A minimum barrier distance for multivariate images with applications

Distance transforms and the saliency maps they induce are widely used in image processing, computer vision, and pattern recognition. The minimum barrier distance (MBD) has proved to provide accurate results in this context. Recently, Geraud et al. have presented a fast-to-compute alternative definition of this distance, called the Dahu pseudo-distance. This distance is efficient, powerful, and have many important applications. However, it is restricted to grayscale images. In this article we revisit this pseudo-distance. First, we offer an extension to multivariate image. We call this extension the vectorial Dahu pseudo-distance. We provide an efficient way to compute it. This new version is not only able to deal with color images but also multi-spectral and multimodal ones. Besides, through our benchmarks, we demonstrate how robust and competitive the vectorial Dahu pseudo-distance is, compared to other MB-based distances. This shows that this distance is promising for salient object detection, shortest path finding, and object segmentation. Secondly, we combine the Dahu pseudo-distance with the geodesic distance to take into account spatial information from the image. This combination of distances provides efficient results in many applications such as segmentation of thin elements or path finding in images.