695 research outputs found
Shape Calculus for Shape Energies in Image Processing
Many image processing problems are naturally expressed as energy minimization
or shape optimization problems, in which the free variable is a shape, such as
a curve in 2d or a surface in 3d. Examples are image segmentation, multiview
stereo reconstruction, geometric interpolation from data point clouds. To
obtain the solution of such a problem, one usually resorts to an iterative
approach, a gradient descent algorithm, which updates a candidate shape
gradually deforming it into the optimal shape. Computing the gradient descent
updates requires the knowledge of the first variation of the shape energy, or
rather the first shape derivative. In addition to the first shape derivative,
one can also utilize the second shape derivative and develop a Newton-type
method with faster convergence. Unfortunately, the knowledge of shape
derivatives for shape energies in image processing is patchy. The second shape
derivatives are known for only two of the energies in the image processing
literature and many results for the first shape derivative are limiting, in the
sense that they are either for curves on planes, or developed for a specific
representation of the shape or for a very specific functional form in the shape
energy. In this work, these limitations are overcome and the first and second
shape derivatives are computed for large classes of shape energies that are
representative of the energies found in image processing. Many of the formulas
we obtain are new and some generalize previous existing results. These results
are valid for general surfaces in any number of dimensions. This work is
intended to serve as a cookbook for researchers who deal with shape energies
for various applications in image processing and need to develop algorithms to
compute the shapes minimizing these energies
A variational approach for viewpoint-based visibility maximization
We present a variational method for unfolding of the cortex based on a user-chosen point of view as an alternative to more traditional global flattening methods, which incur more distortion around the region of interest. Our approach involves three novel contributions. The first is an energy function and its corresponding gradient flow to measure the average visibility of a region of interest of a surface from a given viewpoint. The second is an additional energy function and flow designed to preserve the 3D topology of the evolving surface. This latter contribution receives significant focus in this thesis as it is crucial to obtain the desired unfolding effect derived from the first energy functional and flow. Without it, the resulting topology changes render the unconstrained evolution uninteresting for the purpose of cortical visualization, exploration, and inspection. The third is a method that dramatically improves the computational speed of the 3D topology-preservation approach by creating a tree structure of the triangulated surface and using a recursion technique.Ph.D.Committee Chair: Allen R. Tannenbaum; Committee Member: Anthony J. Yezzi; Committee Member: Gregory Turk; Committee Member: Joel R. Jackson; Committee Member: Patricio A. Vel
High order direct Arbitrary-Lagrangian-Eulerian schemes on moving Voronoi meshes with topology changes
We present a new family of very high order accurate direct
Arbitrary-Lagrangian-Eulerian (ALE) Finite Volume (FV) and Discontinuous
Galerkin (DG) schemes for the solution of nonlinear hyperbolic PDE systems on
moving 2D Voronoi meshes that are regenerated at each time step and which
explicitly allow topology changes in time.
The Voronoi tessellations are obtained from a set of generator points that
move with the local fluid velocity. We employ an AREPO-type approach, which
rapidly rebuilds a new high quality mesh rearranging the element shapes and
neighbors in order to guarantee a robust mesh evolution even for vortex flows
and very long simulation times. The old and new Voronoi elements associated to
the same generator are connected to construct closed space--time control
volumes, whose bottom and top faces may be polygons with a different number of
sides. We also incorporate degenerate space--time sliver elements, needed to
fill the space--time holes that arise because of topology changes. The final
ALE FV-DG scheme is obtained by a redesign of the fully discrete direct ALE
schemes of Boscheri and Dumbser, extended here to moving Voronoi meshes and
space--time sliver elements. Our new numerical scheme is based on the
integration over arbitrary shaped closed space--time control volumes combined
with a fully-discrete space--time conservation formulation of the governing PDE
system. In this way the discrete solution is conservative and satisfies the GCL
by construction.
