The multiresolution Fourier transform : a general purpose tool for image analysis
Calway, Andrew David (1989) The multiresolution Fourier transform : a general purpose tool for image analysis. PhD thesis, University of Warwick.
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The extraction of meaningful features from an image forms an important area of image
analysis. It enables the task of understanding visual information to be implemented in a
coherent and well defined manner. However, although many of the traditional approaches to
feature extraction have proved to be successful in specific areas, recent work has suggested
that they do not provide sufficient generality when dealing with complex analysis problems
such as those presented by natural images.
This thesis considers the problem of deriving an image description which could form the basis
of a more general approach to feature extraction. It is argued that an essential property of such
a description is that it should have locality in both the spatial domain and in some
classification space over a range of scales. Using the 2-d Fourier domain as a classification
space, a number of image transforms that might provide the required description are investigated.
These include combined representations such as a 2-d version of the short-time Fourier
transform (STFT), and multiscale or pyramid representations such as the wavelet transform.
However, it is shown that these are limited in their ability to provide sufficient locality in both
domains and as such do not fulfill the requirement for generality.
To overcome this limitation, an alternative approach is proposed in the form of the multiresolution
Fourier transform (MFT). This has a hierarchical structure in which the outermost levels
are the image and its discrete Fourier transform (DFT), whilst the intermediate levels are
combined representations in space and spatial frequency. These levels are defined to be
optimal in terms of locality and their resolution is such that within the transform as a whole
there is a uniform variation in resolution between the spatial domain and the spatial frequency
domain. This ensures that locality is provided in both domains over a range of scales. The
MFT is also invertible and amenable to efficient computation via familiar signal processing
techniques. Examples and experiments illustrating its properties are presented.
The problem of extracting local image features such as lines and edges is then considered. A
multiresolution image model based on these features is defined and it is shown that the MET
provides an effective tool for estimating its parameters.. The model is also suitable for
representing curves and a curve extraction algorithm is described. The results presented for
synthetic and natural images compare favourably with existing methods. Furthermore, when
coupled with the previous work in this area, they demonstrate that the MFT has the potential
to provide a basis for the solution of general image analysis problems.
|Item Type:||Thesis or Dissertation (PhD)|
|Subjects:||T Technology > TA Engineering (General). Civil engineering (General)|
|Library of Congress Subject Headings (LCSH):||Image analysis, Fourier transformations|
|Official Date:||September 1989|
|Institution:||University of Warwick|
|Theses Department:||Department of Computer Science|
|Supervisor(s)/Advisor:||Wilson, Roland, 1949-|
|Sponsors:||Science and Engineering Research Council (Great Britain) (SERC)|
|Extent:||, 196 p.|
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