© 2014

Geometrical Multiresolution Adaptive Transforms

Theory and Applications


Part of the Studies in Computational Intelligence book series (SCI, volume 545)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Agnieszka Lisowska
    Pages 1-12
  3. Multismoothlet Transform

    1. Front Matter
      Pages 13-13
    2. Agnieszka Lisowska
      Pages 15-26
    3. Agnieszka Lisowska
      Pages 27-38
    4. Agnieszka Lisowska
      Pages 39-50
  4. Applications

    1. Front Matter
      Pages 51-51
    2. Agnieszka Lisowska
      Pages 53-66
    3. Agnieszka Lisowska
      Pages 67-82
    4. Agnieszka Lisowska
      Pages 83-95
    5. Agnieszka Lisowska
      Pages 97-100
  5. Back Matter
    Pages 101-107

About this book


Modern image processing techniques are based on multiresolution geometrical methods of image representation. These methods are efficient in sparse approximation of digital images. There is a wide family of functions called simply ‘X-lets’, and these methods can be divided into two groups: the adaptive and the nonadaptive. This book is devoted to the adaptive methods of image approximation, especially to multismoothlets.

Besides multismoothlets, several other new ideas are also covered. Current literature considers the black and white images with smooth horizon function as the model for sparse approximation but here, the class of blurred multihorizon is introduced, which is then used in the approximation of images with multiedges. Additionally, the semi-anisotropic model of multiedge representation, the introduction of the shift invariant multismoothlet transform and sliding multismoothlets are also covered.

Geometrical Multiresolution Adaptive Transforms should be accessible to both mathematicians and computer scientists. It is suitable as a professional reference for students, researchers and engineers, containing many open problems and will be an excellent starting point for those who are beginning new research in the area or who want to use geometrical multiresolution adaptive methods in image processing, analysis or compression.


Edge Detection Geometrical Methods Image Compression Image Denoising Multiresolution Multismoothlets Smoothlets Sparse Representation Wedgelets

Authors and affiliations

  1. 1.University of Silesia Institute of Computer ScienceKatowicePoland

About the authors

Agnieszka Lisowska is an assistant professor at the Institute of Computer Science, University of Silesia, where in 2006 she obtained her PhD with distinctions in the area of geometrical wavelets in Computer Science. In 2001 she completed her MSc in Mathematics at the same university. Her scientific research is concentrated on sparse representations and geometrical multiresolution methods of image processing. She invented smoothlets and multismoothlets, and the fast methods of their computations. She is the author of several journal and conference papers published among others by Springer, Elsevier or IEEE.

Bibliographic information

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From the book reviews:

“The book is divided into two parts. The first part is devoted to the theory of multismoothlets. … The second part of the book is devoted to applications of the presented transforms. … The author gives many examples presenting the notations and problems considered, so it makes the learning easier. It is suitable for students, researchers and engineers interested in multiresolution representation of images and its applications.” (Krzystof Gdawiec, zbMATH, Vol. 1297, 2014)