Multiresolution signal decomposition schemes

[PNA-R9810] Interest in multiresolution techniques for signal processing and analysis is increasing steadily. An important instance of such a technique is the so-called pyramid decomposition scheme. This report proposes a general axiomatic pyramid decomposition scheme for signal analysis and synthesis. This scheme comprises the following ingredients: (i) the pyramid consists of a (finite or infinite) number of levels such that the information content decreases towards higher levels; (ii) each step towards a higher level is constituted by an (information-reducing) analysis operator, whereas each step towards a lower level is modeled by an (information-preserving) synthesis operator. One basic assumption is necessary: synthesis followed by analysis yields the identity operator, meaning that no information is lost by these two consecutive steps. In this report, several examples are described of linear as well as nonlinear (e.g., morphological) pyramid decomposition schemes. Some of these examples are known from the literature (Laplacian pyramid, morphological granulometries, skeleton decomposition) and some of them are new (morphological Haar pyramid, median pyramid). Furthermore, the report makes a distinction between single-scale and multiscale decomposition schemes (i.e. without or with sample reduction).#[PNA-R9905] In its original form, the wavelet transform is a linear tool. However, it has been increasingly recognized that nonlinear extensions are possible. A major impulse to the development of nonlinea

Fusion of MultiSpectral and Panchromatic Images Based on Morphological Operators

International audienceNonlinear decomposition schemes constitute an alternative to classical approaches for facing the problem of data fusion. In this paper we discuss the application of this methodology to a popular remote sensing application called pansharpening, which consists in the fusion of a low resolution multispectral image and a high resolution panchromatic image. We design a complete pansharpening scheme based on the use of morphological half gradients operators and demonstrate the suitability of this algorithm through the comparison with state of the art approaches. Four datasets acquired by the Pleiades, Worldview-2, Ikonos and Geoeye-1 satellites are employed for the performance assessment, testifying the effectiveness of the proposed approach in producing top-class images with a setting independent of the specific sensor

Multiresolution signal decomposition schemes. Part 2: Morphological wavelets

In its original form, the wavelet transform is a linear tool. However, it has been increasingly recognized that nonlinear extensions are possible. A major impulse to the development of nonlinear wavelet transforms has been given by the introduction of the lifting scheme by Sweldens. The aim of this report, which is a sequel to a previous report devoted exclusively to the pyramid transform, is to present an axiomatic framework encompassing most existing linear and nonlinear wavelet decompositions. Furthermore, it introduces some, thus far unknown, wavelets based on mathematical morphology, such as the morphological Haar wavelet, both in one and two dimensions. A general and flexible approach for the construction of nonlinear (morphological) wavelets is provided by the lifting scheme. This paper discusses one example in considerable detail, the max-lifting scheme, which has the intriguing property that it preserves local maxima in a signal over a range of scales, depending on how local or global these maxima are

The Multigrid Image Transform

A second order partial differential operator is applied to an image function. To this end we consider both the Laplacian and a more general elliptic operator. By using a multigrid operator known from the so-called approximation property, we derive a multiresolution decomposition of the image without blurring of edges at coarser levels. We investigate both a linear and a nonlinear variant and compare to some established methods

Flat zones filtering, connected operators, and filters by reconstruction

This correspondence deals with the notion of connected operators. Starting from the definition for operator acting on sets, it is shown how to extend it to operators acting on function. Typically, a connected operator acting on a function is a transformation that enlarges the partition of the space created by the flat zones of the functions. It is shown that from any connected operator acting on sets, one can construct a connected operator for functions (however, it is not the unique way of generating connected operators for functions). Moreover, the concept of pyramid is introduced in a formal way. It is shown that, if a pyramid is based on connected operators, the flat zones of the functions increase with the level of the pyramid. In other words, the flat zones are nested. Filters by reconstruction are defined and their main properties are presented. Finally, some examples of application of connected operators and use of flat zones are described.Peer ReviewedPostprint (published version

A matlab toolbox for image fusion (MATIFUS).

The MATIFUS toolbox is presented. It is a collection of functions and furnished with a graphical user interface that supports a range of image fusion operations. Almost all of the toolbox functions are written in the MATLAB language. Implementations of multiresolution schemes are used that are either publicly available or can be purchased as licensed software. MATIFUS can be downloaded from a website and is available under the conditions of an agreement with the Dutch Technology Foundation ST