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split-and-merge algorithms defined on topological maps for 3D image segmentation

GRAPHICAL MODELS 2003年第1-3期65卷 149-167页

作者： Damiand, G Resch, P SIC IRCOM F-86962 Futuroscope France LIRMM F-34392 Montpellier 5 France

split-and-merge algorithms define a class of image segmentation methods. Topological maps are a mathematical model that represents image subdivisions in 2D and 3D. This paper discusses a split-and-merge method for 3D image data based on the topological map model. This model allows representations of states of segmentations and of merge and split operations. Indeed, it can be used as data structure for dynamic changes of segmentation. The paper details such an algorithmic approach and analyzes its time complexity. A general introduction into combinatorial and topological maps is given to support the understanding of the proposed algorithms. (C) 2003 Elsevier Science (USA). All rights reserved.

关键词： topological maps split-and-merge image segmentation image processing

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split-and-merge segmentation of magnetic resonance medical images: Performance evaluation and extension to three dimensions

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COMPUTERS AND BIOMEDICAL RESEARCH 1998年第6期31卷 393-412页

作者： Manousakas, IN Undrill, PE Cameron, GG Redpath, TW Univ Aberdeen Dept Biomed Phys & Bioengn Aberdeen AB25 2ZD Scotland

Intensity- or edge-based methods of segmentation are often insufficiently robust to be applied to images containing complex anatomical objects, such as those seen in high-resolution magnetic resonance imaging systems. split-and-merge techniques attempt to overcome these difficulties by using homogeneity measures. Simple modifications to the basic 2D split-and-merge method, based on the principles of simulated annealing and controlled boundary elimination, are developed and discussed. Simulated annealing reduced the number of regions by 22% with a further reduction of 21% achieved through boundary elimination. Smoother regional boundaries are also produced. These methods are extended to true 3D and quantitatively compared with their 2D counterparts. The main advantage of 3D methods is that they produce segmented volumes by directly preserving the connectivity between slices, whereas in 2D, segments have to be grouped together in a post-split-and-merge process. Finally, the properties of the 3D approach are demonstrated by the automatic quantitation of brain ventricle volume, producing estimates to within 7% of validated manual methods. (C) 1998 Academic Press.

关键词： segmentation volumetry split-and-merge magnetic resonance imaging

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split-and-merge method for 3-D model reconstruction

Split-and-merge method for 3-D model reconstruction

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Conference on 3-Dimensional Image Capture and Applications IV

作者： Huang, YJ Nishida, H Ricoh Co Ltd Softwear Res Ctr Bunkyo Ku Tokyo 1120002 Japan

ISBN: (纸本)0819439762

The factorization method is known to be robust and efficient for the recovery of shape and motion from an image sequence by applying Singular Value Decomposition to the tracking matrix. To get all-around 3-D data of an object, the all-around view of the object must be taken as pictures. This means that a long image sequence is required, and there is almost no feature point that can be tracked throughout all frames. This occurs because of occlusion. Consequently a large tracking matrix in which most elements are unknown is acquired. It is impractical to apply the conventional factorization method directly to such a tracking matrix, because most of the elements are unknown. Instead of applying the factorization method directly to the tracking matrix, the matrix is first divided into sub-matrices having overlapping portions. After unknown elements are estimated in each sub-matrix, the factorization method is applied to each sub-matrix to recover the partial 3-D data. Then the partial 3-D data is integrated into a whole according to the overlapped portions of each pair of sub-matrices. By modifying the factorization method in this split-and-merge manner, not only can the all-around 3-D data be recovered, but also the computation time is decreased dramatically.

