Affiliations: [a] Facultad de Matemáticas, Universidad Complutense de Madrid, Madrid, Spain
| [b] Instituto de Matemáticas, Universidad de Antioquia, Medellín, Colombia
| [c] Facultad de Estudios Estadísticos, Universidad Complutense de Madrid, Madrid, Spain
| [d] Instituto IGEO (UCM-CSIC), Universidad Complutense de Madrid, Madrid, Spain
Correspondence:
[*]
Corresponding author. Carely Guada, Facultad de Matemáticas, Universidad Complutense de Madrid, 28040
Madrid, Spain. E-mail: cguada@ucm.es.
Abstract: In this paper, an efficient and polynomial edge detection algorithm based on a hierarchical graph-partition approach is presented. After transforming a digital image into a graph network, the proposed algorithm proceeds by iteratively dividing the image into regions, and then transforming this hierarchical region map into a sequence of boundary maps. This allows the proposed algorithm to operate naturally with colour or hyperspectral images, as well as to detect edges at different levels of detail in a simultaneous and consistent manner. Such a sequence of edge maps can be seen as jointly approximating the different levels of detail that humans may use when recognizing objects in an image. This idea is taken to base the evaluation methodology of the proposed algorithm, that extends the usual boundary-based evaluation methodology based on the matching of the automatic maps with a set of human ground truth, reference maps. The computational experiences carried out to benchmark the performance of the proposed algorithm over the BSDS500 dataset suggest that the proposed method attains a statistically significant better performance than some well-known detectors as Canny or Sobel.
