组件树理论和方法研究综述
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摘要
组件树方法是数学形态学理论及方法的进一步发展,它利用一系列阈值截集产生连通分量,构造其上的层次关系。利用组件树方法发展出的一系列高效的图像处理算法,非常适合图像底层特征的快速提取,在广大的领域,尤其是医学图像处理领域,得到了广泛的应用。对组件树方法的发展和现状进行了系统的回顾,概述了现存的组件树建树算法以及基于组件树的图像处理算法。对组件树在多值(彩色)图像相关领域、树的快速构建、并行化处理算法方面的研究进行了展望。
Component tree method is the further development of mathematical morphology theory and method. It uses a series of threshold sets to generate connected components, and constructs the hierarchical relations on them. A series of efficient image processing algorithms developed by using the component tree method are very suitable for the rapid extraction of the underlying features of the image, and have been widely used in many fields, especially in the field of medical image processing. In this paper, the development and present situation of component tree methods are reviewed systematically, and the existing component tree building algorithms and image processing algorithms based on component trees are summarized. Finally, this paper looks forward to the research of component tree in multi-valued(color)image correlation field, the fast construction of tree, and the parallel processing algorithm.
Component tree method is the further development of mathematical morphology theory and method. It uses a series of threshold sets to generate connected components, and constructs the hierarchical relations on them. A series of efficient image processing algorithms developed by using the component tree method are very suitable for the rapid extraction of the underlying features of the image, and have been widely used in many fields, especially in the field of medical image processing. In this paper, the development and present situation of component tree methods are reviewed systematically, and the existing component tree building algorithms and image processing algorithms based on component trees are summarized. Finally, this paper looks forward to the research of component tree in multi-valued(color)image correlation field, the fast construction of tree, and the parallel processing algorithm.
引文
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[2]Wilkinson M H F,Gao H,Hesselink W H,et al.Concurrent computation of attribute filters on shared memory parallel machines[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2008,30(10):1800-1813.
[3]Carlinet E,Géraud T.A comparative review of component tree computation algorithms[J].IEEE Transactions on Image Processing,2014,23(9):3885-3895.
[4]Matas P,Dokladalova E,Akil M,et al.Parallel algorithm for concurrent computation of connected component tree[C]//Proceedings of International Conference on Advanced Concepts for Intelligent Vision Systems.Berlin,Heidelberg:Springer,2008:230-241.
[5]Najman L,Couprie M.Building the component tree in quasi-linear time[J].IEEE Transactions on Image Processing,2006,15(11):3531-3539.
[6]Souza R,Rittner L,Lotufo R,et al.An array-based nodeoriented max-tree representation[C]//IEEE International Conference on Image Processing(ICIP),2015:3620-3624.
[7]Berger C,Géraud T,Levillain R,et al.Effective component tree computation with application to pattern recognition in astronomical imaging[C]//IEEE International Conference on Image Processing,2007:41-44.
[8]Salembier P,Serra J.Flat zones filtering,connected operators,and filters by reconstruction[J].IEEE Transactions on Image Processing,1995,4(8):1153-1160.
[9]Salembier P,Wilkinson M H F.Connected operators[J].IEEE Signal Processing Magazine,2009,26(6):136-157.
[10]Souza R,Rittner L,Machado R,et al.Maximal max-tree simplification[C]//Proceedings of the 22nd International Conference on Pattern Recognition,2014:3132-3137.
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[13]Souza R,Rittner L,Machado R,et al.iamxt:Max-tree toolbox for image processing and analysis[J].SoftwareX,2017,6:81-84.
[14]Moschini U,Meijster A,Wilkinson M H F.A hybrid shared-memory parallel max-tree algorithm for extreme dynamic-range images[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2018,40(3):513-526.
[15]Tavares L A,Souza R M,Rittner L,et al.Interactive max-tree visualization tool for image processing and analysis[C]//International Conference on Image Processing Theory,Tools and Applications,2015:119-124.
[16]Tavares L A,Souza R M,Rittner L,et al.A max-tree simplification proposal and applications for the interactive max-tree visualization tool[C]//29th SIBGRAPI Conference on Graphics,Patterns and Images,2016:313-320.
[17]Matas P.Connected component tree construction for embedded systems[D].Marne-la-Vallée,France:UniversitéParisEst,2014.
