Euler arc splines for curve completion

This paper introduces a special arc spline called an Euler arc spline as the basic form for visually pleasing completion curves. It is considered as an extension of an Euler curve in the sense that the points in the Euler curve are replaced by arcs. A simple way for specifying it, which is suitable for shape completion, is presented. It is shown that Euler arc splines have several properties desired by aesthetics of curves, in addition to computational simplicity and NURBS representation. An algorithm is proposed for curve completion using Euler arc splines. The development of the algorithm involves two optimization processes, which are converted into a single minimization problem in two variables solved by the Levenberg–Marquardt algorithm. Compared to previous methods, the proposed algorithm always guarantees the interpolation of two boundary conditions.

An Euler arc spline curve and its associate construction algorithm are introduced for completing contour beyond an occluson. This has applications in graphics and vision such as image inpainting for proper filling-in and avoiding unnecessary diffusion.Figure optionsDownload high-quality image (180 K)Download as PowerPoint slideHighlights
► Euler arc splines are introduced for curve completion.
► Euler arc splines are shown to have properties desired by aesthetics of curves.
► A curve completion algorithm guarantees the interpolation of boundary conditions.