Shape gradients for histogram segmentation using active contours (original) (raw)
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Image Segmentation Using Active Contours: Calculus of Variations or Shape Gradients?
SIAM Journal on Applied Mathematics, 2003
We consider the problem of segmenting an image through the minimization of an energy criterion involving region and boundary functionals. We show that one can go from one class to the other by solving Poisson's or Helmholtz's equation with well-chosen boundary conditions. Using this equivalence, we study the case of a large class of region functionals by standard methods of the calculus of variations and derive the corresponding Euler-Lagrange equations. We revisit this problem using the notion of a shape derivative and show that the same equations can be elegantly derived without going through the unnatural step of converting the region integrals into boundary integrals. We also define a larger class of region functionals based on the estimation and comparison to a prototype of the probability density distribution of image features and show how the shape derivative tool allows us to easily compute the corresponding Gâteaux derivatives and Euler-Lagrange equations. Finally we apply this new functional to the problem of regions segmentation in sequences of color images. We briefly describe our numerical scheme and show some experimental results.
2014 IEEE International Conference on Image Processing (ICIP), 2014
This article deals with statistical region-based active contour segmentation using the alpha-divergence family as similarity measure between the density probability functions of the background and the object regions of interest. Following previous publications on that topic, main originality of this contribution is in the proposed joint optimization of the energy steering the evolution of the active curve and the parameter alpha related to the metric of the divergence and closely related to the statistical luminance distribution of the data. Experiments are shown on both synthetic noisy and textured data as well as on real images (natural and medical ones). We show that the joint optimization process leads to satisfying results for every targeted tasks: above all, it is shown that the proposed approach overcome classic statistical-based region active contour approach using Kullback-Leibler divergence as similarity measure, that can stuck in local extrema during the usual optimization process.
A New Region-based Active Contour Model for Object Segmentation
Journal of Mathematical Imaging and Vision, 2015
We present a novel region based active contour model that segments one or more image regions that are visually similar to an object of interest, said prior. The region evolution equation of our model is defined by a simple heuristic rule and it is not derived by minimizing an energy functional, as in the classic variational approaches. The prior and the evolving region are described by the probability density function (pdf) of a photometric feature, as color or intensity. The heuristic rule enlarges or contracts an initial region of the image in order to equalize pointwise the pdf's of the prior and of the region. Such heuristic rule can be modeled by many mathematical monotonic decreasing functions, each defining an evolution equation for the initial image region. The choice of a particular function is remitted to the user, that in this way can even integrate a priori knowledge possibly useful to break down the computational charge of the method and to increase the detection accuracy. Here we propose two different evolution equations for the general purpose of prior detection without a priori information and we discuss empirically the performances of our model on real-world and synthetic datasets. These experiments show that our model is a valid alternative to the classic models.
Image Segmentation using Active Contours Without Edge
In this paper, we propose a segmentation method based on an active contour model without edges which, given an input image or image sequence, generates a mask of the desired object(s). This model is then extended to be used in multi-object tracking. Our method allows us to detect objects which are not necessarily delimited by gradient. In other terms, we do not need to detect edges of the object we want to extract from the image to perform our segmentation. To perform this segmentation, we base our model on techniques of curve evolution, the Mumford-Shah functional and level sets. Our problem can be seen as a particular case of the minimal partition problem in minimizing energy domain. The goal of this survey is also to present an interactive and parametrizable software which helps the understanding of the model and allows to test its limits. After presenting our model, we will give the numerical algorithms and the discrete approximations we used. Finally, various experimental results will be presented and commented.
