Related papers: Watersheds in disordered media
The watershed is one of the most used tools in image segmentation. We present how its concept is born and developed over time. Its implementation as an algorithm or a hardwired device evolved together with the technology which allowed it.…
We find that watersheds in real and artificial landscapes can be strongly affected by small, local perturbations like landslides or tectonic motions. We observe power-law scaling behavior for both the distribution of areas enclosed by the…
We present an algebraic approach to the watershed adapted to edge or node weighted graphs. Starting with the flooding adjunction, we introduce the flooding graphs, for which node and edge weights may be deduced one from the other. Each node…
Watersheds have been defined both for node and edge weighted graphs. We show that they are identical: for each edge (resp.\ node) weighted graph exists a node (resp. edge) weighted graph with the same minima and catchment basin.
The hierarchy of channel networks in landscapes displays features that are characteristic of non-equilibrium complex systems. Here we show that a sequence of increasingly complex ridge and valley networks is produced by a system of partial…
Superclusters are a convenient way to partition and characterize the large scale structure of the Universe. In this Letter we explore the advantages of defining superclusters as watershed basins in the divergence velocity field. We apply…
Image segmentation is the process of partitioning an image into meaningful segments. The meaning of the segments is subjective due to the definition of homogeneity is varied based on the users perspective hence the automation of the…
The physics of swash i.e. a layer of water that washes up on the beach after an incoming wave has broken is complicated and intriguing. It includes perplexed hydrodynamic and sediment transport events. In our paper we address to the…
The watershed is a powerful tool for segmenting objects whose contours appear as crest lines on a gradient image. The watershed transform associates to a topographic surface a partition into catchment basins, defined as attraction zones of…
Landscapes that are rhythmically dissected by natural drainage channels exist in various geologic and climatic settings. Such landscapes are characterized by a length-scale for the lateral spacing between channels. We observe a small-scale…
A cellular model introduced for the evolution of the fluvial landscape is revisited using extensive numerical and scaling analyses. The basic network shapes and their recurrence especially in the aggregation structure are then addressed.…
This article is the first in a series of three papers investigating the detailed geometry of river networks. Large-scale river networks mark an important class of two-dimensional branching networks, being not only of intrinsic interest but…
Many image processing applications rely on partitioning an image into disjoint regions whose pixels are 'similar.' The watershed and waterfall transforms are established mathematical morphology pixel clustering techniques. They are both…
The segmentation, seen as the association of a partition with an image, is a difficult task. It can be decomposed in two steps: at first, a family of contours associated with a series of nested partitions (or hierarchy) is created and…
Learned boundary maps are known to outperform hand- crafted ones as a basis for the watershed algorithm. We show, for the first time, how to train watershed computation jointly with boundary map prediction. The estimator for the merging…
We study the morphology of watersheds in two and three dimensional systems subjected to different degrees of spatial correlations. The response of these objects to small, local perturbations is also investigated with extensive numerical…
Accurate and scalable hydrologic models are essential building blocks of several important applications, from water resource management to timely flood warnings. However, as the climate changes, precipitation and rainfall-runoff pattern…
We investigate the consequences of fluid flowing on a continuous surface upon the geometric and statistical distribution of the flow. We find that the ability of a surface to collect water by its mere geometrical shape is proportional to…
Turbulent boundary layers over flat walls in the presence of a hill are frequently found in nature and industry. Some examples are the air flows over hills and desert dunes, but also water flows over aquatic dunes inside closed conduits.…
Water governing systems are twisted with complex interplays among levels and scales which embody their structures. Typically, the mismatch between human-generated and natural systems produces externalities and inefficiencies reflectable in…