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
Multiscale median and morphological filters for 2D pattern recognition
Proceedings of of the IEEE winter workshop on Nonlinear digital signal processing
Morphological signal processing and the slope transform
Signal Processing - Special issue on mathematical morphology and its applications to signal processing
Scale-Space Properties of the Multiscale Morphological Dilation-Erosion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multiscale Nonlinear Decomposition: The Sieve Decomposition Theorem
IEEE Transactions on Pattern Analysis and Machine Intelligence
Periodic lines: Definition, cascades, and application to granulometries
Pattern Recognition Letters
Scale-Space Using Mathematical Morphology
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fast computation of morphological operations with arbitrary structuring elements
Pattern Recognition Letters
The Morphological Structure of Images: The Differential Equations of Morphological Scale-Space
IEEE Transactions on Pattern Analysis and Machine Intelligence
Morphological Image Analysis: Principles and Applications
Morphological Image Analysis: Principles and Applications
SCIA'03 Proceedings of the 13th Scandinavian conference on Image analysis
Evolution equations for continuous-scale morphological filtering
IEEE Transactions on Signal Processing
Constrained and dimensionality-independent path openings
IEEE Transactions on Image Processing
On the Continuity of Granulometry
Journal of Mathematical Imaging and Vision
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Morphological sieves are capable of classifying objects in images according to their size. They yield a granulometry, which describes the imaged structure. The discrete sieve has some disadvantages that its continuous-domain counterpart does not have: sampled disks (used as isotropic structuring elements) are rather anisotropic, especially at small scales, and their area, as a function of the size in the continuous domain, shows jumps at apparently arbitrary locations. These problems cause a severe bias and low precision of the derived size distribution. Therefore we propose a new digitization scheme for implementing continuous sieves. First we increase the sampling density of the structuring element and the image. This does not add new detail to the image, but yields a sampled structuring element that is a much better approximation to its continuous counterpart, and thereby substantially reduces the discretization error. The second innovation is to shift the structuring element with respect to the sampling grid; this makes the size increments smoother, and further reduces the discretization errors. These ideas are validated on synthetic images. We also show that the proposed improvements allow for a finer scale sampling.