Algorithms for clustering data
Algorithms for clustering data
A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Multiscanning Approach Based on Morphological Filtering
IEEE Transactions on Pattern Analysis and Machine Intelligence
Pattern Spectrum and Multiscale Shape Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Multiresolution Hierarchical Approach to Image Segmentation Based on Intensity Extrema
IEEE Transactions on Pattern Analysis and Machine Intelligence
Pattern Recognition
Neural Computation
Scale-Space Properties of the Multiscale Morphological Dilation-Erosion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Theoretical aspects of morphological filters by reconstruction
Signal Processing
Set-Theoretical Algebraic Approaches to Connectivityin Continuous or Digital Spaces
Journal of Mathematical Imaging and Vision
Morphologically Constrained GRFs: Applications to Texture Synthesis and Analysis
IEEE Transactions on Pattern Analysis and Machine Intelligence
Connectivity on Complete Lattices
Journal of Mathematical Imaging and Vision
Connected morphological operators for binary images
Computer Vision and Image Understanding
Connected filtering and segmentation using component trees
Computer Vision and Image Understanding
Connections for sets and functions
Fundamenta Informaticae - Special issue on mathematical morphology
Clustering by Scale-Space Filtering
IEEE Transactions on Pattern Analysis and Machine Intelligence
Shape Connectivity: Multiscale Analysis and Application to Generalized Granulometries
Journal of Mathematical Imaging and Vision
The Morphological Structure of Images: The Differential Equations of Morphological Scale-Space
IEEE Transactions on Pattern Analysis and Machine Intelligence
Connectivity on complete lattices: new results
Computer Vision and Image Understanding
Morphological Image Analysis: Principles and Applications
Morphological Image Analysis: Principles and Applications
A multiscale approach to connectivity
Computer Vision and Image Understanding
A Theoretical Tour of Connectivity in Image Processing and Analysis
Journal of Mathematical Imaging and Vision
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
Multiscale Connected Operators
Journal of Mathematical Imaging and Vision
Constructing multiscale connectivities
Computer Vision and Image Understanding
Antiextensive connected operators for image and sequence processing
IEEE Transactions on Image Processing
Nonlinear multiresolution signal decomposition schemes. I. Morphological pyramids
IEEE Transactions on Image Processing
Grayscale level connectivity: theory and applications
IEEE Transactions on Image Processing
Flat zones filtering, connected operators, and filters by reconstruction
IEEE Transactions on Image Processing
Scale-based clustering using the radial basis function network
IEEE Transactions on Neural Networks
Size-density spectra and their application to image classification
Pattern Recognition
A Comparison of Spatial Pattern Spectra
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
Component-hypertrees for image segmentation
ISMM'11 Proceedings of the 10th international conference on Mathematical morphology and its applications to image and signal processing
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This paper introduces a novel approach for image analysis based on the notion of multiscale connectivity. We use the proposed approach to design several novel tools for object-based image representation and analysis which exploit the connectivity structure of images in a multiscale fashion. More specifically, we propose a nonlinear pyramidal image representation scheme, which decomposes an image at different scales by means of multiscale grain filters. These filters gradually remove connected components from an image that fail to satisfy a given criterion. We also use the concept of multiscale connectivity to design a hierarchical data partitioning tool. We employ this tool to construct another image representation scheme, based on the concept of component trees, which organizes partitions of an image in a hierarchical multiscale fashion. In addition, we propose a geometrically-oriented hierarchical clustering algorithm which generalizes the classical single-linkage algorithm. Finally, we propose two object-based multiscale image summaries, reminiscent of the well-known (morphological) pattern spectrum, which can be useful in image analysis and image understanding applications.