A Statistical Approach to Feature Detection and Scale Selection in Images
Eine Statistische Methode zur Merkmalsextraktion und Skalenselektion in Bildern.
by Peter Majer
Date of Examination:2000-07-07
Date of issue:2000-12-13
Advisor:Prof. Dr. Walter Zucchini
Referee:Prof. Dr. Walter Zucchini
Referee:Prof. Dr. Tony Lindeberg
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EnglishIn computer vision "feature detection" refers to some procedure that determines candidate positions at which a particular feature, e.g. an edge or a line, could be located. "Scale selection" aims to find the scale or size of the feature of interest. Applied together, feature detection and scale selection allow to determine for example both the position and the width of linelike structures such as blood vessels in medical images. A method for automatic scale selection was proposed in 1993 by Lindeberg. This method requires choosing a parameter called the gamma-parameter. How to choose the gamma-parameter and why to do scale selection according to Lindebergs proposal are the main question addressed by this thesis. A statistical approach is described that defines any "particularly informative parameters" of an operator response, be they positions, scales or other, in conceptually the same way. The idea is to evaluate an operator response relative to the response of the same operator to random images that contain by construction or definition less structural information than the observed image. From this point of view different choices of gamma parameter in Lindebergs method for scale selection correspond to different distributions of random images relative to which the operator response is evaluated. The detection of linelike structures, ridges, is considered in detail and serves to illustrate the implications of the choice of gamma parameter. It is demonstrated that a suitable choice of gamma allows a second derivative of Gaussian operator to detect ridges and "escape" edges. At fixed scales this detector frequently produces false responses to edges. At variable scales, however, edges are not detected if gamma is chosen greater than the critical gamma value of an edge, gamma=1. Some examples of ridges computed with this second derivative of Gaussian detector and scale selection are shown and the algorithms used for the computation are described. Another contribution of the thesis is concerned with "local entropies" and a monotonicity property of local entropies in scale-space. This property captures in a mathematically rigorous way the intuitive idea that smoothing simplifies images both globally and, more importantly, also locally.
Schlagwörter: computer vision; machine vision; image analysis; image processing; scale-space; scale selection; feature detection; ridge detection; local entropy