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.

Abstract-Morphological attribute filters have not previously been parallelized mainly because they are both global and nonseparable. We propose a parallel algorithm that achieves efficient parallelism for a large class of attribute filters, including attribute openings, closings, thinnings, and thickenings, based on Salembier's 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 percent on a single-core processor due to reduced cache thrashing.

Virtually all acetylacetonate (acac) complexes [the only exceptions known so far are Ru(acac), and Rh(acac),] react with coordinatively unsaturated (c.u.s.) A13+ sites of y-alumina surfaces. As far as the surface OH groups are concerned, there appears to be a correlation between the acid/base sensitivity of an acac complex and its reactivity towards these groups, i.e. acac complexes which are unstable in the presence of OH-react with the basic OH groups, and those which are sensitive to H+ react (to a certain extent) with the acidic ones. High metal loadings cannot be achieved through controlled adsorption at room temperature, however ; the reactivity of acidic OH groups is very low, and neutral OH groups are not involved at all. On the other hand, the M(acac),/Al,O, interactions are sufficiently well behaved (i) to enable the quantitative determination of C.U.S. A13+ sites and basic OH groups and (ii) to follow surface modifications as a result of pretreatment(s).

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A general algorithm for computing Euclidean skeletons of 2D and 3D data sets in linear time is presented. These skeletons are defined in terms of a new concept, called the integer medial axis (IMA) transform. We prove a number of fundamental properties of the IMA skeleton, and compare these with properties of the CMD (centers of maximal disks) skeleton. Several pruning methods for IMA skeletons are introduced (constant, linear and square-root pruning) and their properties studied. The algorithm for computing the IMA skeleton is based upon the feature transform, using a modification of a linear-time algorithm for Euclidean distance transforms. The skeletonization algorithm has a time complexity which is linear in the number of input points, and can be easily parallelized. We present experimental results for several data sets, looking at skeleton quality, memory usage and computation time, both for 2D images and 3D volumes.