772 research outputs found
Disconnected Skeleton: Shape at its Absolute Scale
We present a new skeletal representation along with a matching framework to
address the deformable shape recognition problem. The disconnectedness arises
as a result of excessive regularization that we use to describe a shape at an
attainably coarse scale. Our motivation is to rely on the stable properties of
the shape instead of inaccurately measured secondary details. The new
representation does not suffer from the common instability problems of
traditional connected skeletons, and the matching process gives quite
successful results on a diverse database of 2D shapes. An important difference
of our approach from the conventional use of the skeleton is that we replace
the local coordinate frame with a global Euclidean frame supported by
additional mechanisms to handle articulations and local boundary deformations.
As a result, we can produce descriptions that are sensitive to any combination
of changes in scale, position, orientation and articulation, as well as
invariant ones.Comment: The work excluding {\S}V and {\S}VI has first appeared in 2005 ICCV:
Aslan, C., Tari, S.: An Axis-Based Representation for Recognition. In
ICCV(2005) 1339- 1346.; Aslan, C., : Disconnected Skeletons for Shape
Recognition. Masters thesis, Department of Computer Engineering, Middle East
Technical University, May 200
A Low-Dimensional Representation for Robust Partial Isometric Correspondences Computation
Intrinsic isometric shape matching has become the standard approach for pose
invariant correspondence estimation among deformable shapes. Most existing
approaches assume global consistency, i.e., the metric structure of the whole
manifold must not change significantly. While global isometric matching is well
understood, only a few heuristic solutions are known for partial matching.
Partial matching is particularly important for robustness to topological noise
(incomplete data and contacts), which is a common problem in real-world 3D
scanner data. In this paper, we introduce a new approach to partial, intrinsic
isometric matching. Our method is based on the observation that isometries are
fully determined by purely local information: a map of a single point and its
tangent space fixes an isometry for both global and the partial maps. From this
idea, we develop a new representation for partial isometric maps based on
equivalence classes of correspondences between pairs of points and their
tangent spaces. From this, we derive a local propagation algorithm that find
such mappings efficiently. In contrast to previous heuristics based on RANSAC
or expectation maximization, our method is based on a simple and sound
theoretical model and fully deterministic. We apply our approach to register
partial point clouds and compare it to the state-of-the-art methods, where we
obtain significant improvements over global methods for real-world data and
stronger guarantees than previous heuristic partial matching algorithms.Comment: 17 pages, 12 figure
Non-Euclidean geometry in nature
I describe the manifestation of the non-Euclidean geometry in the behavior of
collective observables of some complex physical systems. Specifically, I
consider the formation of equilibrium shapes of plants and statistics of sparse
random graphs. For these systems I discuss the following interlinked questions:
(i) the optimal embedding of plants leaves in the three-dimensional space, (ii)
the spectral statistics of sparse random matrix ensembles.Comment: 52 pages, 21 figures, last section is rewritten, a reference to
chaotic Hamiltonian systems is adde
Understanding the Structure of 3D Shapes
Compact representations of three dimensional objects are very often used
in computer graphics to create effective ways to analyse, manipulate and
transmit 3D models. Their ability to abstract from the concrete shapes and
expose their structure is important in a number of applications, spanning
from computer animation, to medicine, to physical simulations. This thesis
will investigate new methods for the generation of compact shape representations.
In the first part, the problem of computing optimal PolyCube base
complexes will be considered. PolyCubes are orthogonal polyhedra used
in computer graphics to map both surfaces and volumes. Their ability to
resemble the original models and at the same time expose a very simple and
regular structure is important in a number of applications, such as texture
mapping, spline fitting and hex-meshing. The second part will focus on
medial descriptors. In particular, two new algorithms for the generation
of curve-skeletons will be presented. These methods are completely based
on the visual appearance of the input, therefore they are independent from
the type, number and quality of the primitives used to describe a shape,
determining, thus, an advancement to the state of the art in the field
Understanding the Structure of 3D Shapes
Compact representations of three dimensional objects are very often used
in computer graphics to create effective ways to analyse, manipulate and
transmit 3D models. Their ability to abstract from the concrete shapes and
expose their structure is important in a number of applications, spanning
from computer animation, to medicine, to physical simulations. This thesis
will investigate new methods for the generation of compact shape representations.
In the first part, the problem of computing optimal PolyCube base
complexes will be considered. PolyCubes are orthogonal polyhedra used
in computer graphics to map both surfaces and volumes. Their ability to
resemble the original models and at the same time expose a very simple and
regular structure is important in a number of applications, such as texture
mapping, spline fitting and hex-meshing. The second part will focus on
medial descriptors. In particular, two new algorithms for the generation
of curve-skeletons will be presented. These methods are completely based
on the visual appearance of the input, therefore they are independent from
the type, number and quality of the primitives used to describe a shape,
determining, thus, an advancement to the state of the art in the field
Efficient Point-Cloud Processing with Primitive Shapes
This thesis presents methods for efficient processing of point-clouds based on primitive shapes. The set of considered simple parametric shapes consists of planes, spheres, cylinders, cones and tori. The algorithms developed in this work are targeted at scenarios in which the occurring surfaces can be well represented by this set of shape primitives which is the case in many man-made environments such as e.g. industrial compounds, cities or building interiors. A primitive subsumes a set of corresponding points in the point-cloud and serves as a proxy for them. Therefore primitives are well suited to directly address the unavoidable oversampling of large point-clouds and lay the foundation for efficient point-cloud processing algorithms. The first contribution of this thesis is a novel shape primitive detection method that is efficient even on very large and noisy point-clouds. Several applications for the detected primitives are subsequently explored, resulting in a set of novel algorithms for primitive-based point-cloud processing in the areas of compression, recognition and completion. Each of these application directly exploits and benefits from one or more of the detected primitives' properties such as approximation, abstraction, segmentation and continuability
Photonic band structure design using persistent homology
The machine learning technique of persistent homology classifies complex
systems or datasets by computing their topological features over a range of
characteristic scales. There is growing interest in applying persistent
homology to characterize physical systems such as spin models and multiqubit
entangled states. Here we propose persistent homology as a tool for
characterizing and optimizing band structures of periodic photonic media. Using
the honeycomb photonic lattice Haldane model as an example, we show how
persistent homology is able to reliably classify a variety of band structures
falling outside the usual paradigms of topological band theory, including "moat
band" and multi-valley dispersion relations, and thereby control the properties
of quantum emitters embedded in the lattice. The method is promising for the
automated design of more complex systems such as photonic crystals and Moire
superlattices.Comment: Published version; 9 pages, 7 figure
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