7,269 research outputs found
A graph-based mathematical morphology reader
This survey paper aims at providing a "literary" anthology of mathematical
morphology on graphs. It describes in the English language many ideas stemming
from a large number of different papers, hence providing a unified view of an
active and diverse field of research
Combining Geometric and Topological Information for Boundary Estimation
A fundamental problem in computer vision is boundary estimation, where the
goal is to delineate the boundary of objects in an image. In this paper, we
propose a method which jointly incorporates geometric and topological
information within an image to simultaneously estimate boundaries for objects
within images with more complex topologies. We use a topological
clustering-based method to assist initialization of the Bayesian active contour
model. This combines pixel clustering, boundary smoothness, and potential prior
shape information to produce an estimated object boundary. Active contour
methods are knownto be extremely sensitive to algorithm initialization, relying
on the user to provide a reasonable starting curve to the algorithm. In the
presence of images featuring objects with complex topological structures, such
as objects with holes or multiple objects, the user must initialize separate
curves for each boundary of interest. Our proposed topologically-guided method
can provide an interpretable, smart initialization in these settings, freeing
up the user from potential pitfalls associated with objects of complex
topological structure. We provide a detailed simulation study comparing our
initialization to boundary estimates obtained from standard segmentation
algorithms. The method is demonstrated on artificial image datasets from
computer vision, as well as real-world applications to skin lesion and neural
cellular images, for which multiple topological features can be identified.Comment: 38 pages with appendices, 15 figure
Steklov Spectral Geometry for Extrinsic Shape Analysis
We propose using the Dirichlet-to-Neumann operator as an extrinsic
alternative to the Laplacian for spectral geometry processing and shape
analysis. Intrinsic approaches, usually based on the Laplace-Beltrami operator,
cannot capture the spatial embedding of a shape up to rigid motion, and many
previous extrinsic methods lack theoretical justification. Instead, we consider
the Steklov eigenvalue problem, computing the spectrum of the
Dirichlet-to-Neumann operator of a surface bounding a volume. A remarkable
property of this operator is that it completely encodes volumetric geometry. We
use the boundary element method (BEM) to discretize the operator, accelerated
by hierarchical numerical schemes and preconditioning; this pipeline allows us
to solve eigenvalue and linear problems on large-scale meshes despite the
density of the Dirichlet-to-Neumann discretization. We further demonstrate that
our operators naturally fit into existing frameworks for geometry processing,
making a shift from intrinsic to extrinsic geometry as simple as substituting
the Laplace-Beltrami operator with the Dirichlet-to-Neumann operator.Comment: Additional experiments adde
STV-based Video Feature Processing for Action Recognition
In comparison to still image-based processes, video features can provide rich and intuitive information about dynamic events occurred over a period of time, such as human actions, crowd behaviours, and other subject pattern changes. Although substantial progresses have been made in the last decade on image processing and seen its successful applications in face matching and object recognition, video-based event detection still remains one of the most difficult challenges in computer vision research due to its complex continuous or discrete input signals, arbitrary dynamic feature definitions, and the often ambiguous analytical methods. In this paper, a Spatio-Temporal Volume (STV) and region intersection (RI) based 3D shape-matching method has been proposed to facilitate the definition and recognition of human actions recorded in videos. The distinctive characteristics and the performance gain of the devised approach stemmed from a coefficient factor-boosted 3D region intersection and matching mechanism developed in this research. This paper also reported the investigation into techniques for efficient STV data filtering to reduce the amount of voxels (volumetric-pixels) that need to be processed in each operational cycle in the implemented system. The encouraging features and improvements on the operational performance registered in the experiments have been discussed at the end
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