Morphology with parabolic structuring elements
Morphological erosion and dilation filters employ a structuring function, with flat structuring functions being the most common example. This article will use the term ``parabolic'', but much of the literature uses ``quadratic'' structuring functions are less [...]

Consolidated morphology
Grayscale dilation and erosion are basic transformations of mathematical morphology. Used together or with other transformations, they are very useful tools for image analysis. However, they can be very time consuming, especially with 3D images, and with [...]

Integration of Fuzzy Mathematical Morphology and Fuzzy Spatial Relationships into ITK
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The aim of this paper is to present the integration of new filters computing fuzzy mathematical morphology and spatial relationships into ITK and to share our experience with the Open source community. Our implementation architecture follows the essential [...]

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Morphological gradients enhance the variation of pixel intensity in a given neighborhood.

Label object representation and manipulation with ITK
Richard Beare has recently introduced a new filter to efficiently labelize the connected components with ITK, and has also proposed to use the run-length encoding used in that filter to implement some of the most useful binary mathematical morphology [...]

A filter to impose to the input image the minima defined in the marker image.

Tophap by area
The tophat transform is a well know and widely used transform based of morphological opening or closing. It is often used to remove the background in an image, where the background is defined as the zones which do not fit in the user provided [...]

Finding regional extrema - methods and performance
Finding regional extrema of images is an important step in a number of morphological algorithms, such as some versions of the watershed transformfootnote{This work started because we were trying to compare different watershed algorithms}. Regional extrema [...]

Component tree: an efficient representation of grayscale connected components
Connected component is a well known and very useful notion in binary case. As often in mathematical morphology, this notion can be extended to the grayscale case, and allow to perform lot of the useful transforms based on binary connected components in the [...]

4D Morphological segmentation and the MICCAI LV-segmentation grand challenge
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The goal of the Cardiac MR Left Ventricle Segmentation Challenge at MICCAI 2009 is to compare state-of-the-art LV segmentation methods. This goal is facilitated through an evaluation system and a database of cardiac cine MR images, as well as expert contours, [...]

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