A correction method for 3-D reconstructed shapes by error weighting

This paper proposes a new method for iteratively correcting three dimensional (3-D) shapes by weighting reconstruction errors when the shape is reconstructed from more than three 2-D perspective images using linear camera models such as weak- or para-perspective cameras. The method can compensate measurement errors by using its variance-covariance matrix, where the measurement errors are composed of random noise and the disparity between the linear camera models and non-linearity of perspective cameras, and can reduce mean reconstruction errors by adjusting the tolerance range of the reconstruction errors in accordance with the measurement error variances and also by eliminating the covariances between these errors. In numerical experiments using synthetic and real images, our method achieves correction results that are almost equivalent to those obtained by using variance-covariance matrices determined by a precise 3-D shape. The method also achieves a considerable amount of correction for both essentially nonlinear camera images and approximately linear camera images if the random noise is not strong and if more than twenty 2-D images are available.