Yi Jun Xiao and Y. F. Li, "Optimized stereo reconstruction of free-form space curves based on a nonuniform rational B-spline model," J. Opt. Soc. Am. A 22, 1746-1762 (2005)
Analytical reconstruction of 3D curves from their stereo images is an important issue in computer vision. We present an optimization framework for such a problem based on a nonuniform rational B-spline (NURBS) curve model that converts reconstruction of a 3D curve into reconstruction of control points and weights of a NURBS representation of the curve, accordingly bypassing the error-prone point-to-point correspondence matching. Perspective invariance of NURBS curves and constraints deduced on stereo NURBS curves are employed to formulate the 3D curve reconstruction problem into a constrained nonlinear optimization. A parallel rectification technique is then adopted to simplify the constraints, and the Levenberg–Marquardt algorithm is applied to search for the optimal solution of the simplified problem. The results from our experiments show that the proposed framework works stably in the presence of different data samplings, randomly posed noise, and partial loss of data and is potentially suitable for real scenes.
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, , denote errors in 3D, left retina, and right retina, respectively.
Each column vector contains the values of mean, maximum, minimum, and SD in descending order.
Table 2
Errors of Reconstructiona with Corrupted Data, in Pixels
, , denote errors in 3D, left retina, and right retina, respectively.
Each column vector contains the values of mean, maximum, minimum, and SD in descending order.
Table 3
Errors of Reconstructiona with Fragmented Data, in Pixels
, , denote errors in 3D, left retina, and right retina, respectively.
Each column vector contains the values of mean, maximum, minimum, and SD in descending order.
Table 4
Reconstruction Errorsa of the Fan Model, in Pixels
, denote errors in left retina and right retina, respectively.
Each column vector contains the values of mean, maximum, minimum, and SD in descending order.
Table 5
Reconstruction Errorsa of the Bent Wire Objects, in Pixels
, denote errors in left retina and right retina, respectively.
Each column vector contains the values of mean, maximum, minimum, and SD in descending order.
Tables (5)
Table 1
Errors of Reconstructiona with Sampling Differences, in Pixels
, , denote errors in 3D, left retina, and right retina, respectively.
Each column vector contains the values of mean, maximum, minimum, and SD in descending order.
Table 2
Errors of Reconstructiona with Corrupted Data, in Pixels
, , denote errors in 3D, left retina, and right retina, respectively.
Each column vector contains the values of mean, maximum, minimum, and SD in descending order.
Table 3
Errors of Reconstructiona with Fragmented Data, in Pixels
, , denote errors in 3D, left retina, and right retina, respectively.
Each column vector contains the values of mean, maximum, minimum, and SD in descending order.
Table 4
Reconstruction Errorsa of the Fan Model, in Pixels
, denote errors in left retina and right retina, respectively.
Each column vector contains the values of mean, maximum, minimum, and SD in descending order.
Table 5
Reconstruction Errorsa of the Bent Wire Objects, in Pixels
, denote errors in left retina and right retina, respectively.
Each column vector contains the values of mean, maximum, minimum, and SD in descending order.