关键词： paraperspective projection factorization method singular value decomposition occlusion split-and-merge rotation

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The split-and-merge method in general purpose computation on GPUs

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PARALLEL COMPUTING 2012年第6-7期38卷 277-288页

作者： Argueello, F. Heras, D. B. Boo, M. Lamas-Rodriguez, J. Univ Santiago de Compostela Dept Elect & Comp Santiago De Compostela 15782 Spain

The split-and-merge method is an algorithm design paradigm sometimes used in the field of parallel computing. It is applied to multilevel algorithms such as the wavelet transforms and some tridiagonal system solvers. In this paper we present the application of the method in the context of general purpose computation on GPUs. The split-and-merge method allows us to efficiently use the CUDA parallel programming model, where a multithreaded program is partitioned into blocks of threads that execute independently from each other. Thus we can solve the data dependency problem at the block boundaries and efficiently take advantage of the memory hierarchy of the GPU. The results obtained show a significant acceleration compared with the direct implementation of the algorithms on the GPU. (c) 2012 Published by Elsevier B.V.

关键词： GPGPU CUDA split-and-merge Multilevel algorithm Wavelet

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A projection-based split-and-merge clustering algorithm

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EXPERT SYSTEMS WITH APPLICATIONS 2019年 116卷 121-130页

作者： Cheng, Mingchang Ma, Tiefeng Liu, Youbo Southwestern Univ Finance & Econ Sch Stat Chengdu 611130 Sichuan Peoples R China Sichuan Univ Sch Elect Engn & Informat Chengdu 610065 Sichuan Peoples R China

A novel split-and-merge clustering algorithm is proposed by using projection technology and K-means method. There are two key technologies in the proposed method: shape recognition based on projection and split-and-merge process based on K-means. By projecting the data onto the connection of any two cluster centers, no matter how large the dimension of data is, we can always obtain an one-dimension density curve of the projection to guarantee an acceptable amount of calculation. Further embedded the kernel density estimate, we can determine the distribution of clusters by the shape of the one-dimensional density curve. In the split-and-merge process, this algorithm not only addresses the sensitivity in selecting initial cluster centers, but also automatically give a reasonable number of clusters. We also discuss the possibility to extend the projection split-and-merge method from K-means to density based methods (as EM algorithm and Cross-entropy clustering). Both simulation and real data experimental results show that our method performance well especially under strict data conditions. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： split-and-merge Projection K-means Density curve

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On-line signature verification based on split-and-merge matching mechanism

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PATTERN RECOGNITION LETTERS 1997年第7期18卷 665-673页

作者： Wu, QZ Lee, SY Jou, IC NATL CHIAO TUNG UNIV DEPT COMP SCI & INFORMAT ENGNHSINCHUTAIWAN MINIST COMMUN TELECOMMUN LABSCHUNGLITAIWAN CHANG GUNG COLL MED & TECHNOL DEPT ELECT ENGNTAYUANTAIWAN

In this paper, an on-line signature verification scheme based on split-and-merge matching mechanism is proposed. Each word in the signature is specified with static and dynamic features: a sequence of (x, y) coordinates and a sequence of (x, y) velocities. We employ the split-and-merge matching mechanism for each input sequence of coordinates or velocities with the corresponding sequence of the reference template. Alignment and refinement are exploited in the matching to justify the data skew problem. The accumulated coordinate and velocity distances are compared with corresponding verification thresholds to determine the genuineness of the input signature, Algorithms to compute reference templates and verification thresholds are also proposed. The performed simulation results support the effectiveness of this signature verification scheme.

关键词： signature verification split-and-merge distance measurement dynamic feature static feature

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ADAPTIVE split-and-merge SEGMENTATION BASED ON PIECEWISE LEAST-SQUARE APPROXIMATION

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IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 1993年第8期15卷 808-815页

作者： WU, XL Dept. of Comput. Sci. Western Ontario Univ. London Ont. Canada

The performance of the classic split-and-merge segmentation algorithm is severely hampered by its rigid split-and-merge processes, which are insensitive to the image semantics. This correspondence proposes efficient algorithms and data structures to optimize the split-and-merge processes by piecewise least-square approximation of image intensity functions. This optimization aims at the unification of segment finding and edge detection. The optimized split-and-merge algorithm is shown to be adaptive to the image semantics and, hence, improves the segmentation validity of the previous algorithms. The new algorithm also appeared to work well on noisy sources. Since the optimization is done within the split-and-merge framework, the better segmentation performance is achieved at the same order of time complexity as the previous algorithms.

