# Connected Filtering on Tree-Based Shape-Spaces

## Abstract

Connected filters are well-known for their good contour preservation property. A popular implementation strategy relies on tree-based image representations: for exampleone can compute an attribute characterizing the connected component represented by each node of the tree and keep only the nodes for which the attribute is sufficiently high. This operation can be seen as a thresholding of the tree, seen as a graph whose nodes are weighted by the attribute. Rather than being satisfied with a mere thresholding, we propose to expand on this idea, and to apply connected filters on this latest graph. Consequentlythe filtering is performed not in the space of the imagebut in the space of shapes built from the image. Such a processing of shape-space filtering is a generalization of the existing tree-based connected operators. Indeed, the framework includes the classical existing connected operators by attributes. It also allows us to propose a class of novel connected operators from the leveling family, based on non-increasing attributes. Finally, we also propose a new class of connected operators that we call morphological em shapings. Some illustrations and quantitative evaluations demonstrate the usefulness and robustness of the proposed shape-space filters.

## Bibtex (lrde.bib)

@Article{	  xu.15.pami,
author	= {Yongchao Xu and Thierry G\'eraud and Laurent Najman},
title		= {Connected Filtering on Tree-Based Shape-Spaces},
journal	= {IEEE Transactions on Pattern Analysis and Machine
Intelligence},
year		= {2016},
volume	= {38},
number	= {6},
pages		= {1126--1140},
month		= jun,
abstract	= {Connected filters are well-known for their good contour
preservation property. A popular implementation strategy
relies on tree-based image representations: for example,
one can compute an attribute characterizing the connected
component represented by each node of the tree and keep
only the nodes for which the attribute is sufficiently
high. This operation can be seen as a thresholding of the
tree, seen as a graph whose nodes are weighted by the
attribute. Rather than being satisfied with a mere
thresholding, we propose to expand on this idea, and to
apply connected filters on this latest graph. Consequently,
the filtering is performed not in the space of the image,
but in the space of shapes built from the image. Such a
processing of shape-space filtering is a generalization of
the existing tree-based connected operators. Indeed, the
framework includes the classical existing connected
operators by attributes. It also allows us to propose a
class of novel connected operators from the leveling
family, based on non-increasing attributes. Finally, we
also propose a new class of connected operators that we
call morphological {\em shapings}. Some illustrations and
quantitative evaluations demonstrate the usefulness and
robustness of the proposed shape-space filters.}
}