Generalized Conics: Properties and applications
Aysylu Gabdulkhakova, Walter G. Kropatsch · 2021
In this paper the properties of the generalized conics are used to create a unified framework for generating various types of the distance fields. The main concept behind this work is a metric that measures the distance from a point to a line segment according to the definition of the ellipse. The proposed representation provides a possibility to efficiently compute the proximity, arithmetic mean of the distances and a space tessellation with regard to the given set of polygonal objects, line segments and points. In addition, the weights can be introduced for objects, their parts and combinations. This fact leads to a hierarchical representation that can be efficiently obtained using the pixel-wise operations. The practical value of the proposed ideas is demonstrated on an example of applications like skeletonization, smoothing and optimal location finding.