VI.—On Professor Hull's Carboniferous Classification

Safe Hulls

The visual hull is widely used as a proxy for novel view synthesis in computer vision. This paper introduces the safe hull, the first visual hull reconstruction technique to produce a surface containing only foreground parts. A theoretical basis underlies this novel approach which, unlike any previous work, can also identify phantom volumes attached to real objects. Using an image-based method,...

Winsor , Major Professor Albert Choi , Minor Professor

Formalizing Convex Hulls Algorithms

We study the development of formally proved algorithms for computational geometry. The result of this work is a formal description of the basic principles that make convex hull algorithms work and two programs that implement convex hull computation and have been automatically obtained from formally verified mathematical proofs. A special attention has been given to handling degenerated cases th...

Kernels from hulls

The kernel of a polygon has long been an object of study in computational geometry, especially in the context of art gallery theorems. In this paper, we present two new algorithms for computing the kernel of a plane curve. We show that the computation of the kernel of a plane curve can be reduced to the computation of the convex hull of a plane curve, revealing the computational and structural ...

Image-Based Photo Hulls

We present an efficient image-based rendering algorithm that computes photo hulls of a scene photographed from multiple viewpoints. Our algorithm, Image-Based Photo Hulls (IBPH), like the Image-Based Visual Hulls (IBVH) algorithm from Matusik et. al. on which it is based, takes advantage of epipolar geometry to efficiently reconstruct the geometry and visibility of a scene. Our IBPH algorithm d...