关键词： ALGORITHMS EDGE DETECTION PIECEWISE LEAST-SQUARE APPROXIMATION REGION ADJACENCY GRAPH SEGMENTATION split-and-merge

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An adaptive split-and-merge method for binary image contour data compression

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PATTERN RECOGNITION LETTERS 2001年第3-4期22卷 299-307页

作者： Xiao, Y Zou, JJ Yan, H Univ Sydney Sch Elect & Informat Engn Sydney NSW 2006 Australia

The split-and-merge method is a well-known algorithm for polygonal approximation in computer Vision applications such as feature extracting and pattern matching. Its accuracy depends on the tolerance, that is the error threshold value. This study presents a split-and-merge method with an adaptive tolerance value for compressing image contours. The tolerance value, which depends on the grid constant D and the line length of line L in a collinearity test, is adopted to reduce quantization error while keeping its original shape. A contour tracing method that achieves the right shape representation of binary images is also discussed. Experimental results for real binary contours show the method is effective for compression of a binary image. The proposed method allows a precise description of the original image and can smooth coarse contours. It is also computationally efficient. (C) 2001 Elsevier Science B.V. All rights reserved.

关键词： contour representation data compression polygonal approximation split-and-merge tolerance

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A NEW split-and-merge CLUSTERING TECHNIQUE

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PATTERN RECOGNITION LETTERS 1992年第6期13卷 399-409页

作者： CHAUDHURI, D CHAUDHURI, BB MURTHY, CA Electronics & Communication Sciences Unit Indian Statistical Institute 203 Barrackpore Trunk Road Calcutta 700 035 India

A new clustering algorithm is developed for efficient classification of data in R(q) when there exists no a priori information about the number of clusters. The algorithm is based on a split-and-merge technique. The type-I splitting is guided by density of data over strips at different directions around the centroid of the data. The type-II splitting is the usual K-means clustering algorithm (K=2) and rechecked with the help of a merging technique. A theorem on the convergence of this algorithm is proved.

关键词： CLUSTER ANALYSIS split-and-merge K-MEANS CLUSTERING

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Edge-Based split-and-merge Superpixel Segmentation

Edge-Based Split-and-Merge Superpixel Segmentation

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IEEE International Conference on Information and Automation 2015

作者： Li, Li Yao, Jian Tu, Jinge Lu, Xiaohu Li, Kai Liu, Yahui Wuhan Univ Sch Remote Sensing & Informat Engn Wuhan Hubei Peoples R China

ISBN: (纸本)9781467391047

Superpixels are an oversegmentation of an image and popularly used as a preprocessing in many computer vision applications. Many state-of-the-art superpixel segmentation algorithms rely either on minimizing special energy functions or on clustering pixels in the effective distance space. While in this paper, we introduce a novel algorithm to produce superpixels based on the edge map by utilizing a split-andmerge strategy. Firstly, we obtain the initial superpixels with uniform size and shape. Secondly, in the splitting stage, we find all possible splitting contours for each superpixel by overlapping the boundaries of this superpixel with the edge map, and then choose the best one to split it which ensure the superpixels produced by this splitting are dissimilarity in color and similarity in size. Thirdly, in the merging stage, the Bhattacharyya distance between two color histograms in the RGB space for each pair of adjacent superpixels is computed to evaluate their color similarity for merging superpixels. At last, we iterate the split-and-merge steps until no superpixels have changed. Experimental results on the Berkeley Segmentation Dataset (BSD) show that the proposed algorithm can achieve a good performance compared with the state-of-the-art superpixel segmentation algorithms.

关键词： Superpixels Edge Drawing split-and-merge Image Segmentation

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