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In this paper, we introduce an efficient method for computing curves minimizing a variant of the Euler--Mumford elastica energy, with fixed endpoints and tangents at these endpoints, where the bending energy is enhanced with a user-defined and datadriven scalar-valued term referred to as the curvature prior. In order to guarantee that the globally optimal curve is extracted, the proposed method involves the numerical computation of the viscosity solution to a specific static Hamilton--Jacobi--Bellman (HJB) partial differential equation (PDE). For that purpose, we derive the explicit Hamiltonian associated with this variant model equipped with a curvature prior, discretize the resulting HJB PDE using an adaptive finite difference scheme, and solve it in a single pass using a generalized fast-marching method. In addition, we also present a practical method for estimating the curvature prior values from image data, designed for the task of accurately tracking curvilinear structure centerlines. Numerical experiments on synthetic and real-image data illustrate the advantages of the considered variant of the elastica model with a prior curvature enhancement in complex scenarios where challenging geometric structures appear. [ABSTRACT FROM AUTHOR]

Tubular structure tracking is a crucial task in the fields of computer vision and medical image analysis. The minimal paths-based approaches have exhibited their strong ability in tracing tubular structures, by which a tubular structure can be naturally modeled as a minimal geodesic path computed with a suitable geodesic metric. However, existing minimal paths-based tracing approaches still suffer from difficulties such as the shortcuts and short branches combination problems, especially when dealing with the images involving complicated tubular tree structures or background. In this paper, we introduce a new minimal paths-based model for minimally interactive tubular structure centerline extraction in conjunction with a perceptual grouping scheme. Basically, we take into account the prescribed tubular trajectories and curvature-penalized geodesic paths to seek suitable shortest paths. The proposed approach can benefit from the local smoothness prior on tubular structures and the global optimality of the used graph-based path searching scheme. Experimental results on both synthetic and real images prove that the proposed model indeed obtains outperformance comparing with the state-of-the-art minimal paths-based tubular structure tracing algorithms. [ABSTRACT FROM AUTHOR]

A novel approach is presented which is based on perceptual grouping in spatiotemporal volume. The ability of the algorithm to the intermittent objects in sequences of synthetic data and in experimental measurements obtained with individual quantum dots (QD)-tagged receptors in the membrane of live neurons is demonstrated.

Minimal paths are regarded as a powerful and efficient tool for boundary detection and image segmentation due to its global optimality and the well-established numerical solutions such as fast marching method. In this paper, we introduce a flexible interactive image segmentation model based on the Eikonal partial differential equation (PDE) framework in conjunction with region-based homogeneity enhancement. A key ingredient in the introduced model is the construction of local geodesic metrics, which are capable of integrating anisotropic and asymmetric edge features, implicit region-based homogeneity features and/or curvature regularization. The incorporation of the region-based homogeneity features into the metrics considered relies on an implicit representation of these features, which is one of the contributions of this work. Moreover, we also introduce a way to build simple closed contours as the concatenation of two disjoint open curves. Experimental results prove that the proposed model indeed outperforms state-of-the-art minimal paths-based image segmentation approaches. [ABSTRACT FROM AUTHOR]

The Voronoi diagram-based dual-front scheme is known as a powerful and efficient technique for addressing the image segmentation and domain partitioning problems. In the basic formulation of existing dual-front approaches, the evolving contour can be considered as the interfaces of adjacent Voronoi regions. Among these dual-front models, a crucial ingredient is regarded as the geodesic metrics by which the geodesic distances and the corresponding Voronoi diagram can be estimated. In this paper, we introduce a new dual-front model based on asymmetric quadratic metrics. These metrics considered are built by the integration of the image features and a vector field derived from the evolving contour. The use of the asymmetry enhancement can reduce the risk for the segmentation contours being stuck at false positions, especially when the initial curves are far away from the target boundaries or the images have complicated intensity distributions. Moreover, the proposed dual-front model can be applied for image segmentation in conjunction with various region-based homogeneity terms. The numerical experiments on both synthetic and real images show that the proposed dual-front model indeed achieves encouraging results. [ABSTRACT FROM AUTHOR]