3,949 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
Randomized progressive iterative approximation for B-spline curve and surface fittings
For large-scale data fitting, the least-squares progressive iterative
approximation is a widely used method in many applied domains because of its
intuitive geometric meaning and efficiency. In this work, we present a
randomized progressive iterative approximation (RPIA) for the B-spline curve
and surface fittings. In each iteration, RPIA locally adjusts the control
points according to a random criterion of index selections. The difference for
each control point is computed concerning the randomized block coordinate
descent method. From geometric and algebraic aspects, the illustrations of RPIA
are provided. We prove that RPIA constructs a series of fitting curves (resp.,
surfaces), whose limit curve (resp., surface) can converge in expectation to
the least-squares fitting result of the given data points. Numerical
experiments are given to confirm our results and show the benefits of RPIA
Statistical extraction of process zones and representative subspaces in fracture of random composite
We propose to identify process zones in heterogeneous materials by tailored
statistical tools. The process zone is redefined as the part of the structure
where the random process cannot be correctly approximated in a low-dimensional
deterministic space. Such a low-dimensional space is obtained by a spectral
analysis performed on pre-computed solution samples. A greedy algorithm is
proposed to identify both process zone and low-dimensional representative
subspace for the solution in the complementary region. In addition to the
novelty of the tools proposed in this paper for the analysis of localised
phenomena, we show that the reduced space generated by the method is a valid
basis for the construction of a reduced order model.Comment: Submitted for publication in International Journal for Multiscale
Computational Engineerin
A partitioned model order reduction approach to rationalise computational expenses in multiscale fracture mechanics
We propose in this paper an adaptive reduced order modelling technique based
on domain partitioning for parametric problems of fracture. We show that
coupling domain decomposition and projection-based model order reduction
permits to focus the numerical effort where it is most needed: around the zones
where damage propagates. No \textit{a priori} knowledge of the damage pattern
is required, the extraction of the corresponding spatial regions being based
solely on algebra. The efficiency of the proposed approach is demonstrated
numerically with an example relevant to engineering fracture.Comment: Submitted for publication in CMAM
- …