[18]Urbach E R,Wilkinson M H F.Shape-only granulometries and grey-scale shape filters[C]//Proceedings of Intarnational Symposium on Mathematical Morphology,2002:305-314.
[19]Jones R.Connected filtering and segmentation using component trees[J].Computer Vision and Image Understanding,1999,75(3):215-228.
[20]Tarjan R E.Efficiency of a good but not linear set union algorithm[J].Journal of the ACM,1975,22(2):215-225.
[21]Hesselink W H.Salembier’s min-tree algorithm turned into breadth first search[J].Information Processing Letters,2003,88(5):225-229.
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[23]Nistér D,Stewénius H.Linear time maximally stable extremal regions[C]//European Conference on Computer Vision.Berlin,Heidelberg:Springer,2008:183-196.
[24]Ouzounis G K,Wilkinson M H F.A parallel implementation of the dual-input max-tree algorithm for attribute filtering[C]//Proceedings of 8th International Symposium on Mathematical Morphology,2007:449-460.
[25]Meijster A.Efficient sequential and parallel algorithms for morphological image processing[D].Groningen,Netherlands:University of Groningen,2004.
[26]Staal J,Abràmoff M D,Niemeijer M,et al.Ridge-based vessel segmentation in color images of the retina[J].IEEETransactions on Medical Imaging,2004,23(4):501-509.
[27]Hu Y.Efficient,high-quality force-directed graph drawing[J].Mathematica Journal,2005,10(1):37-71.
[28]Westenberg M A,Roerdink J B T M,Wilkinson M H F.Volumetric attribute filtering and interactive visualization using the max-tree representation[J].IEEE Transactions on Image Processing,2007,16(12):2943-2952.
[29]Ouzounis G K,Gueguen L.Interactive collection of training samples from the max-tree structure[C]//18th IEEEInternational Conference on Image Processing,2011:1449-1452.
[30]Passat N,Naegel B,Rousseau F,et al.Interactive segmentation based on component-trees[J].Pattern Recognition,2011,44(10/11):2539-2554.
[31]Dougherty E R,Lotufo R A.Hands-on morphological image processing[M].[S.l.]:SPIE Press,2003.
[32]Levillain R,Géraud T,Najman L.Milena:write generic morphological algorithms once,run on many kinds of images[C]//International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing.Berlin,Heidelberg:Springer,2009:295-306.
[33]Couprie M,Marak L,Talbot H.The pink image processing library[EB/OL].(2011)[2018-08-08].https://perso.esiee.fr/~coupriem/Pink/doc/html.
[34]Vincent L.Morphological area openings and closings for grey-scale images[M]//Shape in picture.Berlin,Heidelberg:Springer,1994:197-208.
[35]Teeninga P,Moschini U,Trager S C,et al.Improved detection of faint extended astronomical objects through statistical attribute filtering[C]//Proceedings of International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing.Cham:Springer,2015:157-168.
[36]Wang Z,Bovik A C,Sheikh H R,et al.Image quality assessment:from error visibility to structural similarity[J].IEEE Transactions on Image Processing,2004,13(4):600-612.
[37]Dokládal P,Bloch I,Couprie M,et al.Topologically controlled segmentation of 3D magnetic resonance images of the head by using morphological operators[J].Pattern Recognition,2003,36(10):2463-2478.
[38]Caldairou B,Naegel B,Passat N.Segmentation of complex images based on component-trees:methodological tools[C]//Proceedings of International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing.Berlin,Heidelberg:Springer,2009:171-180.
[39]Naegel B,Passat N,Boch N,et al.Segmentation using vector-attribute filters:methodology and application to dermatological imaging[C]//International Symposium on Mathematical Morphology,2006:239-250.
[40]Sghaier M O,Foucher S,Lepage R,et al.A multiscale based approach for river extraction from SAR images using attribute filters[C]//2018 IEEE International Geoscience and Remote Sensing Symposium,2018:9245-9248.
[41]Salembier P,Garrido L.Binary partition tree as an efficient representation for image processing,segmentation,and information retrieval[J].IEEE Transactions on Image Processing,2000,9(4):561-576.
[42]Ouzounis G K,Wilkinson M H F.Mask-based secondgeneration connectivity and attribute filters[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2007,29(6):990-1004.
[43]Monasse P,Guichard F.Fast computation of a contrastinvariant image representation[J].IEEE Transactions on Image Processing,2000,9(5):860-872.
