Image-Based Reconstruction and Visual Hull from Imprecise Input
Author(s)
He, Peng
Type
Thesis
Abstract
Image-based reconstruction is a series of computer vision processes which takes 2D images
of the scene as input and outputs the geometric shape approximate of the scene. It has
vast applications in industrial design, manufacture, gaming, filming, heritage protection
and many other areas. The visual hull of a polyhedral (or polygonal) scene in R3 (or
R2) is the best 3D (or 2D) shape that one can retrieve from its silhouettes. It has great
advantage in obstacle avoidance, robotic navigation, 3D model acquisition and human
motion tracking. A 3D visual hull is bounded by planes and quadratic surfaces. Classical
image-based reconstruction and visual hull methods fail to maintain the exactness and
robustness when the input is imprecise.
In the solid domain of 3D objects in R3, geometric shapes with imprecision are well
modelled and carefully studied. Each partial geometric object is defined by two disjoint
open sets : interior and exterior. The interior (respectively, exterior) is an open set that
contains all the points definitely known to be inside (respectively, outside) the object.
Partial objects, ordered with subset inclusion, form a continuous Scott domain in which
each object approximates the target object at a certain level of precision.
We study the image-based reconstruction and visual hull in the solid domain which allows
the notion of the partial polyhedron and the partial visual hull. They capture the
imprecision in the input polyhedral scenes and outputs the exact information about what
points are definitely inside or outside the reconstructed scene and the visual hull. The
partial image-based reconstruction and the partial visual hull algorithm maintain the
same computational complexity as the corresponding classical methods. The outputs of
the algorithms are partial objects or partial visual hulls which converge to their classical
counterparts as the input converges to an exact value. For the image-based reconstruction
and the 2D visual hull, we show that their construction processes with imprecise input are
Hausdro and the Scott continuity. For the 3D visual hull algorithm, we show its Hausdro
and the Scott continuity of the domain-theoretic construction in the Solid domain
of the projective 3 space P3. Furthermore, we prove the computability of the image-based
reconstruction, the 2D and the 3D visual hull.
of the scene as input and outputs the geometric shape approximate of the scene. It has
vast applications in industrial design, manufacture, gaming, filming, heritage protection
and many other areas. The visual hull of a polyhedral (or polygonal) scene in R3 (or
R2) is the best 3D (or 2D) shape that one can retrieve from its silhouettes. It has great
advantage in obstacle avoidance, robotic navigation, 3D model acquisition and human
motion tracking. A 3D visual hull is bounded by planes and quadratic surfaces. Classical
image-based reconstruction and visual hull methods fail to maintain the exactness and
robustness when the input is imprecise.
In the solid domain of 3D objects in R3, geometric shapes with imprecision are well
modelled and carefully studied. Each partial geometric object is defined by two disjoint
open sets : interior and exterior. The interior (respectively, exterior) is an open set that
contains all the points definitely known to be inside (respectively, outside) the object.
Partial objects, ordered with subset inclusion, form a continuous Scott domain in which
each object approximates the target object at a certain level of precision.
We study the image-based reconstruction and visual hull in the solid domain which allows
the notion of the partial polyhedron and the partial visual hull. They capture the
imprecision in the input polyhedral scenes and outputs the exact information about what
points are definitely inside or outside the reconstructed scene and the visual hull. The
partial image-based reconstruction and the partial visual hull algorithm maintain the
same computational complexity as the corresponding classical methods. The outputs of
the algorithms are partial objects or partial visual hulls which converge to their classical
counterparts as the input converges to an exact value. For the image-based reconstruction
and the 2D visual hull, we show that their construction processes with imprecise input are
Hausdro and the Scott continuity. For the 3D visual hull algorithm, we show its Hausdro
and the Scott continuity of the domain-theoretic construction in the Solid domain
of the projective 3 space P3. Furthermore, we prove the computability of the image-based
reconstruction, the 2D and the 3D visual hull.
Date Issued
2012-06
Date Awarded
2012-08
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
Advisor
Welton, Tom
Publisher Department
Computing
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)