Convex contouring of volumetric data

Multi-resolution Dual Contouring from Volumetric Data

We present a Multi-Resolution Dual method based on an incremental octree-based refinement strategy. Our solution is able to generate multi-resolution surfaces from segmented volumetric data. It extends the Dual Marching Cubes algorithm over a generalized octree and guarantees that the produced surfaces are always manifold by introducing a new cell-based criterion for dual vertices generation. M...

Adaptive surface extraction from anisotropic volumetric data: contouring on generalized octrees

In this article, we present an algorithm to extract adaptive surfaces from anisotropic volumetric data. For example, this kind of data can be obtained from a set of segmented images, from the sampling of an implicit function or it can be built by using depth images produced by time-of-flight cameras. However, for many applications as geometry modelling, rendering or finite elements, it is bette...

The volumetric barrier for convex quadratic constraints

Let Q = fx j s i (x) 0; i = 1; : : : ; kg, where s i (x) = a T i x ?x T Q i x ?c i , and Q i is an n n positive semideenite matrix. We prove that the volumetric and combined volumetric-logarithmic barriers for Q are O(p kn) and O(p kn) self-concordant, respectively. Our analysis uses the semideenite programming (SDP) representation for the convex quadratic constraints deening Q, and our earlier...

Measuring Interval Efficiency in Convex Hull of Data Using DEA

Ellipsoidal Approximations of Convex Sets Based on the Volumetric Barrier

Let C R n be a convex set. We assume that kxk 1 1 for all x 2 C, and that C contains a ball of radius 1=R. For x 2 R n , r 2 R, and B an n n symmetric positive deenite matrix, let E(x; B; r) = fy j (y ? x) T B(y ? x) r 2 g. A-rounding of C is an ellipsoid E(x; B; r) such that E(x; B; r==) C E(x; B; r). In the case that C is characterized by a separation oracle, it is well known that an O(n 3=2)...