Ellipse-preserving Hermite interpolation and subdivision

We introduce a family of piecewise-exponential functions that have the Hermite interpolation property. Our design is motivated by the search for an effective scheme for the joint interpolation of points and associated tangents on a curve with the ability to perfectly reproduce ellipses. We prove that the proposed Hermite functions form a Riesz basis and that they reproduce prescribed exponential polynomials. We present a method based on Green's functions to unravel their multi-resolution and approximation-theoretic properties. Finally, we derive the corresponding vector and scalar subdivision schemes, which lend themselves to a fast implementation. The proposed vector scheme is interpolatory and level-dependent, but its asymptotic behaviour is the same as the classical cubic Hermite spline algorithm. The same convergence properties---i.e., fourth order of approximation---are hence ensured

Multiresolution Subdivision Snakes

We present a new family of snakes that satisfy the property of multiresolution by exploiting subdivision schemes. We show in a generic way how to construct such snakes based on an admissible subdivision mask. We derive the necessary energy formulations and provide the formulas for their efficient computation. Depending on the choice of the mask, such models have the ability to reproduce trigonometric or polynomial curves. They can also be designed to be interpolating, a property that is useful in user-interactive applications. We provide explicit examples of subdivision snakes and illustrate their use for the segmentation of bioimages. We show that they are robust in the presence of noise and provide a multiresolution algorithm to enlarge their basin of attraction, which decreases their dependence on initialization compared to singleresolution snakes. We show the advantages of the proposed model in terms of computation and segmentation of structures with different sizes

Periodic Splines and Gaussian Processes for the Resolution of Linear Inverse Problems

This paper deals with the resolution of inverse problems in a periodic setting or, in other terms, the reconstruction of periodic continuous-domain signals from their noisy measurements. We focus on two reconstruction paradigms: variational and statistical. In the variational approach, the reconstructed signal is solution to an optimization problem that establishes a tradeoff between fidelity to the data and smoothness conditions via a quadratic regularization associated to a linear operator. In the statistical approach, the signal is modeled as a stationary random process defined from a Gaussian white noise and a whitening operator; one then looks for the optimal estimator in the mean-square sense. We give a generic form of the reconstructed signals for both approaches, allowing for a rigorous comparison of the two.We fully characterize the conditions under which the two formulations yield the same solution, which is a periodic spline in the case of sampling measurements. We also show that this equivalence between the two approaches remains valid on simulations for a broad class of problems. This extends the practical range of applicability of the variational method

Trophic Interactions in a Semiaquatic Snake Community: Insights into the Structure of a Floodplain Food Web

Food webs provide a useful conceptual framework for evaluating the relationships that exist within ecological systems. Characterizing the interactions within these webs can improve our understanding of how communities are structured and what mechanisms stabilize them. Untangling these interactions can be an intractable problem in complex systems and insights gained from conventional methods are often accompanied by inherent sources of bias. This study used stable isotope analysis, an alternative to traditional methods, to investigate the roles and relative contributions of consumers at the top of a food web to community structure and stability. I compared the niche parameters of five syntopic semi-aquatic snake species using the ratios of naturally occurring carbon and nitrogen isotopes to determine their relative trophic positions and estimate the contributions of potential prey sources to their diets. Analyses using Bayesian mixing models revealed evidence of niche partitioning among consumer groups and indicated that competitive dynamics have helped to shape the structure of this community. I identified ontogenetic differences in the trophic niches occupied by distinct age classes from three consumer species. I also detected temporal shifts in trophic structure that might be the result of intra-annual variation in resource availability. While competition appears to play a role in structuring this community, the trophic niches occupied by consumer groups seem to be somewhat plastic. Temporal shifts in resource availability have the potential to influence not only the relationships among competing consumers, but also their interactions with prey groups. Future research should examine how periodic fluctuations in prey abundance influences the connectivity, and by extension the stability, of this community

Trophic Interactions in a Semiaquatic Snake Community: Insights into the Structure of a Floodplain Food Web

Food webs provide a useful conceptual framework for evaluating the relationships that exist within ecological systems. Characterizing the interactions within these webs can improve our understanding of how communities are structured and what mechanisms stabilize them. Untangling these interactions can be an intractable problem in complex systems and insights gained from conventional methods are often accompanied by inherent sources of bias. This study used stable isotope analysis, an alternative to traditional methods, to investigate the roles and relative contributions of consumers at the top of a food web to community structure and stability. I compared the niche parameters of five syntopic semi-aquatic snake species using the ratios of naturally occurring carbon and nitrogen isotopes to determine their relative trophic positions and estimate the contributions of potential prey sources to their diets. Analyses using Bayesian mixing models revealed evidence of niche partitioning among consumer groups and indicated that competitive dynamics have helped to shape the structure of this community. I identified ontogenetic differences in the trophic niches occupied by distinct age classes from three consumer species. I also detected temporal shifts in trophic structure that might be the result of intra-annual variation in resource availability. While competition appears to play a role in structuring this community, the trophic niches occupied by consumer groups seem to be somewhat plastic. Temporal shifts in resource availability have the potential to influence not only the relationships among competing consumers, but also their interactions with prey groups. Future research should examine how periodic fluctuations in prey abundance influences the connectivity, and by extension the stability, of this community

A Family of Smooth and Interpolatory Basis Functions for Parametric Curve and Surface Representation

Interpolatory basis functions are helpful to specify parametric curves or surfaces that can be modified by simple user-interaction. Their main advantage is a characterization of the object by a set of control points that lie on the shape itself (i.e., curve or surface). In this paper, we characterize a new family of compactly supported piecewise-exponential basis functions that are smooth and satisfy the interpolation property. They can be seen as a generalization and extension of the Keys interpolation kernel using cardinal exponential B-splines. The proposed interpolators can be designed to reproduce trigonometric, hyperbolic, and polynomial functions or combinations of them. We illustrate the construction and give concrete examples on how to use such functions to construct parametric curves and surfaces