By Molk J. (ed.)
ISBN-10: 2876471108
ISBN-13: 9782876471108
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If and only if the line intersects the origin. Fig. 4. A 3D line may be determined by two points which intersect with two planes of the coordinate system; the two points have 2 degrees of freedom since they are fixed to planes (left). Two Euclidean points and define a 3D line (middle). In this work we choose two 3-vectors for the representation of L: the direction of the line and the 3-vector We assume to have the length equal to the distance of the 3D line L to the origin (right). e. Thus the 6-vector L has 4 degrees of freedom, considering both the orthogonality and homogeneous constraint.
DEBEVEC et al. 1996, which especially aims on photo-realistic reconstruction. It uses parametrized models, that are interactively specified by the user with the aid of a precomputed image segmentation result. The final model is then optimized by a minimization function. There are two commercial systems with a similar purpose, IMAGEMODELER by Realviz (REALVIZ 2002) and PHOTOMODELER (PHOTOMODELER 2002). 6 Overview of Thesis This work presents a unified approach for representing, combining and estimating points, lines and planes in 2D and 3D taking uncertainty information into account.
2 on page 44. In the following, we concentrate on the following types of transformations: Linear mappings within image space resp. object space, called homographies in 2D and 3D with affine transformations and similarity transformations as special cases Linear mapping from object space to image space, called projective camera transformations with affine camera transformations as a special case Linear mapping between two different images, called fundamental matrix. 2 on page 56. Matrix and Vector Representation The transformations will generally be represented by a matrix M, such that If a matrix is a transformation of homogeneous vectors, then it is a homogeneous transformation as it is defined up to scale, denoted be upright sans-serif letters.
Encyclopedie des sciences mathematiques. Fondements de la geometrie by Molk J. (ed.)
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