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: DBLP

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]. "
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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.
Full-text · Article · Nov 2015 · IEEE Transactions on Image Processing
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• "Existing methods for segmenting multiple convex structures are specifically designed for certain shapes like ellipsoids or rods, as e.g. [5]. Such methods do not enforce generic convexity, but instead employ priors of specific shapes that happen to be convex. "
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ABSTRACT: Segmenting an image into multiple components is a central task in computer vision. In many practical scenarios, prior knowledge about plausible components is available. Incorporating such prior knowledge into models and algorithms for image segmentation is highly desirable, yet can be non-trivial. In this work, we introduce a new approach that allows, for the first time, to constrain some or all components of a segmentation to have convex shapes. Specifically, we extend the Minimum Cost Multicut Problem by a class of constraints that enforce convexity. To solve instances of this APX-hard integer linear program to optimality, we separate the proposed constraints in the branch-and-cut loop of a state-of-the-art ILP solver. Results on natural and biological images demonstrate the effectiveness of the approach as well as its advantage over the state-of-the-art heuristic.
Full-text · Article · Sep 2015
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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]. "
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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.
Full-text · Article · Feb 2015 · Applied Mathematics and Computation