Generalized structure tensor: Difference between revisions

Revision as of 20:56, 4 January 2016

Revision as of 21:05, 4 January 2016

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==Basic concept for its use==

Efficient detection of <math>\theta</math> in images is possible by image processing, if the pair <math>\xi</math>, <math>\eta</math> is given. Complex convolutions (or the corresponding matrix operations) and point-wise non-linear mappings are the basic computational elements of GST implementations. A total least square error estimation of <math>2\theta</math> is then obtained, along with the two errors, <math>\lambda_{max}</math> and <math>\lambda_{min}</math>, in analogy with the Cartesian [[Structure tensor]]. The estimated <math>2\theta</math> can be used as a shape feature whereas <math>\lambda_{max}-\lambda_{min}</math> alone or in combination with

<math>\lambda_{max}+\lambda_{min}</math> can be used as a quality (confidence, certainty) measure ()for the estimation.

Logarithmic spirals, including circles, can for instance be detected by (complex) convolutions and non-linear mappings.<ref name=bigun04pami3 /> The spirals can be in gray (valued) images or in a binary image, i.e. locations of edge elements of the concerned patterns, such as contours of circles or spirals, must not be known or marked otherwise.

Generalized structure tensor can be used as an alternative to [[Hough transform]] in [[image processing]] and [[computer vision]] to detect patterns whose local orientations can be modelled, for example junction points. The main differences comprise: