This paper introduces a new way of extracting affine invariant features from image functions. The presented approach is based on combining affine moment invariants (AMI) with multiscale invariants, in particular multiscale autoconvolution (MSA) and spatial multiscale affine invariants (SMA). Our approach includes all of these invariants as special cases, but also makes it possible to construct ...

The multiscale autoregressive (MAR) framework was introduced in the last decade to process signals that exhibit multiscale features. It provides the method for identifying the multiscale structure in signals and a filtering procedure, and thus is an efficient way to solve the optimal estimation problem for many high-dimensional dynamic systems. Later, an ensemble version of this multiscale filt...

A recently developed multiresolution estimation framework offers the possibility of highly efficient statistical analysis, interpolation, and smoothing of extremely large data sets in a multiscale fashion. This framework enjoys a number of advantages not shared by other statistically-based methods, particularly in terms of the ability to evaluate estimates and error variances in a computational...

In this paper, we present the Multiscale Finite Element Method (MsFEM) for problems on rough heterogeneous surfaces. We consider the diffusion equation on oscillatory surfaces. Our objective is to represent small-scale features of the solution via multiscale basis functions described on a coarse grid. This problem arises in many applications where processes occur on surfaces or thin layers. We ...

In this thesis, we develop image processing algorithms and applications for a particular class of multiscale stochastic models. First, we provide background on the model class, including a discussion of its relationship to wavelet transforms and the details of a two-sweep algorithm for estimation. A multiscale model for the error process associated with this algorithm is derived. Next, we illus...

A fast, recently developed, multiscale optimal interpolation algorithm has been adapted to the mapping of hydrographic and other oceanographi c data. This algorithm produces solution and error estimates which are consistent with those obtained from exact least squares methods, but at a small fraction of the computational cost. Problems whose solution would be completely impractical using exact ...

MOTIVATIONS Physiological systems are ruled by mechanisms operating across multiple temporal scales. A recently proposed approach, multiscale entropy analysis, measures the complexity at different time scales and has been successfully applied to long term electrocardiographic recordings. The purpose of this work is to show the applicability of this methodology, rooted on statistical physics ide...

We present multiscale description of hydrodynamic turbulence in incompressible fluid based on continuous wavelet transform. The wavelet transform of the velocity field is taken in L 1 norm, so that the wavelet coefficients u l (x) have the meaning of the velocity fluctuations of scale l. An extra contribution to the energy transfer from large to smaller scales is derived. It is shown that the K...

A new methodology for the simulation of multiscale processes, called Macro-Micro Interlocked (MMI) Simulation, is introduced. The MMI simulation is carried out by the two-way connection of different numerical models, which may handle macroscopic and microscopic dynamics, respectively. The MMI simulation are applied to several multiscale phenomena, for instance, cloud formation, gas detonation, ...

The multiscale techniques for edge detection aim to combine the advantages of small and large scale methods, usually by blending their results. In this work we introduce a method for the multiscale extension of the Gravitational Edge Detector based on a t-norm T . We smoothen the image with a Gaussian filter at different scales then perform inter-scale edge tracking. Results are included illust...