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Objects as Volumes: A Stochastic Geometry View of Opaque Solids

Bailey Miller · Hanyu Chen · Alice Lai · Ioannis Gkioulekas

Arch 4A-E Poster #412
[ ] [ Project Page ]
Wed 19 Jun 10:30 a.m. PDT — noon PDT
Oral presentation: Orals 1B Vision and Graphics
Wed 19 Jun 9 a.m. PDT — 10:30 a.m. PDT


We develop a theory for the representation of opaque solids as volumes. Starting from a stochastic representation of opaque solids as random indicator functions, we prove the conditions under which such solids can be modeled using exponential volumetric transport. We also derive expressions for the volumetric attenuation coefficient as a functional of the probability distributions of the underlying indicator functions. We generalize our theory to account for isotropic and anisotropic scattering at different parts of the solid, and for representations of opaque solids as stochastic implicit surfaces. We derive our volumetric representation from first principles, which ensures that it satisfies physical constraints such as reciprocity and reversibility. We use our theory to explain, compare, and correct previous volumetric representations, as well as propose meaningful extensions that lead to improved performance in 3D reconstruction tasks.

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