Numerical convergence studies as well as a large set of benchmarks for
hydrodynamics and magnetohydrodynamics (MHD) demonstrate the accuracy and
robustness of the proposed method. Our numerical results clearly show that the
new combination of very high order schemes with regenerated meshes with
topology changes lead to substantial improvements compared to direct ALE
methods on conforming meshes
Aquatics reconstruction software: the design of a diagnostic tool based on computer vision algorithms
Computer vision methods can be applied to a variety of medical and surgical applications, and many techniques and algorithms are available that can be used to recover 3D shapes and information from images range and volume data. Complex practical applications, however, are rarely approachable with a single technique, and require detailed analysis on how they can be subdivided in subtasks that are computationally treatable and that, at the same time, allow for the appropriate level of user-interaction. In this paper we show an example of a complex application where, following criteria of efficiency, reliability and user friendliness, several computer vision techniques have been selected and customized to build a system able to support diagnosis and endovascular treatment of Abdominal Aortic Aneurysms. The system reconstructs the geometrical representation of four different structures related to the aorta (vessel lumen, thrombus, calcifications and skeleton) from CT angiography data. In this way it supports the three dimensional measurements required for a careful geometrical evaluation of the vessel, that is fundamental to decide if the treatment is necessary and to perform, in this case, its planning. The system has been realized within the European trial AQUATICS (IST-1999-20226 EUTIST-M WP 12), and it has been widely tested on clinical data
A higher-order active contour model of a `gas of circles' and its application to tree crown extraction
Many image processing problems involve identifying the region in the image
domain occupied by a given entity in the scene. Automatic solution of these
problems requires models that incorporate significant prior knowledge about the
shape of the region. Many methods for including such knowledge run into
difficulties when the topology of the region is unknown a priori, for example
when the entity is composed of an unknown number of similar objects.
Higher-order active contours (HOACs) represent one method for the modelling of
non-trivial prior knowledge about shape without necessarily constraining region
topology, via the inclusion of non-local interactions between region boundary
points in the energy defining the model. The case of an unknown number of
circular objects arises in a number of domains, e.g. medical, biological,
nanotechnological, and remote sensing imagery. Regions composed of an a priori
unknown number of circles may be referred to as a `gas of circles'. In this
report, we present a HOAC model of a `gas of circles'. In order to guarantee
stable circles, we conduct a stability analysis via a functional Taylor
expansion of the HOAC energy around a circular shape. This analysis fixes one
of the model parameters in terms of the others and constrains the rest. In
conjunction with a suitable likelihood energy, we apply the model to the
extraction of tree crowns from aerial imagery, and show that the new model
outperforms other techniques
Geodatabase Design for Resource and Land Management GIS: Missoula Field Office BLM Case Study
The Bureau of Land Management (BLM) is in the process of improving their geographic information system (GIS). The main intention is to upgrade their data and present their employees with the geospatial means necessary to accomplish their resource and land management responsibilities. Environmental Systems Research Institute (ESRI„µ) designed the geodatabase model, which provides multiple advantages in organization, management, and maintenance of geographic data. The geodatabase model implements advanced relationships between geospatial features and database tables, creates platforms available in organization and editing, and instills GIS functionality to ensure data integrity. The main goal of this work is to investigate the daily, annual, and future geospatial objectives of the Missoula Field Office BLM from the ground up, and design a geodatabase model based on the individual resource specialist¡¦s needs. It is intended that this model can be used to as the basis to allow an all encompassing geodatabase model to be build that would serve BLM field offices throughout the United States. Six resource disciplines are investigated according to their GIS needs. In order to accomplish this work, the current GIS condition is assessed, regulations and policies are examined, and GIS aspirations are considered. Within the six resource disciplines examined, thirty-three feature classes, eleven object classes, ten relationship classes, fifty-one domains and three subtypes were created to establish this geodatabase design. This geodatabase design will prove successful for the Missoula Field Office to document, organize, edit, manage, and analyze their many geospatial requirements. The model developed will aid the Missoula Field Office BLM to adequately fulfill their land management data responsibilities, and assist their GIS demands as a federal agency
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