The Ovuscule

Abstract

Abstract-We propose an active contour (a.k.a. snake) that takes the shape of an ellipse. Its evolution is driven by surface terms made of two contributions: the integral of the data over an inner ellipse, counterbalanced by the integral of the data over an outer elliptical shell. We iteratively adapt the active contour to maximize the contrast between the two domains, which results in a snake that seeks elliptical bright blobs. We provide analytic expressions for the gradient of the snake with respect to its defining parameters, which allows for the use of efficient optimizers. An important contribution here is the parameterization of the ellipse which we define in such a way that all parameters have equal importance; this creates a favorable landscape for the proceedings of the optimizer. We validate our construct with synthetic data and illustrate its use on real data as well.

Spline-based framework for interactive segmentation in biomedical imaging

“…It is usually designed with the purpose of finding particular features within the image. There are many strategies which can broadly be categorized in two families: 1) edge-based schemes, which use gradient information to detect contours [3,[12][13][14] and 2) region-based methods, which use statistical information to distinguish different regions [3,[15][16][17]. Most region energies are expressed as surface integrals of an integrand g over the domain S enclosed by the curve [3], like in…”

A shape-template based two-stage corpus callosum segmentation technique for sagittal plane T1-weighted brain magnetic resonance images

“…The deformable template consists of a pair of nested contours and allowed to move in the template's RAT space. Thévenaz and Unser [18,19] employed a shapespecific parametrization and regularization to maintain shape specificity. In [20], we provided a unified approach for segmentation of circular and elliptical shaped objects.…”

“…On the energy front, many techniques rely on region-and gradient-based energies or functions derived thereof [17]. Recently, Thévenaz and Unser [18,19] proposed a new contrast-based energy for optimizing concentric circles and ellipses. The contrast is defined between the pixel intensities inside the inner contour and those lying in the annular region between the inner and outer contours.…”

“…The snake is manually initialized and is allowed to deform in the RAT space of the template. The snake energy used is the contrast-based energy introduced in [18,19]. This stage results in a coarse but fast segmentation.…”

A new hybrid Bayesian-variational particle filter with application to mitotic cell tracking

“…The fact that the search is multimodal is important when modeling uncertainties of association in dividing targets. In the role of the parametric contours, we chose an elliptical snake named the ovuscule that is robust against noise and has a convenient parameterization [10]. As shown in Figure 1, this snake is defined by only three points.…”