A fast and flexible algorithm for computing watersheds in digital gray-scale images is introduced. A review of watersheds and related motion is first presented, and the major methods to determine watersheds are discussed. The algorithm is based on an immersion process analogy, in which the flooding of the water in the picture is efficiently simulated using of queue of pixel. It is described in detail provided in a pseudo C language. The accuracy of this algorithm is proven to be superior to that of the existing implementations, and it is shown that its adaptation to any kind of digital grid and its generalization to n-dimensional images (and even to graphs) are straightforward. The algorithm is reported to be faster than any other watershed algorithm. Applications of this algorithm with regard to picture segmentation are presented for magnetic resonance (MR) imagery and for digital elevation models. An example of 3-D watershed is also provided. >

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Watersheds in digital spaces: an efficient algorithm based on immersion simulations

For the purposes of object or defect identification required in industrial vision applications, the operations of mathematical morphology are more useful than the convolution operations employed in signal processing because the morphological operators relate directly to shape. The tutorial provided in this paper reviews both binary morphology and gray scale morphology, covering the operations of dilation, erosion, opening, and closing and their relations. Examples are given for each morphological concept and explanations are given for many of their interrelationships.

Image Analysis Using Mathematical Morphology

Digital topology deals with the topological properties of digital images: or, more generally, of discrete arrays in two or more dimensions. It provides the theoretical foundations for important image processing operations such as connected component labeling and counting, border following, contour filling, and thinning—and their generalizations to three- (or higher-) dimensional “images.” This paper reviews the fundamental concepts of digital topology and surveys the major theoretical results in the field. A bibliography of almost 140 references is included.

Digital topology: introduction and survey

Transformations morphologiques, morphologie euclidienne, erosion et notions derivees, ouvertures et fermetures, amincissements et epaississements

Introduction to mathematical morphology

In recent years, a number of data structures for global geo-referenced data sets have been proposed based on regular, multi-resolution partitions of polyhedra. We present a survey of the most promising of such systems, which we call Geodesic Discrete Global Grid Systems (Geodesic DGGSs). We show that Geodesic DGGS alternatives can be constructed by specifying five substantially independent design choices: a base regular polyhedron, a fixed orientation of the base regular polyhedron relative to the Earth, a hierarchical spatial partitioning method defined symmetrically on a face (or set of faces) of the base regular polyhedron, a method for transforming that planar partition to the corresponding spherical/ellipsoidal surface, and a method for assigning point representations to grid cells. The majority of systems surveyed are based on the icosahedron, use an aperture 4 triangle or hexagon partition, and are either created directly on the surface of the sphere or by using an equal-area transformation. An exa...

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Geodesic Discrete Global Grid Systems

The concept of the two-dimensional (2-D) parallel computer with square module arrays was first introduced by Unger. It is the purpose of this paper to discuss the relative merits of square and hexagonal module arrays, to propose an operational symbolism for the various basic hexagonal modular transformations which may be performed by these comupters, to illustrate some logical circuit implementation, and to describe a few elementary applications.

M.J.E. Golay

Papers

Hexagonal Parallel Pattern Transformations