4,293 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
Reconstruction of a function from its spherical (circular) means with the centers lying on the surface of certain polygons and polyhedra
We present explicit filtration/backprojection-type formulae for the inversion
of the spherical (circular) mean transform with the centers lying on the
boundary of some polyhedra (or polygons, in 2D). The formulae are derived using
the double layer potentials for the wave equation, for the domains with certain
symmetries. The formulae are valid for a rectangle and certain triangles in 2D,
and for a cuboid, certain right prisms and a certain pyramid in 3D. All the
present inversion formulae yield exact reconstruction within the domain
surrounded by the acquisition surface even in the presence of exterior sources.Comment: 9 figure
Ball surface representations using partial differential equations
Over two decades ago, geometric modelling using partial differential equations (PDEs) approach was widely studied in Computer Aided Geometric Design (CAGD). This approach was initially introduced by some researchers to deal with Bèzier surface related to the minimal surface area determined by prescribed boundary curves. However, Bèzier surface representation can be improved in terms of computation time and minimal surface area by employing Ball surface representation. Thus, this research develops
an algorithm to generalise Ball surfaces from boundary curves using elliptic PDEs. Two specific Ball surfaces, namely harmonic and biharmonic, are first constructed in developing the proposed algorithm. The former and later surfaces require two and four boundary conditions respectively. In order to generalise Ball surfaces in the polynomial solution of any fourth order PDEs, the Dirichlet method is then employed. The numerical results obtained on well-known example of data points show that the
proposed generalised Ball surfaces algorithm performs better than BCzier surface representation in terms of computation time and minimal surface area. Moreover, the new constructed algorithm also holds for any surfaces in CAGD including the Bèzier surface. This algorithm is then tested in positivity preserving of surface and image enlargement
problems. The results show that the proposed algorithm is comparable with the existing methods in terms of accuracy. Hence, this new algorithm is a viable alternative for constructing generalized Ball surfaces. The findings of this study contribute towards the body of knowledge for surface reconstruction based on PDEs approach in the area of geometric modelling and computer graphics
A Plane Wave Virtual Element Method for the Helmholtz Problem
We introduce and analyze a virtual element method (VEM) for the Helmholtz
problem with approximating spaces made of products of low order VEM functions
and plane waves. We restrict ourselves to the 2D Helmholtz equation with
impedance boundary conditions on the whole domain boundary. The main
ingredients of the plane wave VEM scheme are: i) a low frequency space made of
VEM functions, whose basis functions are not explicitly computed in the element
interiors; ii) a proper local projection operator onto the high-frequency
space, made of plane waves; iii) an approximate stabilization term. A
convergence result for the h-version of the method is proved, and numerical
results testing its performance on general polygonal meshes are presented
Constructing minimum deflection fixture arrangements using frame invariant norms
This paper describes a fixture planning method that minimizes object deflection under external loads. The method takes into account the natural compliance of the contacting bodies and applies to two-dimensional and three-dimensional quasirigid bodies. The fixturing method is based on a quality measure that characterizes the deflection of a fixtured object in response to unit magnitude wrenches. The object deflection measure is defined in terms of frame-invariant rigid body velocity and wrench norms and is therefore frame invariant. The object deflection measure is applied to the planning of optimal fixture arrangements of polygonal objects. We describe minimum-deflection fixturing algorithms for these objects, and make qualitative observations on the optimal arrangements generated by the algorithms. Concrete examples illustrate the minimum deflection fixturing method. Note to Practitioners-During fixturing, a workpiece needs to not only be stable against external perturbations, but must also stay within a specified tolerance in response to machining or assembly forces. This paper describes a fixture planning approach that minimizes object deflection under applied work loads. The paper describes how to take local material deformation effects into account, using a generic quasirigid contact model. Practical algorithms that compute the optimal fixturing arrangements of polygonal workpieces are described and examples are then presented
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