291 research outputs found
A Two-stage Classification Method for High-dimensional Data and Point Clouds
High-dimensional data classification is a fundamental task in machine
learning and imaging science. In this paper, we propose a two-stage multiphase
semi-supervised classification method for classifying high-dimensional data and
unstructured point clouds. To begin with, a fuzzy classification method such as
the standard support vector machine is used to generate a warm initialization.
We then apply a two-stage approach named SaT (smoothing and thresholding) to
improve the classification. In the first stage, an unconstraint convex
variational model is implemented to purify and smooth the initialization,
followed by the second stage which is to project the smoothed partition
obtained at stage one to a binary partition. These two stages can be repeated,
with the latest result as a new initialization, to keep improving the
classification quality. We show that the convex model of the smoothing stage
has a unique solution and can be solved by a specifically designed primal-dual
algorithm whose convergence is guaranteed. We test our method and compare it
with the state-of-the-art methods on several benchmark data sets. The
experimental results demonstrate clearly that our method is superior in both
the classification accuracy and computation speed for high-dimensional data and
point clouds.Comment: 21 pages, 4 figure
Joint Image Reconstruction and Segmentation Using the Potts Model
We propose a new algorithmic approach to the non-smooth and non-convex Potts
problem (also called piecewise-constant Mumford-Shah problem) for inverse
imaging problems. We derive a suitable splitting into specific subproblems that
can all be solved efficiently. Our method does not require a priori knowledge
on the gray levels nor on the number of segments of the reconstruction.
Further, it avoids anisotropic artifacts such as geometric staircasing. We
demonstrate the suitability of our method for joint image reconstruction and
segmentation. We focus on Radon data, where we in particular consider limited
data situations. For instance, our method is able to recover all segments of
the Shepp-Logan phantom from angular views only. We illustrate the
practical applicability on a real PET dataset. As further applications, we
consider spherical Radon data as well as blurred data
Discrete stochastic approximations of the Mumford-Shah functional
We propose a -convergent discrete approximation of the Mumford-Shah
functional. The discrete functionals act on functions defined on stationary
stochastic lattices and take into account general finite differences through a
non-convex potential. In this setting the geometry of the lattice strongly
influences the anisotropy of the limit functional. Thus we can use
statistically isotropic lattices and stochastic homogenization techniques to
approximate the vectorial Mumford-Shah functional in any dimension.Comment: 47 pages, reorganized versio
A PDE Method to Segment Image Linear Objects with Application to Lens Distortion Removal
In this paper, we propose a partial differential equation based method to segment image objects, which have a given parametric shape based on energy functional. The energy functional is composed of a term that detects object boundaries and a term that constrains the contour to find a shape compatible with the parametric shape. While the shape constraints guiding the PDE may be determined from object's shape statistical models, we demonstrate the proposed approach on the extraction of objects with explicit shape parameterization, such as linear image segments. Several experiments are reported on synthetic and real images to evaluate our approach. We also demonstrate the successful application of the proposed method to the problem of removing camera lens distortion, which can be significant in medium to wide-angle lenses
- …