimation of projective depths based on genetic algorithm

“…If there is no noise in the 2D image coordinates, W is rank 4 and cr5 = • • =N = 0 , V1 diag(01, . .,a4)UJ is a full rank factorization of W. Therefore Q = V1 , X = diag(o1,.,r4)UJ (4) The above factorization method can only be used ifprojective depths 1u can be found. Now we estimate projective depths LI using genetic algorithm.…”

“…Therefore the most crucial problem in perspective factorization is how to estimate these projective depths. In 1996, Christy [4] proposed a method for shape recovery from projective images in which the projective depths were iteratively estimated by iterating factorization of the measurement matrix starting from the paraperspective camera model. In 1 996, SturmI5J proposed a non-iterative factorization method for uncalibrated perspective images.…”

Two Algorithms and Error Analysis for 3D Terrain Reconstruction of Small Body

“…So the approximation error to orthographic projection [6] in the recovered shape may be very large. Therefore, various improved factorization method by avoiding the orthographic projection have been proposed, such as using the paraperspective projection [7] , or the perspective projection [8] . However, those are still suffered by the approximation of 1 Supported by Doctoral Found of QUST(0022408) the camera model.…”

Stochastic filtering for motion trajectory in image sequences using a Monte Carlo filter with estimation of hyper-parameters

“…The factorization based method [1] which can eliminate the projection error due to affine approximation of perspective projection was used to estimate motion and shape from motion trajectories of feature points. 62 feature points on sphere and motion trajectoies of them obtained from synthetic motion were used.…”

“…False matching leads to outliers in the feature motion trajectory. The effect of outliers must be reduced to yield good data for subsequent processing such as shape from motion [1] [2].…”