Extracting a 3D realizable line drawing object from a set of crossing lines

Abstract

A new aspect of 3D realizability problem is studied. Given a 3D realizable object hidden under crossing lines, such lines in realizable object will be identified and extracted. In this dissertation, a rule-based approach algorithm is proposed to identify and extract a 3D realizable object from a given set of crossing lines. The proposed algorithm will be beneficial and applicable to obtain a 3D object in forms of a wired frame directly from its given 2D image. All the proposed rules are generated based on researching and studying characteristics of 3D realizable objects. The proposed algorithm consists of five main processes. In the first process, the significant junctions and significant segments are identified which result in a set of significant faces candidates of a 3D realizable object. The significant faces candidates are verified as the real significant faces in the second process using the first set of rules. In the third process, the essential junctions and essential segments are identified to be the potential essential faces. The second set of rules is applied in the forth process to verify the potential essential faces as the real essential faces. The remaining problem lines are verified by the final rule in the fifth process. The unused lines will be also considered before the identified 3D realizable object is extracted. The proposed algorithm is applied to 169 polyhedral line drawing images obtained from Varley's thesis. From the experiment, the algorithm correctly extracted all the relevant line segments and points up to 94.68%. The time complexity of the proposed algorithm is O(mn), where n is a number of initial crossing points counted and m is a number of lines.