7,105 research outputs found
Image Segmentation with Eigenfunctions of an Anisotropic Diffusion Operator
We propose the eigenvalue problem of an anisotropic diffusion operator for
image segmentation. The diffusion matrix is defined based on the input image.
The eigenfunctions and the projection of the input image in some eigenspace
capture key features of the input image. An important property of the model is
that for many input images, the first few eigenfunctions are close to being
piecewise constant, which makes them useful as the basis for a variety of
applications such as image segmentation and edge detection. The eigenvalue
problem is shown to be related to the algebraic eigenvalue problems resulting
from several commonly used discrete spectral clustering models. The relation
provides a better understanding and helps developing more efficient numerical
implementation and rigorous numerical analysis for discrete spectral
segmentation methods. The new continuous model is also different from
energy-minimization methods such as geodesic active contour in that no initial
guess is required for in the current model. The multi-scale feature is a
natural consequence of the anisotropic diffusion operator so there is no need
to solve the eigenvalue problem at multiple levels. A numerical implementation
based on a finite element method with an anisotropic mesh adaptation strategy
is presented. It is shown that the numerical scheme gives much more accurate
results on eigenfunctions than uniform meshes. Several interesting features of
the model are examined in numerical examples and possible applications are
discussed
Point Cloud Structural Parts Extraction based on Segmentation Energy Minimization
In this work we consider 3D point sets, which in a typical setting represent unorganized point clouds. Segmentation of these point sets requires first to single out structural components of the unknown surface discretely approximated by the point cloud. Structural components, in turn, are surface patches approximating unknown parts of elementary geometric structures, such as planes, ellipsoids, spheres and so on. The approach used is based on level set methods computing the moving front of the surface and tracing the interfaces between different parts of it. Level set methods are widely recognized to be one of the most efficient methods to segment both 2D images and 3D medical images. Level set methods for 3D segmentation have recently received an increasing interest. We contribute by proposing a novel approach for raw point sets. Based on the motion and distance functions of the level set we introduce four energy minimization models, which are used for segmentation, by considering an equal number of distance functions specified by geometric features. Finally we evaluate the proposed algorithm on point sets simulating unorganized point clouds
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