Fast erosion and dilation by contour processing and thresholding of distance maps

Ragnemalm, Ingemar

doi:10.1016/0167-8655(92)90055-5

Cited by 56 publications

(24 citation statements)

References 5 publications

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“…Some example applications are: skeleton computation [Montanari 1968;Danielsson 1980], mathematical morphology operation [Ragnemalm 1992a], and displacement mapping [Wang et al 2003;Donnelly 2005]. Though there are already many approaches to compute distance transform [Cuisenaire 1999], there are still unresolved issues: many approaches compute only an approximation to the distance transform in order to be efficient in applications, and they are sequential in nature that have no good avenue for speedup with parallel computation.…”

Section: Introductionmentioning

confidence: 99%

Jump flooding in GPU with applications to Voronoi diagram and distance transform

Rong

Tan

2006

Proceedings of the 2006 Symposium on Interactive 3D Graphics and Games - SI3D '06

171

154

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Figure 1: With the eight seeds (highlighted and shown in different colors) in a 64×64 grid on the leftmost picture, the progress of each round of the jump flooding algorithm is shown in the other six pictures, with the rightmost being the computed Voronoi diagram. AbstractThis paper studies jump flooding as an algorithmic paradigm in the general purpose computation with GPU. As an example application of jump flooding, the paper discusses a constant time algorithm on GPU to compute an approximation to the Voronoi diagram of a given set of seeds in a 2D grid. The errors due to the differences between the approximation and the actual Voronoi diagram are hardly noticeable to the naked eye in all our experiments. The same approach can also compute in constant time an approximation to the distance transform of a set of seeds in a 2D grid. In practice, such constant time algorithm is useful to many interactive applications involving, for example, rendering and image processing. Besides the experimental evidences, this paper also confirms quantitatively the effectiveness of jump flooding by analyzing the occurrences of errors. The analysis is a showcase of insights to the jump flooding paradigm, and may be of independent interests to other applications of jump flooding.

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Section: Introductionmentioning

confidence: 99%

Jump flooding in GPU with applications to Voronoi diagram and distance transform

Rong

Tan

2006

Proceedings of the 2006 Symposium on Interactive 3D Graphics and Games - SI3D '06

171

154

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“…First, the white phase (ellipsoid phase) of the image is eroded [15] by a suitably chosen erosion depth such the ellipsoids are separated (that is, each ellipsoid is represented by a unique cluster of white voxels), see below for the choice of the erosion depth. A very effective method to calculate the eroded image, is by thresholding the Euclidean distance map (EDM) of the ellipsoid phase [16]. The EDM of the white phase of a binary image labels each voxel with the distance to the nearest black voxel.…”

Section: Tomography and Image Processingmentioning

confidence: 99%

Tomographic analysis of jammed ellipsoid packings

Schaller

Neudecker

Saadatfar

et al. 2013

AIP Conference Proceedings

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“…The use of boundarybased mathematical morphology is a classic way of decreasing the computational costy of the morphological operations. For instance, (Ragnemalm, 1992) and (Meijster et al, 2000) present techniques that apply morphological operations based on analytical calculations of distance between objects' boundary points. Van Vliet and Verwer present algorithms for the calculation of erosion, dilation, skeletonization and propagation of images based on the contour of figures (Van Vliet and Verwer, 1988) and (Wilkinson and Meijer, 1995) show a technique to classify microbiological organisms' images from applying morphological operations to the boundary pixels of organisms.…”

Section: Contributionsmentioning

confidence: 99%

Deterministic mathematical morphology for CAD/CAM

Sarabia-Pérez

Jimeno-Morenilla

Molina-Carmona

2014

Engineering Computations

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Purpose This paper presents a new geometric model based on the mathematical morphology paradigm, specialized to provide determinism to the classic morphological operations. The determinism is needed to model dynamic processes that require an order of application, as is the case for designing and manufacturing objects in CAD/CAM environments. Design/methodology/approach The basic trajectory-based operation is the basis of the proposed morphological specialization. This operation allows the definition of morphological operators that obtain sequentially ordered sets of points from the boundary of the target objects, inexistent determinism in the classical morphological paradigm. From this basic operation, the complete set of morphological operators is redefined, incorporating the concept of boundary and determinism: trajectory-based erosion and dilation, and other morphological filtering operations. Findings This new morphological framework allows the definition of complex threedimensional objects, providing arithmetical support to generating machining trajectories, one of the most complex problems currently occurring in CAD/CAM. Originality/valueThe model proposes the integration of the processes of design and manufacture, so that it avoids the problems of accuracy and integrity that present other classic geometric models that divide these processes in two phases. Furthermore, the morphological operative is based on points sets, so the geometric data structures and the operations are intrinsically simple and efficient. Another important value that no excessive computational resources are needed, because only the points in the boundary are processed.

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Fast erosion and dilation by contour processing and thresholding of distance maps

Cited by 56 publications

References 5 publications

Jump flooding in GPU with applications to Voronoi diagram and distance transform

Jump flooding in GPU with applications to Voronoi diagram and distance transform

Tomographic analysis of jammed ellipsoid packings

Deterministic mathematical morphology for CAD/CAM

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