Henk J. A. M. Heijmans

A new quality metric for image fusion

We present three variants of a new quality metric for image fusion. The interest of our metrics, which are based on an image quality index recently introduced by Wang and Bovik in [Z. Wang et al., March 2002], lies in the fact that they do not require a ground-truth or reference image. We perform several simulations which show that our metrics are compliant with subjective evaluations and can therefore be used to compare different image fusion methods or to find the best parameters for a given fusion algorithm.

Nonlinear multiresolution signal decomposition schemes. II. Morphological wavelets

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 paper presents a general theory for constructing linear as well as nonlinear pyramid decomposition schemes for signal analysis and synthesis. The proposed theory is based on the following ingredients: 1) the pyramid consists of a (finite or infinite) number of levels such that the information content decreases toward higher levels and 2) each step toward a higher level is implemented by an (information-reducing) analysis operator, whereas each step toward a lower level is implemented 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. Several examples of pyramid decomposition schemes are shown to be instances of the proposed theory: a particular class of linear pyramids, morphological skeleton decompositions, the morphological Haar pyramid, median pyramids, etc. Furthermore, the paper makes a distinction between single-scale and multiscale decomposition schemes, i.e., schemes without or with sample reduction. Finally, the proposed theory provides the foundation of a general approach to constructing nonlinear wavelet decomposition schemes and filter banks.

Theoretical aspects of gray-level morphology

After a brief discussion of the extension of mathematical morphology to complete lattices, the space of gray-level functions is considered and the concept of a threshold set is introduced. It is shown how one can use binary morphological operators and thresholding techniques to build a large class of gray-level morphological operators. Particular attention is given to the class of so-called flat operators, i.e. operators which commute with thresholding. It is also shown how to define dilations and erosions with nonflat structuring elements if the gray-level set is finite. It is reported that mere truncation yields wrong results. >

Grey-Scale Morphology Based on Fuzzy Logic

There exist several methods to extend binary morphology to grey-scale images. One of these methods is based on fuzzy logic and fuzzy set theory. Another approach starts from the complete lattice framework for morphology and the theory of adjunctions. In this paper, both approaches are combined. The basic idea is to use (fuzzy) conjunctions and implications which are adjoint in the definition of dilations and erosions, respectively. This gives rise to a large class of morphological operators for grey-scale images. It turns out that this class includes the often used grey-scale Minkowski addition and subtraction.

Path Openings and Closings

This paper lays the theoretical foundations to path openings and closings.The traditional morphological filter used for the analysis of linear structures in images is the union of openings (or the intersection of closings) by linear segments. However structures in images are rarely strictly straight, and as a result a more flexible approach is needed.An extension to the idea of using straight line segments as structuring elements is to use constrained paths, i.e. discrete, one-pixel thick successions of pixels oriented in a particular direction, but in general forming curved lines rather than perfectly straight lines. However the number of such paths is prohibitive and the resulting algorithm by simple composition is inefficient.In this paper we propose a way to compute openings and closings over large numbers of constrained, oriented paths in an efficient manner, suitable for building filters with applications to the analysis of oriented features, such as for example texture.

Adaptive update lifting with a decision rule based on derivative filters

This letter treats a class of adaptive update-lifting schemes that do not require bookkeeping for perfect reconstruction. The choice of the update-lifting filter is triggered by a binary threshold criterion based on a generalized gradient that is chosen in such a way that it only smooths homogeneous regions. This criterion can be chosen so that it ignores portions of a signal that are polynomial up to a given order. The update-lifting filter modifies the signal in these polynomial regions but leaves other portions unaffected.

Composing morphological filters

A morphological filter is an operator on a complete lattice that is increasing and idempotent. Two well-known classes of morphological filters are openings and closings. Furthermore, an interesting class of filters, the alternating sequential filters, is obtained if one composes openings and closings. This paper explains how to construct morphological filters, and derived notions such as overfilters, underfilters, inf-overfilters, and sup-underfilters by composition, the main ingredients being dilations, erosions, openings, and closings. The class of alternating sequential filters is extended by composing overfilters and underfilters. Finally, it is shown that any composition consisting of an equal number of dilations and erosions from an adjunction is a filter. The abstract approach is illustrated with some experimental results.

Fundamenta morphologicae mathematicae

Mathematical morphology is a geometric approach in image processing and analysis with a strong mathematical flavor. Originally, it was developed as a powerful tool for shape analysis in binary and, later, grey-scale images. But it was soon recognized that the underlying ideas could be extended naturally to a much wider class of mathematical objects, namely complete lattices. This paper presents, in a birds eye view, the foundations of mathematical morphology, or more precisely, the theory of morphological operators on complete lattices.

Similarity and symmetry measures for convex shapes using Minkowski addition

This paper is devoted to similarity and symmetry measures for convex shapes whose definition is based on Minkowski addition and the Brunn-Minkowski inequality. This means, in particular, that these measures are region-based, in contrast to most of the literature, where one considers contour-based measures. All measures considered in this paper are invariant under translations; furthermore, they can be chosen to be invariant under rotations, multiplications, reflections, or the class of affine transformations. It is shown that the mixed volume of a convex polygon and a rotation of another convex polygon over an angle /spl theta/ is a piecewise concave function of /spl theta/. This and other results of a similar nature form the basis for the development of efficient algorithms for the computation of the given measures. Various results obtained in this paper are illustrated by experimental data. Although the paper deals exclusively with the two-dimensional case, many of the theoretical results carry over almost directly to higher-dimensional spaces.

Motion compensation and scalability in lifting-based video coding

Abstract Motion-compensated temporal filtering subband video codecs have attracted recently a lot of attention, due to their compression performance comparable with that of state-of-the-art hybrid codecs and due to their additional scalability features. In this paper, we present a scalable video codec based on a 5/3 adaptive temporal lifting decomposition. Different adaptation criteria for coping with the occluded areas are discussed and new criteria for optimizing the temporal prediction are introduced. For our simulations, we use a memory-constraint “on-the-fly” implementation. We also evaluate the temporal scalability properties of this video coding structure.