[44]Géraud T,Carlinet E,Crozet S,et al.A quasi-linear algorithm to compute the tree of shapes of nD images[C]//International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing.Berlin,Heidelberg:Springer,2013:98-110.
[45]Carlinet E,Crozet S,Géraud T.The tree of shapes turned into a Max-Tree:a simple and efficient linear algorithm[C]//The 25th IEEE International Conference on Image Processing,2018:1488-1492.
[46]Xu Y,Géraud T,Najman L.Morphological filtering in shape spaces:applications using tree-based image representations[C]//2012 21st International Conference on Pattern Recognition,2012:485-488.
[47]Xu Y,Géraud T,Najman L.Two applications of shapebased morphology:blood vessels segmentation and a generalization of constrained connectivity[C]//International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing.Berlin,Heidelberg:Springer,2013:390-401.
[48]Xu Y,Carlinet E,Géraud T,et al.Hierarchical segmentation using tree-based shape spaces[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2017,39(3):457-469.
[49]Richard M,Fleute M,Desbat L,et al.Registration of medical images for surgical action:use of optical sensors and matching algorithm[C]//Sixth International Conference on Education and Training in Optics and Photonics,International Society for Optics and Photonics,2000:125-140.
[50]Merino-Gracia C,Lenc K,Mirmehdi M.A head-mounted device for recognizing text in natural scenes[C]//Proceedings of International Workshop on Camera-Based Document Analysis and Recognition.Berlin,Heidelberg:Springer,2011:29-41.
[51]Ghamisi P,Souza R,Benediktsson J A,et al.Extinction profiles for the classification of remote sensing data[J].IEEE Transactions on Geoscience and Remote Sensing,2016,54(10):5631-5645.
[52]Benediktsson J A,Bruzzone L,Chanussot J,et al.Hierarchical analysis of remote sensing data:morphological attribute profiles and binary partition trees[C]//International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing.Berlin,Heidelberg:Springer,2011:306-319.
[53]Dalla Mura M,Benediktsson J A,Bruzzone L.Self-dual attribute profiles for the analysis of remote sensing images[C]//International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing.Berlin,Heidelberg:Springer,2011:320-330.
[54]Wilkinson M H F,Soille P,Pesaresi M,et al.Concurrent computation of differential morphological profiles on giga-pixel images[C]//International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing.Berlin,Heidelberg:Springer,2011:331-342.
[55]Matas J,Chum O,Urban M,et al.Robust wide-baseline stereo from maximally stable extremal regions[J].Image and Vision Computing,2004,22(10):761-767.
[56]Xu Y,Monasse P,Géraud T,et al.Tree-based morse regions:a topological approach to local feature detection[J].IEEE Transactions on Image Processing,2014,23(12):5612-5625.
[57]Li W,Wang Z,Li L,et al.Modified extinction profiles for hyperspectral image classification[C]//The 10th IAPRWorkshop on Pattern Recognition in Remote Sensing,2018:1-5.
[58]Pham M T,Aptoula E,Lefèvre S.Feature profiles from attribute filtering for classification of remote sensing images[J].IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing,2018,11(1):249-256.
[59]Ferdosi B J.Microscopy cell counting and annotation using a Max-Tree representation of the blood cell images[C]//Proceedings of the 3rd International Conference on Biomedical Signal and Image Processing,2018:61-65.
[60]G?tz M,Cavallaro G,Géraud T,et al.Parallel computation of component trees on distributed memory machines[J].IEEE Transactions on Parallel and Distributed Systems,2018,29(11):2582-2598.
[61]Bascoy P G,Quesada-Barriuso P,Heras D B,et al.Extended attribute profiles on GPU applied to hyperspectral image classification[J].The Journal of Supercomputing,2018:1-15.
[62]Souza R,Rittner L,Machado R,et al.A comparison between extinction filters and attribute filters[C]//International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing.Cham:Springer,2015:63-74.
[63]Aptoula E,Lefèvre S.A comparative study on multivariate mathematical morphology[J].Pattern Recognition,2007,40(11):2914-2929.
[64]Angulo J.Morphological colour operators in totally ordered lattices based on distances:application to image filtering,enhancement and analysis[J].Computer Vision and Image Understanding,2007,107(1/2):56-73.
[65]Passat N,Naegel B.An extension of component-trees to partial orders[C]//2009 16th IEEE International Conference on Image Processing,2009:3981-3984.
