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Vector valued nonlinear diffusion and its application to image segmentation

Friday, 30 June, 2006 - 18:00
Campus: Brussels Humanities, Sciences & Engineering campus
D
2.01
Iris Vanhamel
phd defence

The objective of this dissertation is to develop a generic approach for the automatic segmentation of vectorvalued
images and in particular color images. The goal is to obtain a segmentation that captures the image
content at relevant abstraction levels (scale). This entails that the objective is not a single ideal
segmentation but that the interest is a hierarchy of nested partitions. From this hierarchy a 'best'
segmentation can be extracted according to the needs of the subsequent image analysis steps. Moreover by
using a compact representation of the hierarchy of nested partitions, the subsequent processing techniques
should be able to make use of the complete hierarchy, and inducing a direct use of scale within the analysis.
The core of our segmentation process is the gradient watershed transformation, which is a powerful
segmentation tool once the inherent problem of over-segmentation is solved. The latter can be achieved in a
multiscale setting. Multiscale watershed analysis exploits the duality between the local minima in the
gradient magnitude and the detected watershed segments. In combination with scale-space theory, a
powerful segmentation method can be constructed: The scale-space filter reduces the amount of local
minima in the gradient magnitude and the deep image structure provides a way of linking these minima
through scale. The literature reports on several multiscale-techniques based on this principle. The majority
of these schemes uses either a linear scale-space filter or is built within the framework of scalar-valued
images. The first objective of this dissertation is to extend an existing linear multiscale segmentation
method for vector-valued images. Secondly, we advocate the use of a non-linear scale-space filter over the
use of a linear one. A study of non-linear scale-space filters for vector-valued images has been conducted.
We opted for a nonlinear scale-space filter that is based on the well-known Perona and Malik filter, i.e.
using the generalized heat equation (variable conductance filtering). This type of scale-space filters has
several advantages: (i) a well-established methodology for vector-valued images, (ii) fast and stable
numerical schemes, (iii) useful properties such as the existence of Lyapunov functionals. In this
dissertation, we study edge affected variable conductance filtering extensively, propose several
modifications of existing filters and, we provide techniques for the automatic estimation of all the filtering
parameters. The validation of the increased complexity is achieved by comparing the segmentation
algorithm based on nonlinear scale-space with its linear counterpart. We propose two approaches for
extracting partitionings from the hierarchy of nested partitions. Both methods start from the multiscale
region adjacency graph (MS-RAG) which corresponds to the hierarchy of nested partitions. In the first
approach, denoted hierarchical level retrieval, the MS-RAG is transformed to region adjacency graph that
captures the multiscale nature of the scene in the valuation of the graph components. Using a merging
priority sequence and a hypothesis testing based on homogeneity, a set of segmentations (hierarchical
levels) are identified from which the final result is obtained via a segmentation valuation criterion. In the
second approach, graph theory based partitioning algorithms are adapted for direct usage on the MS-RAG.
In this work, we propose a method that extends normalized graph cut criterion for application in the
multiscale RAG. The proposed extension follows a top-down strategy. First large scale structures are
identified where after they are refined through the inclusion of finer scale image structure. A comparative
analysis with a selection of state-of-art generic segmentation methods is presented and the inclusion of
texture information in the proposed segmentation scheme is investigated. Finally, the obtained nonlinear
multiscale gradient-watershed driven segmentation is evaluated within the framework of content based
image retrieval.