955 research outputs found
Unsupervised Multi Class Segmentation of 3D Images with Intensity Inhomogeneities
Intensity inhomogeneities in images constitute a considerable challenge in
image segmentation. In this paper we propose a novel biconvex variational model
to tackle this task. We combine a total variation approach for multi class
segmentation with a multiplicative model to handle the inhomogeneities. Our
method assumes that the image intensity is the product of a smoothly varying
part and a component which resembles important image structures such as edges.
Therefore, we penalize in addition to the total variation of the label
assignment matrix a quadratic difference term to cope with the smoothly varying
factor. A critical point of our biconvex functional is computed by a modified
proximal alternating linearized minimization method (PALM). We show that the
assumptions for the convergence of the algorithm are fulfilled by our model.
Various numerical examples demonstrate the very good performance of our method.
Particular attention is paid to the segmentation of 3D FIB tomographical images
which was indeed the motivation of our work
A Novel Euler's Elastica based Segmentation Approach for Noisy Images via using the Progressive Hedging Algorithm
Euler's Elastica based unsupervised segmentation models have strong
capability of completing the missing boundaries for existing objects in a clean
image, but they are not working well for noisy images. This paper aims to
establish a Euler's Elastica based approach that properly deals with random
noises to improve the segmentation performance for noisy images. We solve the
corresponding optimization problem via using the progressive hedging algorithm
(PHA) with a step length suggested by the alternating direction method of
multipliers (ADMM). Technically, all the simplified convex versions of the
subproblems derived from the major framework of PHA can be obtained by using
the curvature weighted approach and the convex relaxation method. Then an
alternating optimization strategy is applied with the merits of using some
powerful accelerating techniques including the fast Fourier transform (FFT) and
generalized soft threshold formulas. Extensive experiments have been conducted
on both synthetic and real images, which validated some significant gains of
the proposed segmentation models and demonstrated the advantages of the
developed algorithm
A stochastic-variational model for soft Mumford-Shah segmentation
In contemporary image and vision analysis, stochastic approaches demonstrate
great flexibility in representing and modeling complex phenomena, while
variational-PDE methods gain enormous computational advantages over Monte-Carlo
or other stochastic algorithms. In combination, the two can lead to much more
powerful novel models and efficient algorithms. In the current work, we propose
a stochastic-variational model for soft (or fuzzy) Mumford-Shah segmentation of
mixture image patterns. Unlike the classical hard Mumford-Shah segmentation,
the new model allows each pixel to belong to each image pattern with some
probability. We show that soft segmentation leads to hard segmentation, and
hence is more general. The modeling procedure, mathematical analysis, and
computational implementation of the new model are explored in detail, and
numerical examples of synthetic and natural images are presented.Comment: 22 page
Directed Acyclic Graph Continuous Max-Flow Image Segmentation for Unconstrained Label Orderings
Label ordering, the specification of subset–superset relationships for segmentation labels, has been of increasing interest in image segmentation as they allow for complex regions to be represented as a collection of simple parts. Recent advances in continuous max-flow segmentation have widely expanded the possible label orderings from binary background/foreground problems to extendable frameworks in which the label ordering can be specified. This article presents Directed Acyclic Graph Max-Flow image segmentation which is flexible enough to incorporate any label ordering without constraints. This framework uses augmented Lagrangian multipliers and primal–dual optimization to develop a highly parallelized solver implemented using GPGPU. This framework is validated on synthetic, natural, and medical images illustrating its general applicability
Re-initialization-free Level Set Method via Molecular Beam Epitaxy Equation Regularization for Image Segmentation
Variational level set method has become a powerful tool in image segmentation
due to its ability to handle complex topological changes and maintain
continuity and smoothness in the process of evolution. However its evolution
process can be unstable, which results in over flatted or over sharpened
contours and segmentation failure. To improve the accuracy and stability of
evolution, we propose a high-order level set variational segmentation method
integrated with molecular beam epitaxy (MBE) equation regularization. This
method uses the crystal growth in the MBE process to limit the evolution of the
level set function, and thus can avoid the re-initialization in the evolution
process and regulate the smoothness of the segmented curve. It also works for
noisy images with intensity inhomogeneity, which is a challenge in image
segmentation. To solve the variational model, we derive the gradient flow and
design scalar auxiliary variable (SAV) scheme coupled with fast Fourier
transform (FFT), which can significantly improve the computational efficiency
compared with the traditional semi-implicit and semi-explicit scheme. Numerical
experiments show that the proposed method can generate smooth segmentation
curves, retain fine segmentation targets and obtain robust segmentation results
of small objects. Compared to existing level set methods, this model is
state-of-the-art in both accuracy and efficiency
Crystal image analysis using synchrosqueezed transforms
We propose efficient algorithms based on a band-limited version of 2D
synchrosqueezed transforms to extract mesoscopic and microscopic information
from atomic crystal images. The methods analyze atomic crystal images as an
assemblage of non-overlapping segments of 2D general intrinsic mode type
functions, which are superpositions of non-linear wave-like components. In
particular, crystal defects are interpreted as the irregularity of local
energy; crystal rotations are described as the angle deviation of local wave
vectors from their references; the gradient of a crystal elastic deformation
can be obtained by a linear system generated by local wave vectors. Several
numerical examples of synthetic and real crystal images are provided to
illustrate the efficiency, robustness, and reliability of our methods.Comment: 27 pages, 17 figure
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