Neighborhoods for distance transformations using ordered propagation

Ragnemalm, Ingemar

doi:10.1016/1049-9660(92)90050-d

Cited by 69 publications

(47 citation statements)

References 10 publications

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“…In other words, belonging to a given Voronoi tile is not a local property: the tile to which a pixel belongs cannot always be deduced from the tiles to which its neighbors belong. Because they propagate the information locally from neighbor to neighbor, both raster scanning and propagation DT algorithms [2,13,14,17] will provide a wrong value for D(q) at Fig. 1.…”

Section: Voronoi Diagrams and Distance Transformationsmentioning

confidence: 99%

“…Second, raster scanning algorithms were proposed by Mullikin [12] or Saito [19]. Third, propagation or contour-processing algorithms were introduced by Vincent [9], Ragnemalm [14], and Eggers [24].…”

Section: D( P) = Min{dist( P Q) Q ∈ O}mentioning

confidence: 99%

“…Authors of sequential algorithms have proposed methods to emulate this multiple fronts behaviour with a sequential propagation. Ragnemalm [14] explicitly introduces a delayed updating mechanism. Mullikin [12] propagates lists of ties and near ties.…”

Section: Voronoi Diagrams and Distance Transformationsmentioning

confidence: 99%

“…Leymarie [13] showed that, if implemented carefully, both approximations have similar computational cost. Ragnemalm [14] proposed an ordered propagation version of Danielsson's algorithm, as well as a raster scan implementation [17] using a minimal number of scans. While these approximations are good enough for many applications, there are cases for which the exact Euclidean DT is needed.…”

Section: D( P) = Min{dist( P Q) Q ∈ O}mentioning

confidence: 99%

See 3 more Smart Citations

Fast Euclidean Distance Transformation by Propagation Using Multiple Neighborhoods

Cuisenaire

Macq

1999

Computer Vision and Image Understanding

127

108

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We propose a new exact Euclidean distance transformation (DT) by propagation, using bucket sorting. A fast but approximate DT is first computed using a coarse neighborhood. A sequence of larger neighborhoods is then used to gradually improve this approximation. Computations are kept short by restricting the use of these large neighborhoods to the tile borders in the Voronoi diagram of the image. We assess the computational cost of this new algorithm and show that it is both smaller and less image-dependent than all other DTs recently proposed. Contrary to all other propagation DTs, it appears to remain o(n 2 ) even in the worst-case scenario.

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Section: Voronoi Diagrams and Distance Transformationsmentioning

confidence: 99%

Section: D( P) = Min{dist( P Q) Q ∈ O}mentioning

confidence: 99%

Section: Voronoi Diagrams and Distance Transformationsmentioning

confidence: 99%

Section: D( P) = Min{dist( P Q) Q ∈ O}mentioning

confidence: 99%

See 2 more Smart Citations

Fast Euclidean Distance Transformation by Propagation Using Multiple Neighborhoods

Cuisenaire

Macq

1999

Computer Vision and Image Understanding

127

108

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show abstract

“…The most intuitive method would be to use a dynamic list of propagating pixels to scan the image by order of increasing values of D X,S (p), adapting the algorithms of Ragnelmam [18,11] or Cuisenaire [14] for the Euclidean DT. Nevertheless, this is needlessly complex.…”

Section: Dilation and Erosionmentioning

confidence: 99%

Locally adaptable mathematical morphology using distance transformations

Cuisenaire

2006

Pattern Recognition

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We investigate how common binary mathematical morphology operators can be adapted so that the size of the structuring element can vary across the image pixels.We show that when the structuring elements are balls of a metric, locally adaptable erosion and dilation can be efficiently implemented as a variant of distance transformation algorithms. Opening and closing are obtained by a local threshold of a distance transformation, followed by the adaptable dilation.

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A digital geometric approach for discrete Voronoi diagram construction using GPU

Dhar,

Pal,

Bhattacharjee

et al. 2024

Concurrency and Computation

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SummaryVoronoi diagram is a versatile geometric structure used in solving many computational geometry problems in the field of image analysis, computer vision, engineering, medicine, molecular biology and various other disciplines. As a result it is a popular research domain. The literature boasts of many elegant and efficient methods for the construction of the Voronoi diagram in the real space. But these algorithms often fail to perform well when applied to the discrete domain. We present in this paper a novel algorithm for the construction of discrete Voronoi diagram using digital geometric concepts that takes care of the geometric perspective of the Voronoi diagram in the discrete domain. Although our technique is more suited for the CPU but by careful use of some cut‐off heuristics we are able to design a parallel programming approach for the construction of the Voronoi diagram making use of the GPU computational power. The speedup of our algorithm is compatible with the popular GPU technique for Voronoi diagram construction, namely, Jump flood algorithm. But since our algorithm uses the geometric perspective for the construction of Voronoi diagram it gives more accurate output and hence requires no correction step as is the case for the Jump flood algorithm. Furthermore, our approach focuses on extensibility, allowing for easy amenability for construction of higher dimensional Voronoi diagram. This ensures that the Voronoi diagram generation process can be adapted and expanded upon to meet specific requirements or incorporate future enhancements. We present an implementation of the proposed algorithm on a GPU using TAICHI language and describe its performance benefits on multiple input sites.

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Neighborhoods for distance transformations using ordered propagation

Cited by 69 publications

References 10 publications

Fast Euclidean Distance Transformation by Propagation Using Multiple Neighborhoods

Fast Euclidean Distance Transformation by Propagation Using Multiple Neighborhoods

Locally adaptable mathematical morphology using distance transformations

A digital geometric approach for discrete Voronoi diagram construction using GPU

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