Spline-based framework for interactive segmentation in biomedical imaging

Abstract

Active contours constitute a computationally attractive framework for image segmentation. In this paper, we describe a fully parametric design that relies on B-spline bases and is specified by control points on the image. Our technique yields successful segmentation results even for challenging datasets where object contours are not well-defined. We can achieve this because our parametric approach uses few parameters and allows us to constrain the topology of the curve. We provide the details for an efficient implementation and discuss different design alternatives. This work comes with a companion software that gives the end user full control over the snakes. We demonstrate the features of our software which includes an interactive interface where the user can manipulate the position of control points by simple mouse actions.

Exponential pseudo-splines: Looking beyond exponential B-splines

“…Indeed, differently from stationary subdivision schemes, nonstationary subdivision schemes are capable of reproducing conic sections, spirals or, in general, of generating exponential polynomials x r e θx , x ∈ R, r ∈ N ∪ {0}, θ ∈ C. This generation property is important not only in geometric design (see, e.g., [30,32,37,42,43]), but also in many other applications, e.g., in biomedical imaging (see, e.g., [20,21]) and in Isogeometric Analysis (see, e.g., [19,31]). However, the use of nonstationary subdivision schemes in IgA is nowadays limited to the case of exponential B-splines since they are the only functions that have been shown to be able to overcome the NURBS limits while preserving their useful properties.…”

Hermite Snakes With Control of Tangents

“…The analytic expression of φ 1 and φ 2 as well as the mathematical formulation of their joint interpolation properties is discussed in Section III. Parametric snakes are most commonly defined as closed curves (see [18] for a review), although models handling open curves for the segmentation of lines or boundaries also exist [15], [19]- [22]. Our Hermite-snake formulation is particularly well adapted to both scenarios.…”

Tip-seeking active contours for bioimage segmentation

“…The optimal segmentation is found as the minimizer of a cost functional called the snake energy [9]. We now describe our main contribution, a novel feature-based energy that relies on automatically detected corner points.…”