8,278 research outputs found
Segmentation and Restoration of Images on Surfaces by Parametric Active Contours with Topology Changes
In this article, a new method for segmentation and restoration of images on
two-dimensional surfaces is given. Active contour models for image segmentation
are extended to images on surfaces. The evolving curves on the surfaces are
mathematically described using a parametric approach. For image restoration, a
diffusion equation with Neumann boundary conditions is solved in a
postprocessing step in the individual regions. Numerical schemes are presented
which allow to efficiently compute segmentations and denoised versions of
images on surfaces. Also topology changes of the evolving curves are detected
and performed using a fast sub-routine. Finally, several experiments are
presented where the developed methods are applied on different artificial and
real images defined on different surfaces
Contour evolution scheme for variational image segmentation and smoothing
An algorithm, based on the MumfordâShah (MâS) functional, for image contour segmentation and object smoothing in the presence of noise is proposed. However, in the proposed algorithm, contour length minimisation is not required and it is demonstrated that the MâS functional without contour length minimisation becomes an edge detector. Optimisation of this nonlinear functional is based on the method of calculus of variations, which is implemented by using the level set method. Fourier and Legendreâs series are also employed to improve the segmentation performance of the proposed algorithm. The segmentation results clearly demonstrate the effectiveness of the proposed approach for images with low signal-to-noise ratios
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
The Lov\'asz-Softmax loss: A tractable surrogate for the optimization of the intersection-over-union measure in neural networks
The Jaccard index, also referred to as the intersection-over-union score, is
commonly employed in the evaluation of image segmentation results given its
perceptual qualities, scale invariance - which lends appropriate relevance to
small objects, and appropriate counting of false negatives, in comparison to
per-pixel losses. We present a method for direct optimization of the mean
intersection-over-union loss in neural networks, in the context of semantic
image segmentation, based on the convex Lov\'asz extension of submodular
losses. The loss is shown to perform better with respect to the Jaccard index
measure than the traditionally used cross-entropy loss. We show quantitative
and qualitative differences between optimizing the Jaccard index per image
versus optimizing the Jaccard index taken over an entire dataset. We evaluate
the impact of our method in a semantic segmentation pipeline and show
substantially improved intersection-over-union segmentation scores on the
Pascal VOC and Cityscapes datasets using state-of-the-art deep learning
segmentation architectures.Comment: Accepted as a conference paper at CVPR 201
Geometrical-based algorithm for variational segmentation and smoothing of vector-valued images
An optimisation method based on a nonlinear functional is considered for segmentation and smoothing of vector-valued images. An edge-based approach is proposed to initially segment the image using geometrical properties such as metric tensor of the linearly smoothed image. The nonlinear functional is then minimised for each segmented region to yield the smoothed image. The functional is characterised with a unique solution in contrast with the MumfordâShah functional for vector-valued images. An operator for edge detection is introduced as a result of this unique solution. This operator is analytically calculated and its detection performance and localisation are then compared with those of the DroGoperator. The implementations are applied on colour images as examples of vector-valued images, and the results demonstrate robust performance in noisy environments
Tomography: mathematical aspects and applications
In this article we present a review of the Radon transform and the
instability of the tomographic reconstruction process. We show some new
mathematical results in tomography obtained by a variational formulation of the
reconstruction problem based on the minimization of a Mumford-Shah type
functional. Finally, we exhibit a physical interpretation of this new technique
and discuss some possible generalizations.Comment: 11 pages, 5 figure
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
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
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
- âŠ