## Morphological grayscale reconstruction in image analysis: Applications and efficient algorithms (1993)

Venue: | IEEE Transactions on Image Processing |

Citations: | 204 - 1 self |

### BibTeX

@ARTICLE{Vincent93morphologicalgrayscale,

author = {Luc Vincent},

title = {Morphological grayscale reconstruction in image analysis: Applications and efficient algorithms},

journal = {IEEE Transactions on Image Processing},

year = {1993},

volume = {2},

pages = {176--201}

}

### Years of Citing Articles

### OpenURL

### Abstract

Morphological reconstruction is part of a set of image operators often referred to as geodesic. In the binary case, reconstruction simply extracts the connected components of a binary image I (the mask) which are \marked " by a (binary) image J contained in I. This transformation can be extended to the grayscale case, where it turns out to be extremely useful for several image analysis tasks. This paper rst provides two di erent formal de nitions of grayscale reconstruction. It then illustrates the use of grayscale reconstruction in various image processing applications and aims at demonstrating the usefulness of this transformation for image ltering and segmentation tasks. Lastly, the paper focuses on implementation issues: the standard parallel and sequential approaches to reconstruction are brie y recalled; their common drawback is their ine ciency on conventional computers. To improve this situation, a new algorithm is introduced, which is based on the notion of regional maxima and makes use of breadthrst image scannings implemented via a queue of pixels. Its combination with the sequential technique results in a hybrid grayscale reconstruction algorithm which is an order of magnitude faster than any previously known algorithm. Published in the IEEE Transactions on Image Processing, Vol. 2, No. 2, pp. 176{201,

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Citation Context ... algorithm. Published in the IEEE Transactions on Image Processing, Vol. 2, No. 2, pp. 176{201, April 1993. 1s1 Introduction Reconstruction isavery useful operator provided by mathematical morphology =-=[18, 19]-=-. Although it can easily be de ned in itself, it is often presented as part as a set of operators known as geodesic ones [7]. The reconstruction transformation is relatively well-known in the binary c... |

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Citation Context ...tion of setY , de ned as the intersection ofX and the standard dilation ofY . Note that some authors use a di erent terminology and utilize the word \conditional" for what this paper calls \geodesic" =-=[5]-=-. (a) 4-connectivity (b) 8-connectivity Figure 6: Boundaries of the successive geodesic dilations of a set (in black) within a mask. When performing successive elementary geodesic dilations of a setY ... |

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Citation Context ...he minimal number of edges of the grid to cross to go from pixelpto pixelq. In 4-connectivity, this distance is often called city-block distance whereas in 8-connectivity, itisthe chessboard distance =-=[2]-=-. The elementary ball in distancedG is denotedBG, or simplyB. We denote byNG(p) the set of the neighbors of pixelp for gridG. In the following, we often consider two disjoined subsets ofNG(p), denoted... |

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Citation Context ... too many of these crest lines are due to noise in the original data. Therefore, the watersheds of Fig. 15.b yield the over-segmented result of Fig. 15.c. As explained in numerous recent publications =-=[28, 20,30,13]-=-, the correct way to use watersheds for grayscale image segmentation consists in rst detecting markers of the objects to be extracted. The design of robust marker detection techniques involves the use... |

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Citation Context ...one orientation for which the vessels are not completely removed by opening. After taking the supremum of these di erent openings, one gets Fig. 10.b, which is still an algebraic opening of Fig. 10.a =-=[19]-=-. It is used as marker to reconstruct the blood vessels 9sentirely. Fig. 10.c is the result of the grayscale reconstruction of Fig. 10.a from Fig. 10.b. Since the aneurisms are disconnected from the b... |

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Citation Context ...tegically located pixels [23, 26, 22]. These two class of methods can be used to e ciently implement such complex morphological operations as propagation functions [9, 16], watersheds [30], skeletons =-=[24]-=- and many others [17]. Here, we shall be concerned with the second class of algorithms. The breadth- rst scannings involved are implemented by using a queue of pixels, i.e., a First-In-First-Out (FIFO... |

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Citation Context ...nstruction isavery useful operator provided by mathematical morphology [18, 19]. Although it can easily be de ned in itself, it is often presented as part as a set of operators known as geodesic ones =-=[7]-=-. The reconstruction transformation is relatively well-known in the binary case, where it simply extracts the connected components of an image which are \marked" by another image (see x 2). However, r... |

