BACKGROUND The effective geometric modeling of vascular structures is crucial for diagnosis, therapy planning and medical education. These applications require good balance with respect to surface smoothness, surface accuracy, triangle quality and surface size. METHODS Our method first extracts the vascular boundary voxels from the segmentation result, and utilizes these voxels to build a thr...

Shape-from-shading and shape-from-texture methods have the serious drawback that they are applicable only to smooth surfaces, while real surfaces are often rough and crumpled. TO extend such methods to real surfaces we must have a model that also applies to rough surfaces. The fractal surface model [Pentland 831 provides a formalism that is competent to describe such natural 3-D surfaces and, i...

Motivated by boundary value problems for partial differential equations, classical trace and extension theorems characterize traces of spaces of generalized smoothness (e.g., Sobolev, Besov, etc.) to smooth submanifolds of a Euclidean space. But in many cases one needs similar results for subsets of a more complicated geometric structure (for instance, after the change of variables initial data...

In this paper, a novel polynomial-time algorithm is described for solving the optimal net surface detection problem on proper ordered multi-column graphs in N -D space (N ≥ 3). The method is applied to searching for optimal object boundaries with arbitrary smoothness constraints in volumetric medical images. By simple transformations, such optimal surface detection problems can be simplified to...

Optimization of expected values in a stochastic domain is common in real world applications. However, it is often difficult to solve such optimization problems without significant knowledge about the surface defined by the stochastic function. I n this paper we examine local search techniques to solve stochastic Optimization. I n particular, we analyze assumptions of smoothness upon which these...

A smooth surface imaged on the retina produces a smooth flow field. Thus, the visual system may group regions of smoothly varying flow to segment surfaces. We tested this idea by having observers perform a segmentation task on several stimuli that differed in their 3D interpretations but were all matched in the smoothness of their 2D flow fields. Performance varied across conditions with the be...

In order to achieve a smooth surface while rendering a triangle-based mesh, we need to eliminate the mismatch between the smoothness of the shading and the non-smoothness of the geometry that is particularly visible at silhouettes. To eliminate these artifacts, we substitute the geometry of a cubic triangular Bézier curved patch for a triangular flat geometry. Meanwhile a subdivision algorithm ...

Multiresolution techniques for (mesh-based) surface processing have been developed and successfully used in surface progressive transmission, compression and other applications. A triangular mesh allows √ 3, dyadic and √ 7 refinements. The √ 3-refinement is the most appealing one for multiresolution data processing since it has the slowest progression through scale and provides more resolution ...

A key problem in shape-from-shading is how to simultaneously satisfy data-closeness and regularisation (such as surface smoothness) constraints. This paper makes two contributions towards solving this problem. The first is to describe a smoothness constraint which preserves surface structure by adaptively smoothing according to the intensity gradient magnitude. The second is to derive a framewo...

The accuracy of interpolation by a radial basis function φ is usually very satisfactory provided that the approximant f is reasonably smooth. However, for functions which have smoothness below a certain order associated with the basis function φ, no approximation power has yet been established. Hence, the purpose of this study is to discuss the Lp-approximation order (1 ≤ p ≤ ∞) of interpolatio...