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Point sets obtained from computer vision techniques are often noisy and non-uniform. We present a new method of surface reconstruction that can handle such data sets using anisotropic basis functions. Our reconstruction algorithm draws upon the work in variational implicit surfaces for constructing smooth and seamless 3D surfaces. Implicit functions are(More)
In this paper we derive differential equations for evolving radial basis functions (RBFs) to solve segmentation problems. The differential equations result from applying variational calculus to energy functionals designed for image segmentation. Our methodology supports evolution of all parameters of each RBF, including its position, weight, orientation,(More)
Although the natural history of autoimmune hepatitis (AIH) has been characterized, little is known about patients who present asymptomatically. Consequently, whether they require immunosuppressive therapy with its associated complications is unclear. To compare the natural history of asymptomatic AIH with symptomatic AIH, a large cohort of patients from a(More)
Implicit surfaces are often created by summing a collection of radial basis functions. Recently, researchers have begun to create implicit surfaces that exactly interpolate a given set of points by solving a simple linear system to assign weights to each basis function. Due to their ability to interpolate, these implicit surfaces are more easily(More)
Mappings between surfaces have a variety of uses, including texture transfer, multi-way morphing, and surface analysis. Given a 4D implicit function that defines a morph between two implicit surfaces, this article presents a method of calculating a mapping between the two surfaces. We create such a mapping by solving two PDEs over a tetrahedralized(More)
In this article, we describe a multi-layered image-based rendering system that can use different types of input to produce and render new environments. Each separate input that can be manipulated independently is called a layer. In our implementation, the types of layers that can be manipulated are the image-based and 3-D-based layers. The computation(More)
Analytical implicit surfaces composed of radial basis functions (RBFs) have received much recent attention. In this paper, we present a method to compute and visualize implicit surfaces represented by a summation of weighted RBFs. We use a compactly-supported RBF, and discretely sample the 3D basis function into a 3D texture that is mapped to overlapping(More)