2004
DOI: 10.1109/tpami.2004.126
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Recognition by symmetry derivatives and the generalized structure tensor

Abstract: Abstract-We suggest a set of complex differential operators that can be used to produce and filter dense orientation (tensor) fields for feature extraction, matching, and pattern recognition. We present results on the invariance properties of these operators, that we call symmetry derivatives. These show that, in contrast to ordinary derivatives, all orders of symmetry derivatives of Gaussians yield a remarkable invariance: They are obtained by replacing the original differential polynomial with the same polyn… Show more

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Cited by 120 publications
(91 citation statements)
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“…Symmetry features enable the description of symmetric patterns such as lines, circles, parabolas, and so on ( Figure 1). Symmetry features are extracted via symmetry filters, Equation 1, which output how much of a certain symmetry exist in a local image neighborhood [12,13]. …”
Section: Eye Localizationmentioning
confidence: 99%
“…Symmetry features enable the description of symmetric patterns such as lines, circles, parabolas, and so on ( Figure 1). Symmetry features are extracted via symmetry filters, Equation 1, which output how much of a certain symmetry exist in a local image neighborhood [12,13]. …”
Section: Eye Localizationmentioning
confidence: 99%
“…Instead, normal orientations are required to compute structure. Following the approach in [2], such orientations can be extracted from tensors R computed as:…”
Section: Tensor-valued Imagesmentioning
confidence: 99%
“…A related approach based on quadrature filters has been proposed in [19,12]. Furthermore, extensions using higher-order derivatives [9,21], and extensions for curved structures [2] have also been proposed. Despite its popularity, the structure tensor also has important shortcomings, such as detection of features in flat regions, loss of small features, detection of false corners, and misplacement of corners.…”
Section: Introductionmentioning
confidence: 99%
“…Bigun et al [5] use a structure tensor to represent and detect more intricate patterns than straight lines and edges to produce and filter dense orientation fields for feature extraction, matching, and pattern recognition.…”
Section: Related Workmentioning
confidence: 99%