# Scale-Space Properties of the Multiscale Morphological Dilation-Erosion

@article{Jackway1996ScaleSpacePO, title={Scale-Space Properties of the Multiscale Morphological Dilation-Erosion}, author={Paul T. Jackway and Mohamed Deriche}, journal={IEEE Trans. Pattern Anal. Mach. Intell.}, year={1996}, volume={18}, pages={38-51} }

A multiscale morphological dilation-erosion smoothing operation and its associated scale-space expansion for multidimensional signals are proposed. Properties of this smoothing operation are developed and, in particular a scale-space monotonic property for signal extrema is demonstrated. Scale-space fingerprints from this approach have advantages over Gaussian scale-space fingerprints in that: they are defined for negative values of the scale parameter; have monotonic properties in two and…

## 336 Citations

### Morphological scale-space with application to three-dimensional object recognition

- Computer Science
- 1995

The essential scale-space causality property for local extrema of a signal under this operation is proved and it is shown that structuring functions from the "elliptic poweroids" lead to favourable dimensionality and semi-group properties.

### Noise Removal and Feature Extraction Based on Multiscale Morphological Filtering 1

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- 1997

In this paper, a novel multiscale morphological operation is offered, which is a combination of multiscale dilation and erosion, or an extension of morphological opening. With respect to extreme…

### Nonlinear Scale-Space Representation with Morphological Levelings

- MathematicsJ. Vis. Commun. Image Represent.
- 2000

A nonlinear scale-space representation based on a general class of morphological strong filters, the levelings, which include the openings and closings by reconstruction, is presented and a nonlinear partial differential equation is developed.

### Gradient watersheds in morphological scale-space

- MathematicsIEEE Trans. Image Process.
- 1996

A scale-space monotonicity theorem for regions of an image defined by watersheds of a gradient function modified to retain only the local minima or maxima of its smoothed parent image is introduced.

### Morphological Multiscale Gradient Watershed Image Analysis 1..1 Morphological Scale-space

- Mathematics
- 1995

We introduce a scale-space causality theorem for regions of a image deened by watersheds of a gradient function modiied to retain only the local minima or maxima of its parent function. We then…

### Morphological scale-space theory for segmentation problems

- Computer ScienceNSIP
- 1999

An idempotent smoothing operation based on the recently proposed multiscale-morphological-dilation-erosion method is introduced, and some of its features concerned mainly with monotonic-ity and the way the image extrema merge in a multi-scale simpliication process are analyzed.

### Multiscale image representation using scale-space theory

- Computer Science
- 2008

The scale-space properties of a toggle operator defined using mathematical morphology operations are explored, finding that the use of simplified images significantly improves the results.

### Shape representation and recognition through morphological curvature scale spaces

- Computer ScienceIEEE Transactions on Image Processing
- 2006

A multiscale, morphological method for the purpose of shape-based object recognition is presented. A connected operator similar to the morphological hat-transform is defined, and two scale-space…

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