Snakes With an Ellipse-Reproducing Property

Biomed. Imaging Group, Ecole Polytech. federate de Lausanne, Lausanne, Switzerland
IEEE Transactions on Image Processing (Impact Factor: 3.11). 04/2012; 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.

  • [Show abstract] [Hide abstract]
    ABSTRACT: We present a new exponential B-spline basis that enables the construction of active contours for the analysis of biomedical images. Our functions generalize the well-known polynomial Hermite B-splines and provide us with a direct control over the tangents of the parameterized contour, which is absent in traditional spline-based active contours. Our basis functions have been designed to perfectly reproduce elliptical and circular shapes. Moreover, they can approximate any closed curve up to arbitrary precision by increasing the number of anchor points. They are therefore well-suited to the segmentation of the roundish objects that are commonly encountered in the analysis of bioimages. We illustrate the performance of an active contour built using our functions on some examples of real biological data.
    ICASSP 2014 - 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP); 05/2014
  • [Show abstract] [Hide abstract]
    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
  • Source
    [Show abstract] [Hide abstract]
    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 (3 Sources)

Available from
Mar 18, 2015