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Citation Context ... theh-domes of Fig. 13.a. An easy thresholding of this image yields Fig. 13.d, which is an accurate set of cell markers. Additional examples of application of theh-dome transformation can be found in =-=[23, 26, 3]-=-, and more details can be found in [4]. Note that the results of this section can easily be \inverted" to extract minima andh-basins in grayscale images. 3.4 Grayscale reconstruction and binary segmen... |

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Citation Context ...ight) blood vessels and mainly located in the dark central area of the image. Obviously, it is impossible to detect these micro-aneurisms via simple thresholdings. Similarly, a top-hat transformation =-=[12]-=- consisting in subtracting from the original image its morphological opening with respect to a small disc would extract all the \white" features, i.e. aneurisms and blood vessels, which is not desirab... |

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Citation Context ...given mask [16], whereas the algorithms of 19sthe second category regard the images under study as graphs and realize breadth- rst scannings of these graphs starting from strategically located pixels =-=[23, 26, 22]-=-. These two class of methods can be used to e ciently implement such complex morphological operations as propagation functions [9, 16], watersheds [30], skeletons [24] and many others [17]. Here, we s... |

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Citation Context ...esI taking their values inf0; 1;:::;N, 1g, it su ces to consider the successive thresholdsTk(I) ofI, fork= 0toN, 1: Tk(I)=fp2DIjI(p)kg: (4) They are said to constitute the threshold decomposition ofI =-=[10, 11]-=-. As illustrated by Fig. 7, these sets obviously satisfy the following inclusion relationship: 8k2[1;N, 1];Tk(I)Tk,1(I): When applying the increasing operation to each of these sets, their inclusion r... |

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Citation Context .... This segmentation methodology is commonly used in morphology and has been successfully applied to various types of images: NMR images [23], digital elevation models [21], corneal endothelial images =-=[29]-=-, succession of images used for motion estimation [3], and many others. 4 Computing reconstruction in digital images In this section, we are concerned with both the binary and the grayscale case, but ... |

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Citation Context ...e on conventional computers. Two algorithms are introduced to bridge this gap. The rst one is based on the notion of regional maxima and uses breadth- rst image scannings enabled by a queue of pixels =-=[25]-=-. The second one is a combination of this scanning technique with the classical sequential one [14], and it turns out to be the fastest algorithm in almost all practical cases. We shall exclusively be... |

4 | Morphological grayscale reconstruction: definition, efficient algorithm and applications in image analysis - Vincent - 1992 |

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Citation Context ...esI taking their values inf0; 1;:::;N, 1g, it su ces to consider the successive thresholdsTk(I) ofI, fork= 0toN, 1: Tk(I)=fp2DIjI(p)kg: (4) They are said to constitute the threshold decomposition ofI =-=[10, 11]-=-. As illustrated by Fig. 7, these sets obviously satisfy the following inclusion relationship: 8k2[1;N, 1];Tk(I)Tk,1(I): When applying the increasing operation to each of these sets, their inclusion r... |

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Citation Context ...els [23, 26, 22]. These two class of methods can be used to e ciently implement such complex morphological operations as propagation functions [9, 16], watersheds [30], skeletons [24] and many others =-=[17]-=-. Here, we shall be concerned with the second class of algorithms. The breadth- rst scannings involved are implemented by using a queue of pixels, i.e., a First-In-First-Out (FIFO) data structure: the... |

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Citation Context ... nition using threshold superposition It has been known for several years that|at least in the discrete case|any increasing transformation de ned for binary images can be extended to grayscale images =-=[18, 19, 31, 20]-=-. By increasing, we mean a transformation such that 8X;Y Z 2 ;YX =) (Y ) (X): (3) In order to extend such a transformation to grayscale imagesI taking their values inf0; 1;:::;N, 1g, it su ces to cons... |

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Citation Context ... nition using threshold superposition It has been known for several years that|at least in the discrete case|any increasing transformation de ned for binary images can be extended to grayscale images =-=[18, 19, 31, 20]-=-. By increasing, we mean a transformation such that 8X;Y Z 2 ;YX =) (Y ) (X): (3) In order to extend such a transformation to grayscale imagesI taking their values inf0; 1;:::;N, 1g, it su ces to cons... |

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Citation Context ...tion, as illustrated by Fig. 15.f. This segmentation methodology is commonly used in morphology and has been successfully applied to various types of images: NMR images [23], digital elevation models =-=[21]-=-, corneal endothelial images [29], succession of images used for motion estimation [3], and many others. 4 Computing reconstruction in digital images In this section, we are concerned with both the bi... |