2,920 research outputs found
Disjunctive Normal Level Set: An Efficient Parametric Implicit Method
Level set methods are widely used for image segmentation because of their
capability to handle topological changes. In this paper, we propose a novel
parametric level set method called Disjunctive Normal Level Set (DNLS), and
apply it to both two phase (single object) and multiphase (multi-object) image
segmentations. The DNLS is formed by union of polytopes which themselves are
formed by intersections of half-spaces. The proposed level set framework has
the following major advantages compared to other level set methods available in
the literature. First, segmentation using DNLS converges much faster. Second,
the DNLS level set function remains regular throughout its evolution. Third,
the proposed multiphase version of the DNLS is less sensitive to
initialization, and its computational cost and memory requirement remains
almost constant as the number of objects to be simultaneously segmented grows.
The experimental results show the potential of the proposed method.Comment: 5 page
Variational Image Segmentation Model Coupled with Image Restoration Achievements
Image segmentation and image restoration are two important topics in image
processing with great achievements. In this paper, we propose a new multiphase
segmentation model by combining image restoration and image segmentation
models. Utilizing image restoration aspects, the proposed segmentation model
can effectively and robustly tackle high noisy images, blurry images, images
with missing pixels, and vector-valued images. In particular, one of the most
important segmentation models, the piecewise constant Mumford-Shah model, can
be extended easily in this way to segment gray and vector-valued images
corrupted for example by noise, blur or missing pixels after coupling a new
data fidelity term which comes from image restoration topics. It can be solved
efficiently using the alternating minimization algorithm, and we prove the
convergence of this algorithm with three variables under mild condition.
Experiments on many synthetic and real-world images demonstrate that our method
gives better segmentation results in comparison to others state-of-the-art
segmentation models especially for blurry images and images with missing pixels
values.Comment: 23 page
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
Colour image segmentation by the vector-valued Allen-Cahn phase-field model: a multigrid solution
We propose a new method for the numerical solution of a PDE-driven model for
colour image segmentation and give numerical examples of the results. The
method combines the vector-valued Allen-Cahn phase field equation with initial
data fitting terms. This method is known to be closely related to the
Mumford-Shah problem and the level set segmentation by Chan and Vese. Our
numerical solution is performed using a multigrid splitting of a finite element
space, thereby producing an efficient and robust method for the segmentation of
large images.Comment: 17 pages, 9 figure
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