12,609 research outputs found
Dictionary Learning-based Inpainting on Triangular Meshes
The problem of inpainting consists of filling missing or damaged regions in
images and videos in such a way that the filling pattern does not produce
artifacts that deviate from the original data. In addition to restoring the
missing data, the inpainting technique can also be used to remove undesired
objects. In this work, we address the problem of inpainting on surfaces through
a new method based on dictionary learning and sparse coding. Our method learns
the dictionary through the subdivision of the mesh into patches and rebuilds
the mesh via a method of reconstruction inspired by the Non-local Means method
on the computed sparse codes. One of the advantages of our method is that it is
capable of filling the missing regions and simultaneously removes noise and
enhances important features of the mesh. Moreover, the inpainting result is
globally coherent as the representation based on the dictionaries captures all
the geometric information in the transformed domain. We present two variations
of the method: a direct one, in which the model is reconstructed and restored
directly from the representation in the transformed domain and a second one,
adaptive, in which the missing regions are recreated iteratively through the
successive propagation of the sparse code computed in the hole boundaries,
which guides the local reconstructions. The second method produces better
results for large regions because the sparse codes of the patches are adapted
according to the sparse codes of the boundary patches. Finally, we present and
analyze experimental results that demonstrate the performance of our method
compared to the literature
Image Reconstruction from Bag-of-Visual-Words
The objective of this work is to reconstruct an original image from
Bag-of-Visual-Words (BoVW). Image reconstruction from features can be a means
of identifying the characteristics of features. Additionally, it enables us to
generate novel images via features. Although BoVW is the de facto standard
feature for image recognition and retrieval, successful image reconstruction
from BoVW has not been reported yet. What complicates this task is that BoVW
lacks the spatial information for including visual words. As described in this
paper, to estimate an original arrangement, we propose an evaluation function
that incorporates the naturalness of local adjacency and the global position,
with a method to obtain related parameters using an external image database. To
evaluate the performance of our method, we reconstruct images of objects of 101
kinds. Additionally, we apply our method to analyze object classifiers and to
generate novel images via BoVW
Constructing Desirable Scalar Fields for Morse Analysis on Meshes
Morse theory is a powerful mathematical tool that uses the local differential properties of a manifold to make conclusions about global topological aspects of the manifold. Morse theory has been proven to be a very useful tool in computer graphics, geometric data processing and understanding. This work is divided into two parts. The first part is concerned with constructing geometry and symmetry aware scalar functions on a triangulated -manifold. To effectively apply Morse theory to discrete manifolds, one needs to design scalar functions on them with certain properties such as respecting the symmetry and the geometry of the surface and having the critical points of the scalar function coincide with feature or symmetry points on the surface. In this work, we study multiple methods that were suggested in the literature to construct such functions such as isometry invariant scalar functions, Poisson fields and discrete conformal factors. We suggest multiple refinements to each family of these functions and we propose new methods to construct geometry and symmetry-aware scalar functions using mainly the theory of the Laplace-Beltrami operator. Our proposed methods are general and can be applied in many areas such as parametrization, shape analysis, symmetry detection and segmentation. In the second part of the thesis we utilize Morse theory to give topologically consistent segmentation algorithms
2D approach for modelling self-potential anomalies. Application to synthetic and real data
The aim of this work is to present a 2-D Matlab code based on the finite element method
for providing numerical modelling of both groundwater flow and self-potential signals.
The distribution of the self-potential is obtained by starting with the solution of the
groundwater flow, then computing the source current density, and finally calculating
the electrical potential. The reliability of the algorithm is tested with synthetic case
studies in order to simulate both the electric field resulting from the existence of a leak
in the dam and SP signals associated with a pumping test in an unconfined aquifer. In
addition, the algorithm was applied to field data for the localization of piping sinkholes.
The results show that the outputs of the algorithm yielded satisfactory solutions, which
are in good agreement with those of previous studies and field investigations. In details,
the synthetic data and SP anomalies calculated by using the code are very close in
terms of sign and magnitude, while real data tests clearly indicated that the computed
SP signals were found to be consistent with the measured values
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