Active Contour Segmentation with a Parametric Shape Prior: Link with the Shape Gradient
2006 International Conference on Image Processing, 2006
Active contours are adapted to image segmentation by energy minimization. The energies often exhibit local minima, requiring regularization. Such an a priori can be expressed as a shape prior and used in two main ways: (1) a shape prior energy is combined with the segmentation energy into a trade-off between prior compliance and accuracy or (2) the segmentation energy is minimized in the space defined by a parametric shape prior. Methods (1) require the tuning of a data-dependent balance parameter and methods (1) and (2) are often dedicated to a specific prior or contour representation, with the prior and segmentation aspects often meshed together, increasing complexity. A general framework for category (2) is proposed: it is independent of the prior and contour representations and it separates the prior and segmentation aspects. It relies on the relationship shown here between the shape gradient, the prior-induced admissible contour transformations, and the segmentation energy minimization.
Global and local fuzzy energy-based active contours for image segmentation
Nonlinear Dynamics
This paper proposes a novel active contour model for image segmentation based on techniques of curve evolution. The paper introduces an energy functional including a local fuzzy energy and a global fuzzy energy to attract the active contour and stop it on the object boundaries. The local term allows the method to deal with intensity inhomogeneity in images. The global term, aside from driving the contour toward the desired objects, is used to avoid unsatisfying results led by unsuitable initial contour position, a common limitation of models using local information solely. In addition, instead of solving the Euler–Lagrange equation, the paper directly calculates the alterations of the fuzzy energy. By this way, the contour converges quickly to the object boundary. Experimental results on both 2D and 3D images validate the effectiveness of the model when working with intensity inhomogeneous images.
Statistical region-based active contours for segmentation: An overview
IRBM, 2014
In this paper we propose a brief survey on geometric variational approaches and more precisely on statistical region-based active contours for medical image segmentation. In these approaches, image features are considered as random variables whose distribution may be either parametric, and belongs to the exponential family, or non-parametric estimated with a kernel density method. Statistical region-based terms are listed and reviewed showing that these terms can depict a wide spectrum of segmentation problems. A shape prior can also be incorporated to the previous statistical terms. A discussion of some optimization schemes available to solve the variational problem is also provided. Examples on real medical images are given to illustrate some of the given criteria.
Morphological gradient applied to new active contour model for color image segmentation
Proceedings of the 6th International Conference on Ubiquitous Information Management and Communication - ICUIMC '12, 2012
In this paper, we propose a novel segmentation algorithm for color images. This method is a combination of edge information with region information and a geometric active contour without re-initialization, called distance regularized level set evolution. The information given by a new edge detector using morphological gradient is more accurate than normal gradient computing methods for color images. And the information of the region containing objects is relied on Chan-Vese minimal variance criterion. With both of these information, the model can have its initial contour that is more flexible to construct anywhere, fast to evolve and quite exact to stop at the boundary of objects. The suggested algorithm has been applied on natural color images with good performance. Some experimental results have shown to compare our model with others with respect to accuracy and computational efficiency.
2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2012
In this article, a complete original framework for non supervised statistical region based active contour segmentation is proposed. More precisely, the method is based on the maximization of alphadivergences between non paramterically estimated probability density functions (PDF) of the inner and outer regions defined by the evolving curve. In this paper, we define the variational context associated to distance maximization in the particular case of alphadivergence and we also provide the complete derivation of the partial differential equation leading the segmentation. Results on synthetic data (corrupted with a high level of Gaussian and Poisonian noises) but also on clinical images (X-ray images) show that the proposed non supervised approach improves classical approach of that kind.
From snakes to region-based active contours defined by region-dependent parameters
Applied Optics, 2004
This synthetic paper deals with image and sequence segmentation when looking at the segmentation task from a criterion optimization point of view. Such a segmentation criterion involves so-called (boundary and region) descriptors which, in the general case, may depend on their respective boundary or region. This dependency must be taken into account when computing the criterion derivative with respect to the unknown object domain (defined by its boundary). If not, some correctional terms may be omitted. This article focuses computing the derivative of the segmentation criterion using a dynamic scheme. The presented scheme is general enough to provide a framework for a wide variety of applications in segmentation. It also provides a theoretical meaning to the active contour philosophy.