Article

# Snakes With an Ellipse-Reproducing Property

Biomed. Imaging Group, Ecole Polytech. federate de Lausanne, Lausanne, Switzerland
(Impact Factor: 3.63). 04/2012; 21(3):1258 - 1271. DOI: 10.1109/TIP.2011.2169975
Source: IEEE Xplore

ABSTRACT

We present a new class of continuously defined parametric snakes using a special kind of exponential splines as basis functions. We have enforced our bases to have the shortest possible support subject to some design constraints to maximize efficiency. While the resulting snakes are versatile enough to provide a good approximation of any closed curve in the plane, their most important feature is the fact that they admit ellipses within their span. Thus, they can perfectly generate circular and elliptical shapes. These features are appropriate to delineate cross sections of cylindrical-like conduits and to outline bloblike objects. We address the implementation details and illustrate the capabilities of our snake with synthetic and real data.

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Available from: Chandra Sekhar Seelamantula, Mar 18, 2015
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• "There, the evolution of the contour is typically driven by the minimization of a certain energy term [11]. We parameterize continuously the closed curve by means of (exponential) B-spline basis functions [11]–[13] and their corresponding control points; this representation was proved to be effective for fast energy minimization. Additionally, B-splines provide a convenient way to handle intrinsic shape properties of the curve, such as smoothness constraints [14]. "
##### Article: Efficient Shape Priors for Spline-Based Snakes
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ABSTRACT: Parametric active contours are an attractive approach for image segmentation, thanks to their computational efficiency. They are driven by application-dependent energies that reflect the prior knowledge on the object to be segmented. We propose an energy involving shape priors acting in a regularization-like manner. Thereby, the shape of the snake is orthogonally projected onto the space that spans the affine transformations of a given shape prior. The formulation of the curves is continuous, which provides computational benefits when compared with landmark-based (discrete) methods. We show that this approach improves the robustness and quality of spline-based segmentation algorithms, while its computational overhead is negligible. An interactive and ready-to-use implementation of the proposed algorithm is available and was successfully tested on real data in order to segment Drosophila flies and yeast cells in microscopic images.
IEEE Transactions on Image Processing 11/2015; 24(11):3915-3926. DOI:10.1109/TIP.2015.2457335 · 3.63 Impact Factor
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• "Indeed, the level dependency enables to generate new classes of functions such as exponential polynomials, exponential B-splines, etc. This gives a new impulse to development of subdivision schemes and enlarges the scope of their applications, e.g. in biological imaging [23] [43], geometric design [40] [42] or isogeometric analysis [3] [12]. "
##### Article: Limits of level and parameter dependent subdivision schemes: A matrix approach
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ABSTRACT: In this paper, we present a new matrix approach for the analysis of subdivision schemes whose non-stationarity is due to linear dependency on parameters whose values vary in a compact set. Indeed, we show how to check the convergence in $C^{\ell}(\RR^s)$ and determine the H\"older regularity of such level and parameter dependent schemes efficiently via the joint spectral radius approach. The efficiency of this method and the important role of the parameter dependency are demonstrated on several examples of subdivision schemes whose properties improve the properties of the corresponding stationary schemes. Moreover, we derive necessary criteria for a function to be generated by some level dependent scheme and, thus, expose the limitations of such schemes.
Applied Mathematics and Computation 02/2015; DOI:10.1016/j.amc.2015.08.120 · 1.55 Impact Factor
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• "Most parametric snakes are defined as closed curves [2] [9]. Comparatively , there are much fewer solutions that can handle open curves [11] [12]. "
##### Conference Paper: Snakes with tangent-based control and energies for bioimage analysis
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ABSTRACT: We propose a novel active contour for the analysis of filament-like structures and boundaries — features that traditional snakes based on closed curves have difficulties to delineate. Our method relies on a parametric representation of an open curve involving Hermite-spline basis functions. This allows us to impose constraints both on the contour and on its derivatives. The proposed parameterization enables tangential controls and facilitates the design of an energy term that considers oriented features. In this way, our technique can be used to detect edges as well as ridges. The use of the Hermite-spline basis is well suited to a semi-interactive implementation. We developed an ImageJ plugin, and present experimental results on real biological data.
2014 IEEE 11th International Symposium on Biomedical Imaging (ISBI 2014); 04/2014