TY - THES
AU - Ranjan, Vishwa
PY - 1996
TI - A union of spheres representation for 3D objects
KW - Thesis/Dissertation
LA - eng
M3 - Text
AB - Reconstruction of an object from a set of points sampled from its boundary is an important
problem in graphics and vision. Several methods exist to compute and display
surface (e.g., polygonal) and volumetric (e.g., polyhedral) models of objects from the
boundary points.
In order to display, transform, and compare objects, it is often convenient or necessary
to use different representations of objects. Basic desired properties of representations of
objects are efficiency of computation, storage, and display. Other important properties
include stability (small changes in the data, such as noise or small distortions, cause
small changes in the model), the ability to determine the similarities between two data
sets, and the computation of simplified models. A survey of common representations of
objects (e.g., surface, octrees, etc.) shows that some important properties are lacking in
these representations.
In this thesis we study a union of spheres representation (UoS) for the volume enclosed
by an object's boundary. We present algorithms to generate stable union of spheres models
of objects from various sources of data, such as volumetric data (e.g., data from CT
or MRI scanners), range data, and other existing models. The spheres can be simplified
to obtain multi-scale models. We present a method to establish correspondence between
two objects using their union of spheres models and use this to calculate distances between
objects, to register objects, and to interpolate between objects. This establishes
a measure to study and compare such models. Examples with simple and complex objects
show how this measure corresponds closely to the intuitive human understanding
of shape.
N2 - Reconstruction of an object from a set of points sampled from its boundary is an important
problem in graphics and vision. Several methods exist to compute and display
surface (e.g., polygonal) and volumetric (e.g., polyhedral) models of objects from the
boundary points.
In order to display, transform, and compare objects, it is often convenient or necessary
to use different representations of objects. Basic desired properties of representations of
objects are efficiency of computation, storage, and display. Other important properties
include stability (small changes in the data, such as noise or small distortions, cause
small changes in the model), the ability to determine the similarities between two data
sets, and the computation of simplified models. A survey of common representations of
objects (e.g., surface, octrees, etc.) shows that some important properties are lacking in
these representations.
In this thesis we study a union of spheres representation (UoS) for the volume enclosed
by an object's boundary. We present algorithms to generate stable union of spheres models
of objects from various sources of data, such as volumetric data (e.g., data from CT
or MRI scanners), range data, and other existing models. The spheres can be simplified
to obtain multi-scale models. We present a method to establish correspondence between
two objects using their union of spheres models and use this to calculate distances between
objects, to register objects, and to interpolate between objects. This establishes
a measure to study and compare such models. Examples with simple and complex objects
show how this measure corresponds closely to the intuitive human understanding
of shape.
UR - https://open.library.ubc.ca/collections/831/items/1.0051598
ER - End of Reference