Conformal Geometric Algebra Voting Scheme Implemented in Reconfigurable Devices for Geometric Entities Extraction

Abstract

This paper presents an implementation of the conformal voting scheme using a reconfigurable hardware approach in the frame of conformal geometric algebra $\mathcal {G}_{3,1}$ . This algorithm is able to extract geometric entities, such as circles and lines from edged images. The conformal voting scheme is divided into two main stages: a local stage computed using neighborhoods in the image, and a global stage using the results of the local voting stage. In this implementation, we focused on the most computationally demanding stage: the local stage, which is computed in the field-programmable gate array, while the global voting stage continues to be executed on the PC. The results show an average speedup of 3x depending on the features of the input image and a coefficient of variation near to zero in the times of repeated experiments. Finally, our method can be used for multiple applications in real-time image processing.