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Adaptive wavelets and their applications to image fusion and compression

Piella, G.

Publication date

2003

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Citation for published version (APA):

Piella, G. (2003). Adaptive wavelets and their applications to image fusion and compression.

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Chapter 9

Conclusions

In this thesis we have described a framework for multiresolution processing of signals and images. One of our main contributions is the development of non-redundant adaptive wavelets with perfect reconstruction. Another important contribution is the description of an axiomatic-setup for multiresolution-based fusion. Within this formalism, we have developed a new region-based image fusion approach. Finally, we have introduced a quality measure for image fusion to assess the performance of the various fusion algorithms.

T h e results obtained in this thesis have been discussed at length in the various chapters. In the following, we summarize the main results and conclusions.

In Chapter 2, we have presented an axiomatic multiresolution decomposition scheme with perfect reconstruction. Many multiresolution signal decomposition schemes proposed in the literature are special cases of the general schemes discussed here. T h e lifting scheme, usually restricted to wavelet decompositions, has been extended. In particular, it has been shown how lifting can be used in the context of pyramid decompositions.

In Chapters 3-5, we have introduced an adaptive wavelet decomposition based on an adap-tive update lifting step. T h e underlying idea is to choose the update lifting filters according to some decision criterion which depends on local characteristics of the signal. An important feature of our adaptive wavelet decomposition scheme is that it is neither causal nor requires any bookkeeping in order to perform perfect reconstruction.

T h e particular case where the system can choose between two different update filters based on the local gradient has been thoroughly discussed. In Sections 4.1-4.3, we have derived necessary and sufficient conditions for the invertibility of such adaptive schemes for various scenarios. Several simulation results have been given to show the differences between our adaptive decompositions and the non-adaptive decompositions based on a fixed lifting scheme. These examples illustrate the potential of adaptive schemes for preserving the discontinuities in signals and images even at low resolutions. Furthermore, it has been shown in Section 5.4 that adaptive schemes often yield decompositions that have lower entropies than schemes with fixed update filters, a property that is highly relevant in the context of compression. In Section 5.5, we have analyzed the quantization effects on our adaptive scheme. In fact, we have been able'

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184 Chapter 9. Conclusions

to derive conditions that guarantee perfect reconstruction of the decision map (i.e., the choice of t h e u p d a t e filters).

Despite all these attractive properties, a number of open theoretical and practical questions need to be addressed before such schemes become useful in signal processing and analysis applications. For example, we need to get a better understanding how to design update and prediction operators t h a t lead to adaptive wavelet decompositions t h a t satisfy properties key to a given application at hand. In this thesis, we have focused on binary decision maps and as a result, the adaptive scheme can only discriminate between two 'geometric events' (e.g.. edge region or homogeneous region). In order to deal with the great richness of real-world signals and images, one must be able to incorporate the geometrical structure of the signals, for example, by using multiple criteria.

Another issue t h a t needs to be addressed is the stability of the scheme. In particular, the behavior of the adaptive scheme under quantization needs a more thorough investigation. Sta-bility of decompositions is of utmost importance when they are being used in lossy compression schemes for image or video coding.

In order to evaluate the potential of our adaptive schemes in applications such as com-pression, it will be necessary to make a systematic comparison with existing decompositions schemes (such as the ones described in Section 3.1).

Another future research effort will be the extension of the current framework to adaptive prediction lifting steps. Moreover, it would be worthwhile to see if our adaptive scheme can be extended to include also morphological filters.

Chapters 6-8 have been devoted to image fusion. We have introduced an axiomatic frame-work for niultiresolution image fusion. T h e proposed frameframe-work not only encompasses most of the existing multiresolution image fusion schemes, but also allows the construction of new-ones, both pixel and region-based.

T h e region-based fusion scheme presented in Chapter 7 is an extension of the classical pixel-based schemes. T h e basic idea is to perform a nmltiresolution/multisource segmentation of the various input images in order to guide the fusion process. For this purpose, we developed a mul-tiresolution/multisource .segmentation method based on pyramid linking and suggested some combination algorithms which make use of the resulting segmentation. Several experimental results have been shown.

T h e implementation of our region-based fusion approach is still in a preliminary stage and in the experiments performed we did not attempt to optimize its performance. However. the results obtained so far suggest that our approach may be useful for several image fusion applications. We need to investigate this more thoroughly in the future. In particular, we plan to study the effect of the different parameters and functions in the scheme on the final fusion process. We also intend to design new combination algorithms and replace the current segmentation by pyramid linking by some other techniques, such as hierarchical watersheds from mathematical morphology.

A substantial part of our efforts will be devoted to the optimization and extension of the objective measures for image fusion described in Chapter 8. We intend to use such objective measures to evaluate and demonstrate the capacities of our region-based fusion approach, as

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185

well as to compare its performance with other multiresolution fusion schemes. We also plan to explore how these objective measures can be used to guide fusion and improve fusion perfor-mance.

Finally, another interesting research area concerns the development of adaptive fusion tech-niques in which the source images determine the type of multiresolution transform being used as well as the parameters t h a t are involved.

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