8 research outputs found
Video Data Compression by Progressive Iterative Approximation
In the present paper, the B-spline curve is used for reducing the entropy of video data. We consider the color or luminance variations of a spatial position in a series of frames as input data points in Euclidean space R or R3. The progressive and iterative approximation (PIA) method is a direct and intuitive way of generating curve series of high and higher fitting accuracy. The video data points are approximated using progressive and iterative approximation for least square (LSPIA) fitting. The Lossless video data compression is done through storing the B-spline curve control points (CPs) and the difference between fitted and original video data. The proposed method is applied to two classes of synthetically produced and naturally recorded video sequences and makes a reduction in the entropy of both. However, this reduction is higher for syntactically created than those naturally produced. The comparative analysis of experiments on a variety of video sequences suggests that the entropy of output video data is much less than that of input video data
Preconditioned geometric iterative methods for cubic B-spline interpolation curves
The geometric iterative method (GIM) is widely used in data
interpolation/fitting, but its slow convergence affects the computational
efficiency. Recently, much work was done to guarantee the acceleration of GIM
in the literature. In this work, we aim to further accelerate the rate of
convergence by introducing a preconditioning technique. After constructing the
preconditioner, we preprocess the progressive iterative approximation (PIA) and
its variants, called the preconditioned GIMs. We show that the proposed
preconditioned GIMs converge and the extra computation cost brought by the
preconditioning technique is negligible. Several numerical experiments are
given to demonstrate that our preconditioner can accelerate the convergence
rate of PIA and its variants
Fairing-PIA: Progressive iterative approximation for fairing curve and surface generation
The fairing curves and surfaces are used extensively in geometric design,
modeling, and industrial manufacturing. However, the majority of conventional
fairing approaches, which lack sufficient parameters to improve fairness, are
based on energy minimization problems. In this study, we develop a novel
progressive-iterative approximation method for fairing curve and surface
generation (fairing-PIA). Fairing-PIA is an iteration method that can generate
a series of curves (surfaces) by adjusting the control points of B-spline
curves (surfaces). In fairing-PIA, each control point is endowed with an
individual weight. Thus, the fairing-PIA has many parameters to optimize the
shapes of curves and surfaces. Not only a fairing curve (surface) can be
generated globally through fairing-PIA, but also the curve (surface) can be
improved locally. Moreover, we prove the convergence of the developed
fairing-PIA and show that the conventional energy minimization fairing model is
a special case of fairing-PIA. Finally, numerical examples indicate that the
proposed method is effective and efficient.Comment: 21 pages, 10 figure
A sketch-and-project method for solving the matrix equation AXB = C
In this paper, based on an optimization problem, a sketch-and-project method
for solving the linear matrix equation AXB = C is proposed. We provide a
thorough convergence analysis for the new method and derive a lower bound on
the convergence rate and some convergence conditions including the case that
the coefficient matrix is rank deficient. By varying three parameters in the
new method and convergence theorems, the new method recovers an array of
well-known algorithms and their convergence results. Meanwhile, with the use of
Gaussian sampling, we can obtain the Gaussian global randomized Kaczmarz
(GaussGRK) method which shows some advantages in solving the matrix equation
AXB = C. Finally, numerical experiments are given to illustrate the
effectiveness of recovered methods.Comment: arXiv admin note: text overlap with arXiv:1506.03296,
arXiv:1612.06013, arXiv:2204.13920 by other author
Interpolatory Catmull-Clark volumetric subdivision over unstructured hexahedral meshes for modeling and simulation applications
International audienceVolumetric modeling is an important topic for material modeling and isogeometric simulation. In this paper, two kinds of interpolatory Catmull-Clark volumetric subdivision approaches over unstructured hexahedral meshes are proposed based on the limit point formula of Catmull-Clark subdivision volume. The basic idea of the first method is to construct a new control lattice, whose limit volume by the CatmullClark subdivision scheme interpolates vertices of the original hexahedral mesh. The new control lattice is derived by the local push-back operation from one CatmullClark subdivision step with modified geometric rules. This interpolating method is simple and efficient, and several shape parameters are involved in adjusting the shape of the limit volume. The second method is based on progressive-iterative approximation using limit point formula. At each iteration step, we progressively modify vertices of an original hexahedral mesh to generate a new control lattice whose limit volume interpolates all vertices in the original hexahedral mesh. The convergence proof of the iterative process is also given. The interpolatory subdivision volume has C 2-smoothness at the regular region except around extraordinary vertices and edges. Furthermore, the proposed interpolatory volumetric subdivision methods can be used not only for geometry interpolation, but also for material attribute interpolation in the field of volumetric material modeling. The application of the proposed volumetric subdivision approaches on isogeometric analysis is also given with several examples