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Title: Extensions of the hit-or-miss transform for feature detection in noisy images and a novel design tool for estimating its parameters
Author: Murray, Paul
Awarding Body: University of Strathclyde
Current Institution: University of Strathclyde
Date of Award: 2012
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The work presented in this thesis focuses on extending a transform from Mathematical Morphology, known as the Hit-or-Miss transform (HMT), in order to make it more robust for detecting features of interest in the presence of noise in digital images. The extension that is described here requires that a single parameter is determined for correct functionality. A novel design tool which allows this parameter to be accurately estimated is proposed as part of this work. An efficient method for computing the extended transform is also presented. The HMT is a well known morphological transform that is capable of identifying features in digital images. When image features contain noise, texture or some other distortion, the HMT may fail. Various researchers have extended the HMT in different ways to make it more robust to noise. The most successful, and most recent extensions of the HMT for noise robustness, use rank order operators in place of standard morphological erosions and dilations. A major issue with most of these methods is that no technique is provided for calculating the parameters that are introduced to generalise the HMT, and, in most cases, these parameters are determined empirically. In this thesis, a new conceptual interpretation of the HMT is presented which uses percentage occupancy (PO) functions to implement the erosion and dilation operators of the HMT. When implemented in this way, the strictness of these PO functions can easily be relaxed in order to allow slacker fitting of the structuring elements. Relaxing the strict conditions of the transform is shown to improve the performance of the routine when processing noisy data. This thesis also introduces a novel design tool which is derived directly from the operators that are used to implement the aforementioned PO functions. This design tool can be used to determine a suitable value for the only parameter in the proposed extension of the HMT. Further, it can be used to estimate parameters for other generalisations of the HMT that have been described in the literature in order to improve their noise robustness. The power of the proposed technique is demonstrated and tested using sets of very noisy images. Further, a number of comparisons are performed in order to validate the method that is introduced in this work when compared with the most recent extensions of the HMT. One drawback with this method is that a direct implementation of the technique is computationally expensive. However, it is possible to implement the proposed method using rank-order filters in place of the percentage occupancy functions. Rank order filters are used in a multitude of image processing tasks. Their application can range from simple pre-processing tasks which aim to reduce/remove noise, to more complex problems where such filters can be used in combination to detect and segment image features. There is, therefore, a need to develop fast algorithms to compute the output of this class of filter in general. A number of methods for efficiently computing the output of specific rank order filters have been presented over the years. For example, numerous fast algorithms exist that can be used for calculating the output of the median filter. Fast algorithms for calculating morphological erosions and dilations - which, like the median filter, are a special case of the more general rank order filter - have also been proposed. In this thesis, these techniques are extended and combined such that it is possible to efficiently compute any rank, using any arbitrarily shaped window, making it possible to quickly compute the output of any rank order filter. The fast algorithm which is described is compared to an optimised technique for computing the output of this class of filter, and significant gains in speed are demonstrated when using the proposed technique. Further, it is shown that this efficient filtering algorithm can be used to produce an extremely fast implementation of the generalised HMT that is described in this work. The fast generalised HMT is compared with a number of other extensions and generalisations of the HMT that have been proposed in the literature over the years.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available