OTPL: A novel measurement method of structural parallelism based on orientation transformation and geometric constraints

Abstract

Detecting parallel geometric structures from images is a significant step for computer vision tasks. In this paper, an algorithm called Orientation Transformation-based Parallelism Measurement (OTPL) is proposed in this paper to measure the parallelism of structures including both line structures and curve structures. The task is decomposed into measurements of parallel straight line and parallel curve structures due to the inherent geometric differences between them, where the parallelism between curve structures can be further transformed into a matching problem. For parallel straight lines, the angle constraints and the rate of overlapping projection are considered as the parallel relationship selection rules for the candidate lines. For the parallel curves, the approximate vertical growing (AVG) algorithm is proposed to accelerate the search of adjacent curves and each smooth curve is coded as a vector with different angle values. The matching pairs are extracted through cosine similarity transformation and convexity consistency. Finally, the parallel curves are extracted by a decision-making process. The proposed algorithm is evaluated in a comprehensive manner, encompassing both qualitative and quantitative approaches, with the objective of achieving a more robust assessment. The results demonstrate the algorithm's efficacy in identifying parallel structures in both synthetic and natural images.