[66]Kurtz C,Naegel B,Passat N.Multivalued component-tree filtering[C]//Proceedings of the 22nd International Conference on Pattern Recognition,2014:1008-1013.
[67]Passat N,Naegel B.Component-trees and multivalued images:structural properties[J].Journal of Mathematical Imaging and Vision,2014,49(1):37-50.
[68]Passat N,Naegel B,Kurtz C.Implicit component-graph:a discussion[C]//International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing.Cham:Springer,2017:235-248.
[69]Tushabe F,Wilkinson M H F.Color processing using maxtrees:a comparison on image compression[C]//Proceedings of International Conference on Systems and Informatics,2012:1374-1380.
[70]Kurtz C,Naegel B,Passat N.Connected filtering based on multivalued component-trees[J].IEEE Transactions on Image Processing,2014,23(12):5152-5164.
[2]Wilkinson M H F,Gao H,Hesselink W H,et al.Concurrent computation of attribute filters on shared memory parallel machines[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2008,30(10):1800-1813.
[3]Carlinet E,Géraud T.A comparative review of component tree computation algorithms[J].IEEE Transactions on Image Processing,2014,23(9):3885-3895.
[4]Matas P,Dokladalova E,Akil M,et al.Parallel algorithm for concurrent computation of connected component tree[C]//Proceedings of International Conference on Advanced Concepts for Intelligent Vision Systems.Berlin,Heidelberg:Springer,2008:230-241.
[5]Najman L,Couprie M.Building the component tree in quasi-linear time[J].IEEE Transactions on Image Processing,2006,15(11):3531-3539.
[6]Souza R,Rittner L,Lotufo R,et al.An array-based nodeoriented max-tree representation[C]//IEEE International Conference on Image Processing(ICIP),2015:3620-3624.
[7]Berger C,Géraud T,Levillain R,et al.Effective component tree computation with application to pattern recognition in astronomical imaging[C]//IEEE International Conference on Image Processing,2007:41-44.
[8]Salembier P,Serra J.Flat zones filtering,connected operators,and filters by reconstruction[J].IEEE Transactions on Image Processing,1995,4(8):1153-1160.
[9]Salembier P,Wilkinson M H F.Connected operators[J].IEEE Signal Processing Magazine,2009,26(6):136-157.
[10]Souza R,Rittner L,Machado R,et al.Maximal max-tree simplification[C]//Proceedings of the 22nd International Conference on Pattern Recognition,2014:3132-3137.
[11]Urbach E R,Roerdink J B T M,Wilkinson M H F.Connected shape-size pattern spectra for rotation and scale-invariant classification of gray-scale images[J].IEEETransactions on Pattern Analysis and Machine Intelligence,2007,29(2):272-285.
[12]Donoser M,Arth C,Bischof H.Detecting,tracking and recognizing license plates[C]//Proceedings of Asian Conference on Computer Vision.Berlin,Heidelberg:Springer,2007:447-456.
[13]Souza R,Rittner L,Machado R,et al.iamxt:Max-tree toolbox for image processing and analysis[J].SoftwareX,2017,6:81-84.
[14]Moschini U,Meijster A,Wilkinson M H F.A hybrid shared-memory parallel max-tree algorithm for extreme dynamic-range images[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2018,40(3):513-526.
[15]Tavares L A,Souza R M,Rittner L,et al.Interactive max-tree visualization tool for image processing and analysis[C]//International Conference on Image Processing Theory,Tools and Applications,2015:119-124.
[16]Tavares L A,Souza R M,Rittner L,et al.A max-tree simplification proposal and applications for the interactive max-tree visualization tool[C]//29th SIBGRAPI Conference on Graphics,Patterns and Images,2016:313-320.
[17]Matas P.Connected component tree construction for embedded systems[D].Marne-la-Vallée,France:UniversitéParisEst,2014.
[18]Urbach E R,Wilkinson M H F.Shape-only granulometries and grey-scale shape filters[C]//Proceedings of Intarnational Symposium on Mathematical Morphology,2002:305-314.
[19]Jones R.Connected filtering and segmentation using component trees[J].Computer Vision and Image Understanding,1999,75(3):215-228.
[20]Tarjan R E.Efficiency of a good but not linear set union algorithm[J].Journal of the ACM,1975,22(2):215-225.
[21]Hesselink W H.Salembier’s min-tree algorithm turned into breadth first search[J].Information Processing Letters,2003,88(5):225-229.
