Type of Document Dissertation Author Wang, Jie Author's Email Address email@example.com URN etd-07272011-004912 Title EDGE-WEIGHTED CENTROIDAL VORONOI TESSELLATION BASED ALGORITHMS FOR IMAGE SEGMENTATION Degree Doctor of Philosophy Department Scientific Computing, Department of Advisory Committee
Advisor Name Title Xiaoqiang Wang Committee Chair Anter El-Azab Committee Member Janet Peterson Committee Member Max Gunzburger Committee Member Xiaoming Wang University Representative Keywords
- Image Segmentation
- Centroidal Voronoi Tessellation
- Computer Vision
- Edge Detection
- Active Contours
Date of Defense 2011-06-24 Availability unrestricted AbstractCentroidal Voronoi tessellations (CVTs) are special Voronoi tessellations whose generators are also the centers of mass (centroids) of the Voronoi regions with respect
to a given density function. CVT-based algorithms have been proved very useful in
the context of image processing. However when dealing with the image segmentation
problems, classic CVT algorithms are sensitive to noise.
In order to overcome this limitation, we develop an edge-weighted centroidal Voronoi
Tessellation (EWCVT) model by introducing a new energy term related to the boundary length which is called “edge energy”. The incorporation of the edge energy is
equivalent to add certain form of compactness constraint in the physical space. With
this compactness constraint, we can effectively control the smoothness of the clusters’
boundaries. We will provide some numerical examples to demonstrate the effectiveness, efficiency, flexibility and robustness of EWCVT.
Because of its simplicity and flexibility, we can easily embed other mechanisms
with EWCVT to tackle more sophisticated problems. Two models based on EWCVT
are developed and discussed.
The first one is “local variation and edge-weighted centroidal Voronoi Tessellation” (LVEWCVT) model by encoding the information of local variation of colors.
For the classic CVTs or its generalizations (like EWCVT), pixels inside a cluster
share the same centroid. Therefore the set of centroids can be viewed as a piecewise
constant function over the computational domain. And the resulting segmentations
have to be roughly the same with respect to the corresponding centroids. Inspired
by this observation, we propose to calculate the centroids for each pixel separately
and locally. This scheme greatly improves the algorithms’ tolerance of within-cluster
feature variations. By extensive numerical examples and quantitative evaluations, we
demonstrate the excellent performance of LVEWCVT method compared with several state-of-art algorithms. LVEWCVT model is especially suitable for detection of
inhomogeneous targets with distinct color distributions and textures.
Based on EWCVT, we build another model for “Superpixels” which is in fact a
“regularization” of highly inhomogeneous images. We call our algorithm for superpixels as “VCells” which is the abbreviation of “Voronoi cells”. For a wide range
of images, VCells is capable to generate roughly uniform subregions and meanwhile
nicely preserves local image boundaries. The undersegmentation error is effectively
limited in a controllable manner. Moreover, VCells is very efficient. The computational cost is roughly linear in image size with small constant coefficient. For megapixel
sized images, VCells is able to generate very dense superpixels in a matter of seconds. We demonstrate that VCells outperforms several state-of-art algorithms through
extensive qualitative and quantitative results on a wide range of complex images.
Another important contribution of this work is the “Detecting-Segment-Breaking”
(DSB) algorithm which can be used to guarantee the spatial connectedness of resulting segments generated by CVT based algorithms. Since the metric is usually
defined on the color space, the resulting segments by CVT based algorithms are not
necessarily spatially connected. For some applications, this feature is useful and conceptually meaningful, e.g., the forground objects are not spatially connected. But for
some other applications, like the superpixel problem, this “good” feature becomes u-
nacceptable. By simple “extracting-connected-component” and “relabeling” schemes,
DSB successfully overcomes the above difficulty. Moreover, the computational cost
of DSB is roughly linear in image size with a small constant coefficient.
From the theoretical perspective, the innovative idea of EWCVT greatly enriches
the methodology of CVTs. (The idea of EWCVT has already been used for variational
curve smoothing and reconstruction problems.) For applications, this work shows the
great power of EWCVT for image segmentation related problems.
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