• International Journal of CAD/CAM
• /
• v.6 no.1
• /
• pp.59-64
• /
• 2006

A new method to obtain explicit re-parameterization that preserves the curve degree and parametric domain is presented in this paper. The re-parameterization brings a curve very close to the arc length parameterization under $L_2$ norm but with less segmentation. The re-parameterization functions we used are $C^1$ continuous piecewise rational linear functions, which provide more flexibility and can be easily identified by solving a quadratic equation. Based on the outstanding performance of Mobius transformation on modifying pieces with monotonic parametric speed, we first create a partition of the original curve, in which the parametric speed of each segment is of monotonic variation. The values of new parameters corresponding to the subdivision points are specified a priori as the ratio of its cumulative arc length and its total arc length. $C^1$ continuity conditions are imposed to each segment, thus, with respect to the new parameters, the objective function is linear and admits a closed-form optimization. Illustrative examples are also given to assess the performance of our new method.

• Journal of Korean Society for Geospatial Information Science
• /
• v.17 no.3
• /
• pp.115-120
• /
• 2009

Point-based methods with experienced human operators are processed well in traditional photogrammetric activities but not the autonomous environment of digital photogrammetry. To develop more robust and accurate techniques, higher level objects of straight linear features accommodating element other than points are adopted instead of points in aerial triangulation. Even though recent advanced algorithms provide accurate and reliable linear feature extraction, extracting linear features is more difficult than extracting a discrete set of points which can consist of any form of curves. Control points which are the initial input data and break points which are end points of piecewise curves are easily obtained with manual digitizing, edge operators or interest operators. Employing high level features increase the feasibility of geometric information and provide the analytical and suitable solution for the advanced computer technology.