[22]Wilkinson M H F.A fast component-tree algorithm for high dynamic-range images and second-generation connectivity[C]//Proceedings of the 18th IEEE International Conference on Image Processing,2011:1021-1024.
[23]Nistér D,Stewénius H.Linear time maximally stable extremal regions[C]//European Conference on Computer Vision.Berlin,Heidelberg:Springer,2008:183-196.
[24]Ouzounis G K,Wilkinson M H F.A parallel implementation of the dual-input max-tree algorithm for attribute filtering[C]//Proceedings of 8th International Symposium on Mathematical Morphology,2007:449-460.
[25]Meijster A.Efficient sequential and parallel algorithms for morphological image processing[D].Groningen,Netherlands:University of Groningen,2004.
[26]Staal J,Abràmoff M D,Niemeijer M,et al.Ridge-based vessel segmentation in color images of the retina[J].IEEETransactions on Medical Imaging,2004,23(4):501-509.
[27]Hu Y.Efficient,high-quality force-directed graph drawing[J].Mathematica Journal,2005,10(1):37-71.
[28]Westenberg M A,Roerdink J B T M,Wilkinson M H F.Volumetric attribute filtering and interactive visualization using the max-tree representation[J].IEEE Transactions on Image Processing,2007,16(12):2943-2952.
[29]Ouzounis G K,Gueguen L.Interactive collection of training samples from the max-tree structure[C]//18th IEEEInternational Conference on Image Processing,2011:1449-1452.
[30]Passat N,Naegel B,Rousseau F,et al.Interactive segmentation based on component-trees[J].Pattern Recognition,2011,44(10/11):2539-2554.
[31]Dougherty E R,Lotufo R A.Hands-on morphological image processing[M].[S.l.]:SPIE Press,2003.
[32]Levillain R,Géraud T,Najman L.Milena:write generic morphological algorithms once,run on many kinds of images[C]//International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing.Berlin,Heidelberg:Springer,2009:295-306.
[33]Couprie M,Marak L,Talbot H.The pink image processing library[EB/OL].(2011)[2018-08-08].https://perso.esiee.fr/~coupriem/Pink/doc/html.
[34]Vincent L.Morphological area openings and closings for grey-scale images[M]//Shape in picture.Berlin,Heidelberg:Springer,1994:197-208.
[35]Teeninga P,Moschini U,Trager S C,et al.Improved detection of faint extended astronomical objects through statistical attribute filtering[C]//Proceedings of International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing.Cham:Springer,2015:157-168.
[36]Wang Z,Bovik A C,Sheikh H R,et al.Image quality assessment:from error visibility to structural similarity[J].IEEE Transactions on Image Processing,2004,13(4):600-612.
[37]Dokládal P,Bloch I,Couprie M,et al.Topologically controlled segmentation of 3D magnetic resonance images of the head by using morphological operators[J].Pattern Recognition,2003,36(10):2463-2478.
[38]Caldairou B,Naegel B,Passat N.Segmentation of complex images based on component-trees:methodological tools[C]//Proceedings of International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing.Berlin,Heidelberg:Springer,2009:171-180.
[39]Naegel B,Passat N,Boch N,et al.Segmentation using vector-attribute filters:methodology and application to dermatological imaging[C]//International Symposium on Mathematical Morphology,2006:239-250.
[40]Sghaier M O,Foucher S,Lepage R,et al.A multiscale based approach for river extraction from SAR images using attribute filters[C]//2018 IEEE International Geoscience and Remote Sensing Symposium,2018:9245-9248.
[41]Salembier P,Garrido L.Binary partition tree as an efficient representation for image processing,segmentation,and information retrieval[J].IEEE Transactions on Image Processing,2000,9(4):561-576.
[42]Ouzounis G K,Wilkinson M H F.Mask-based secondgeneration connectivity and attribute filters[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2007,29(6):990-1004.
[43]Monasse P,Guichard F.Fast computation of a contrastinvariant image representation[J].IEEE Transactions on Image Processing,2000,9(5):860-872.
[44]Géraud T,Carlinet E,Crozet S,et al.A quasi-linear algorithm to compute the tree of shapes of nD images[C]//International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing.Berlin,Heidelberg:Springer,2013:98-110.
[45]Carlinet E,Crozet S,Géraud T.The tree of shapes turned into a Max-Tree:a simple and efficient linear algorithm[C]//The 25th IEEE International Conference on Image Processing,2018:1488-1492.
