53 research outputs found
Stabilised bias field: segmentation with intensity inhomogeneity
Automatic segmentation in the variational framework is a challenging task within the field of imaging sciences. Achieving robustness is a major problem, particularly for images with high levels of intensity inhomogeneity. The two-phase piecewise-constant case of the Mumford-Shah formulation is most suitable for images with simple and homogeneous features where the intensity variation is limited. However, it has been applied to many different types of synthetic and real images after some adjustments to the formulation. Recent work has incorporated bias field estimation to allow for intensity inhomogeneity, with great success in terms of segmentation quality. However, the framework and assumptions involved lead to inconsistencies in the method that can adversely affect results. In this paper we address the task of generalising the piecewise-constant formulation, to approximate minimisers of the original Mumford-Shah formulation. We first review existing methods for treating inhomogeneity, and demonstrate the inconsistencies with the bias field estimation framework. We propose a modified variational model to account for these problems by introducing an additional constraint, and detail how the exact minimiser can be approximated in the context of this new formulation. We extend this concept to selective segmentation with the introduction of a distance selection term. These models are minimised with convex relaxation methods, where the global minimiser can be found for a fixed fitting term. Finally, we present numerical results that demonstrate an improvement to existing methods in terms of reliability and parameter dependence, and results for selective segmentation in the case of intensity inhomogeneity. </jats:p
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
Active contour driven by scalable local regional information on expandable kernel
An active contour that uses the pixel’s intensity on a set of expandable kernels along the propagating contour for image segmentation is presented in this paper. The objective is this study is to employ the scalable kernels to attract the contour to meet the desired boundary. The key characteristics of this scheme is that the kernels gradually expand to find an object’s boundary. So this scheme could penetrate to the concave boundary more effective and efficient than some other schemes. If a Gaussian kernel is applied, it could trace the object with a blurred or smooth boundary. Moreover, the directional selectivity feature enables in capturing two edge’s types with just one initial position. Its performance showed more desirable segmentation outcomes compared to the other existing active contours using regional information when segmenting the noisy image and the non-uniform (or heterogeneous) textures. Meanwhile, the level set implementation enables topological flexibility to our active contour scheme
Graph Spectral Image Processing
Recent advent of graph signal processing (GSP) has spurred intensive studies
of signals that live naturally on irregular data kernels described by graphs
(e.g., social networks, wireless sensor networks). Though a digital image
contains pixels that reside on a regularly sampled 2D grid, if one can design
an appropriate underlying graph connecting pixels with weights that reflect the
image structure, then one can interpret the image (or image patch) as a signal
on a graph, and apply GSP tools for processing and analysis of the signal in
graph spectral domain. In this article, we overview recent graph spectral
techniques in GSP specifically for image / video processing. The topics covered
include image compression, image restoration, image filtering and image
segmentation
Shape Calculus for Shape Energies in Image Processing
Many image processing problems are naturally expressed as energy minimization
or shape optimization problems, in which the free variable is a shape, such as
a curve in 2d or a surface in 3d. Examples are image segmentation, multiview
stereo reconstruction, geometric interpolation from data point clouds. To
obtain the solution of such a problem, one usually resorts to an iterative
approach, a gradient descent algorithm, which updates a candidate shape
gradually deforming it into the optimal shape. Computing the gradient descent
updates requires the knowledge of the first variation of the shape energy, or
rather the first shape derivative. In addition to the first shape derivative,
one can also utilize the second shape derivative and develop a Newton-type
method with faster convergence. Unfortunately, the knowledge of shape
derivatives for shape energies in image processing is patchy. The second shape
derivatives are known for only two of the energies in the image processing
literature and many results for the first shape derivative are limiting, in the
sense that they are either for curves on planes, or developed for a specific
representation of the shape or for a very specific functional form in the shape
energy. In this work, these limitations are overcome and the first and second
shape derivatives are computed for large classes of shape energies that are
representative of the energies found in image processing. Many of the formulas
we obtain are new and some generalize previous existing results. These results
are valid for general surfaces in any number of dimensions. This work is
intended to serve as a cookbook for researchers who deal with shape energies
for various applications in image processing and need to develop algorithms to
compute the shapes minimizing these energies
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