Efficient Implementation of the Fuzzy c-Means Clustering Algorithms
IEEE Transactions on Pattern Analysis and Machine Intelligence
Three-dimensional boundary following
Computer Vision, Graphics, and Image Processing
Fuzzy connectivity and mathematical morphology
Pattern Recognition Letters
Extraction of intensity connectedness for image processing
Pattern Recognition Letters
Graphical Models and Image Processing
Local Scale Control for Edge Detection and Blur Estimation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Zoom-invariant vision of figural shape: the mathematics of cores
Computer Vision and Image Understanding
User-steered image segmentation paradigms: live wire and live lane
Graphical Models and Image Processing
Scale-based fuzzy connected image segmentation: theory, algorithms, and validation
Computer Vision and Image Understanding - Special issue on analysis of volumetric image
On the optimal detection of curves in noisy pictures
Communications of the ACM
Multiseeded Segmentation Using Fuzzy Connectedness
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computer Vision and Image Understanding
IEEE Computer Graphics and Applications
Composition of Image Analysis Processes Through Object-Centered Hierarchical Planning
IEEE Transactions on Pattern Analysis and Machine Intelligence
MMBIA '00 Proceedings of the IEEE Workshop on Mathematical Methods in Biomedical Image Analysis
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Multiscale image segmentation by integrated edge and region detection
IEEE Transactions on Image Processing
Simultaneous fuzzy segmentation of multiple objects
Discrete Applied Mathematics - Special issue: IWCIA 2003 - Ninth international workshop on combinatorial image analysis
Vectorial scale-based fuzzy-connected image segmentation
Computer Vision and Image Understanding
A framework of fuzzy information fusion for the segmentation of brain tumor tissues on MR images
Image and Vision Computing
Interactive segmentation of image volumes with Live Surface
Computers and Graphics
Iterative relative fuzzy connectedness for multiple objects with multiple seeds
Computer Vision and Image Understanding
Object delineation by κ-connected components
EURASIP Journal on Advances in Signal Processing
Links Between Image Segmentation Based on Optimum-Path Forest and Minimum Cut in Graph
Journal of Mathematical Imaging and Vision
Vectorial scale-based fuzzy-connected image segmentation
Computer Vision and Image Understanding
Affinity functions in fuzzy connectedness based image segmentation I: Equivalence of affinities
Computer Vision and Image Understanding
Computer Vision and Image Understanding
Expert Systems with Applications: An International Journal
Simultaneous fuzzy segmentation of multiple objects
Discrete Applied Mathematics - Special issue: IWCIA 2003 - Ninth international workshop on combinatorial image analysis
Pulmonary nodule classification aided by clustering
SMC'09 Proceedings of the 2009 IEEE international conference on Systems, Man and Cybernetics
Relationships between some watershed definitions and their tie-zone transforms
Image and Vision Computing
Multi-seed segmentation of tomographic volumes based on fuzzy connectedness
ICIC'10 Proceedings of the Advanced intelligent computing theories and applications, and 6th international conference on Intelligent computing
Application of fuzzy connectedness in 3D blood vessel extraction
International Journal of Bioinformatics Research and Applications
Local Orthogonal Cutting Method for Computing Medial Curves and Its Biomedical Applications
SIAM Journal on Scientific Computing
Computer Vision and Image Understanding
SMI 2011: Full Paper: Geometric models with weigthed topology
Computers and Graphics
Generalized hard constraints for graph segmentation
SCIA'11 Proceedings of the 17th Scandinavian conference on Image analysis
User-steered image segmentation using live markers
CAIP'11 Proceedings of the 14th international conference on Computer analysis of images and patterns - Volume Part I
Computer Vision and Image Understanding
Computer Vision and Image Understanding
Geodesic voting for the automatic extraction of tree structures. Methods and applications
Computer Vision and Image Understanding
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The notion of fuzzy connectedness captures the idea of "hanging-togetherness" of image elements in an object by assigning a strength of connectedness to every possible path between every possible pair of image elements. This concept leads to powerful image segmentation algorithms based on dynamic programming whose effectiveness has been demonstrated on 1,000s of images in a variety of applications. In the previous framework, a fuzzy connected object is defined with a threshold on the strength of connectedness. In this paper, we introduce the notion of relative connectedness that overcomes the need for a threshold and that leads to more effective segmentations. The central idea is that an object gets defined in an image because of the presence of other co-objects. Each object is initialized by a seed element. An image element c is considered to belong to that object with respect to whose reference image element c has the highest strength of connectedness. In this fashion, objects compete among each other utilizing fuzzy connectedness to grab membership of image elements. We present a theoretical and algorithmic framework for defining objects via relative connectedness and demonstrate utilizing the theory that the objects defined are independent of reference elements chosen as long as they are not in the fuzzy boundary between objects. An iterative strategy is also introduced wherein the strongest relative connected core parts are first defined and iteratively relaxed to conservatively capture the more fuzzy parts subsequently. Examples from medical imaging are presented to illustrate visually the effectiveness of relative fuzzy connectedness. A quantitative mathematical phantom study involving 160 images is conducted to demonstrate objectively the effectiveness of relative fuzzy connectedness.