[46]Xu Y,Géraud T,Najman L.Morphological filtering in shape spaces:applications using tree-based image representations[C]//2012 21st International Conference on Pattern Recognition,2012:485-488.
[47]Xu Y,Géraud T,Najman L.Two applications of shapebased morphology:blood vessels segmentation and a generalization of constrained connectivity[C]//International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing.Berlin,Heidelberg:Springer,2013:390-401.
[48]Xu Y,Carlinet E,Géraud T,et al.Hierarchical segmentation using tree-based shape spaces[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2017,39(3):457-469.
[49]Richard M,Fleute M,Desbat L,et al.Registration of medical images for surgical action:use of optical sensors and matching algorithm[C]//Sixth International Conference on Education and Training in Optics and Photonics,International Society for Optics and Photonics,2000:125-140.
[50]Merino-Gracia C,Lenc K,Mirmehdi M.A head-mounted device for recognizing text in natural scenes[C]//Proceedings of International Workshop on Camera-Based Document Analysis and Recognition.Berlin,Heidelberg:Springer,2011:29-41.
[51]Ghamisi P,Souza R,Benediktsson J A,et al.Extinction profiles for the classification of remote sensing data[J].IEEE Transactions on Geoscience and Remote Sensing,2016,54(10):5631-5645.
[52]Benediktsson J A,Bruzzone L,Chanussot J,et al.Hierarchical analysis of remote sensing data:morphological attribute profiles and binary partition trees[C]//International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing.Berlin,Heidelberg:Springer,2011:306-319.
[53]Dalla Mura M,Benediktsson J A,Bruzzone L.Self-dual attribute profiles for the analysis of remote sensing images[C]//International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing.Berlin,Heidelberg:Springer,2011:320-330.
[54]Wilkinson M H F,Soille P,Pesaresi M,et al.Concurrent computation of differential morphological profiles on giga-pixel images[C]//International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing.Berlin,Heidelberg:Springer,2011:331-342.
[55]Matas J,Chum O,Urban M,et al.Robust wide-baseline stereo from maximally stable extremal regions[J].Image and Vision Computing,2004,22(10):761-767.
[56]Xu Y,Monasse P,Géraud T,et al.Tree-based morse regions:a topological approach to local feature detection[J].IEEE Transactions on Image Processing,2014,23(12):5612-5625.
[57]Li W,Wang Z,Li L,et al.Modified extinction profiles for hyperspectral image classification[C]//The 10th IAPRWorkshop on Pattern Recognition in Remote Sensing,2018:1-5.
[58]Pham M T,Aptoula E,Lefèvre S.Feature profiles from attribute filtering for classification of remote sensing images[J].IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing,2018,11(1):249-256.
[59]Ferdosi B J.Microscopy cell counting and annotation using a Max-Tree representation of the blood cell images[C]//Proceedings of the 3rd International Conference on Biomedical Signal and Image Processing,2018:61-65.
[60]G?tz M,Cavallaro G,Géraud T,et al.Parallel computation of component trees on distributed memory machines[J].IEEE Transactions on Parallel and Distributed Systems,2018,29(11):2582-2598.
[61]Bascoy P G,Quesada-Barriuso P,Heras D B,et al.Extended attribute profiles on GPU applied to hyperspectral image classification[J].The Journal of Supercomputing,2018:1-15.
[62]Souza R,Rittner L,Machado R,et al.A comparison between extinction filters and attribute filters[C]//International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing.Cham:Springer,2015:63-74.
[63]Aptoula E,Lefèvre S.A comparative study on multivariate mathematical morphology[J].Pattern Recognition,2007,40(11):2914-2929.
[64]Angulo J.Morphological colour operators in totally ordered lattices based on distances:application to image filtering,enhancement and analysis[J].Computer Vision and Image Understanding,2007,107(1/2):56-73.
[65]Passat N,Naegel B.An extension of component-trees to partial orders[C]//2009 16th IEEE International Conference on Image Processing,2009:3981-3984.
[66]Kurtz C,Naegel B,Passat N.Multivalued component-tree filtering[C]//Proceedings of the 22nd International Conference on Pattern Recognition,2014:1008-1013.
[67]Passat N,Naegel B.Component-trees and multivalued images:structural properties[J].Journal of Mathematical Imaging and Vision,2014,49(1):37-50.
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