Arnold Meijster

The watershed transform: definitions, algorithms and parallelization strategies

The watershed transform is the method of choice for image segmentation in the field of mathematical morphology. We present a critical review of several definitions of the watershed transform and the associated sequential algorithms, and discuss various issues which often cause confusion in the literature. The need to distinguish between definition, algorithm specification and algorithm implementation is pointed out. Various examples are given which illustrate differences between watershed transforms based on different definitions and/or implementations. The second part of the paper surveys approaches for parallel implementation of sequential watershed algorithms.

A General Algorithm for Computing Distance Transforms in Linear Time

A new general algorithm for computing distance transforms of digital images is presented. The algorithm consists of two phases. Both phases consist of two scans, a forward and a backward scan. The first phase scans the image column-wise, while the second phase scans the image row-wise. Since the computation per row (column) is independent of the computation of other rows (columns), the algorithm can be easily parallelized on shared memory computers. The algorithm can be used for the computation of the exact Euclidean, Manhattan (L 1 norm), and chessboard distance (L ∞ norm) transforms.

A comparison of algorithms for connected set openings and closings

The implementation of morphological connected set operators for image filtering and pattern recognition is discussed. Two earlier algorithms based on priority queues and hierarchical queues, respectively, are compared to a more recent union-find approach. Unlike the earlier algorithms which process regional extrema in the image sequentially, the union-find method allows simultaneous processing of extrema. In the context of area openings, closings, and pattern spectra, the union-find algorithm outperforms the previous methods on almost all natural and synthetic images tested. Finally, extensions to pattern spectra and the more general class of attribute operators are presented for all three algorithms, and memory usages are compared.

Concurrent Computation of Attribute Filters on Shared Memory Parallel Machines

Morphological attribute filters have not previously been parallelized, mainly because they are both global and non-separable. We propose a parallel algorithm which achieves efficient parallelism for a large class of attribute filters, including attribute openings, closings, thinnings and thickenings, based on Salembiers Max-Trees and Min-trees. The image or volume is first partitioned in multiple slices. We then compute the Max-trees of each slice using any sequential Max-Tree algorithm. Subsequently, the Max-trees of the slices can be merged to obtain the Max-tree of the image. A C-implementation yielded good speed-ups on both a 16-processor MIPS 14000 parallel machine, and a dual-core Opteron-based machine. It is shown that the speed-up of the parallel algorithm is a direct measure of the gain with respect to the sequential algorithm used. Furthermore, the concurrent algorithm shows a speed gain of up to 72% on a single-core processor, due to reduced cache thrashing.

A Proposal for the Implementation of a Parallel Watershed Algorithm

In this paper a parallel implementation of a watershed algorithm is proposed. The algorithm is designed for a ring-architecture with distributed memory and a piece of shared memory using a single program multiple data (SPMD) approach. The watershed transform is generally considered to be inherently sequential. This paper shows that it is possible to exploit parallelism by splitting the computation of the watersheds of an image into three stages that can be executed in parallel.

Fast computation of morphological area pattern spectra

An area based counterpart of the binary structural opening spectra is developed. It is shown that these area opening and closing spectra can be computed using an adaptation of Tarjans (1975) union-find algorithm. These spectra provide rotation, translation, and scale invariant pattern vectors for texture analysis.

Concurrent determination of connected components

Abstract The design is described of a parallel version of Tarjans algorithm for the determination of equivalence classes in graphs that represent images. Distribution of the vertices of the graph over a number of processes leads to a message passing algorithm. The algorithm is mapped to a shared-memory architecture by means of POSIX threads. It is applied to the determination of connected components in image processing. Experiments show a satisfactory speedup for sufficiently large images.

Computation of watersheds based on parallel graph algorithms

In this paper the implementation of a parallel watershed algorithm is described. The algorithm has been implemented on a Cray J932, which is a shared memory architecture with 32 processors. The watershed transform has generally been considered to be inherently sequential, but recently a few research groups, see [5, 9, 10], have designed parallel algorithms for computing watersheds. Most of these parallel algorithms are based on splitting the source image in blocks, computing the watersheds of these blocks and merging the resulting images into the desired result. A disadvantage of this approach is that a lot of communication is necessary at the boundaries of the blocks. It is possible to formulate the computation of the watershed transform as a shortest path searching problem that is commonly found in algorithmic graph theory. In this paper we use a parallel adapted version of Dijkstra’s algorithm for computing shortest paths in undirected graphs.

Towards an Implementation of a Multilevel ILU Preconditioner on Shared-Memory Computers

Recently, substantial progress has been made in the development of multilevel ILU-factorizations. These methods are attractive for very large problems due to their good convergence properties. We consider the parallelization of the instance MRILU, where we restrict to a version intended for scalar problems. The most time consuming parts in using MRILU are repeated multiplication of two sparse matrices in the construction phase and the multiplication of a sparse matrix and a full vector in the solution phase. Algorithms for these operations, as well as matrix transposition, are presented and have been tested on a Cray J90.

Segmentation by watersheds: definition and parallel implementation

In the field of grey scale mathematical morphology the watershed transform, originally proposed by Digabel and Lantuejoul, is frequently used for image segmentation [1, 9, 11]. It can be classified as a region-based segmentation approach. The intuitive idea underlying this method is that of flooding a landscape or topographic relief with water. Basins will fill up with water starting at local minima, and at points where water coming from different basins would meet, dams are built. When the water level has reached the highest peak in the landscape, the process is stopped. The set of dams thus obtained partitions the landscape into regions or ‘catchment basins’ separated by dams. These dams are called watershed lines or simply watersheds. A sketch is given in Fig. 1.