Adaptive Structure Tensors and their Applications

Brox, Thomas; Boomgaard, R. van den; Lauze, François; Weijer, Joost van de; Weickert, Joachim; Mrázek, Pavel; Kornprobst, Pierre

doi:10.1007/3-540-31272-2_2

Cited by 76 publications

(48 citation statements)

References 35 publications

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“…Analysing the differences and understanding the relations between such adaptive filters, robust estimation and nonlinear diffusion methods is a topic of current research; see e.g. [32] for the scalar case and [9] for the tensor case. Our article comprises and extends earlier work presented at conferences [50,10].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear structure tensors

Brox

Weickert

Burgeth

et al. 2006

Image and Vision Computing

Self Cite

219

139

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In this article we introduce nonlinear versions of the popular structure tensor, also known as second moment matrix. These nonlinear structure tensors replace the Gaussian smoothing of the classical structure tensor by discontinuity-preserving nonlinear diffusions. While nonlinear diffusion is a well-established tool for scalar and vectorvalued data, it has not often been used for tensor images so far. Two types of nonlinear diffusion processes for tensor data are studied: an isotropic one with a scalar-valued diffusivity, and its anisotropic counterpart with a diffusion tensor. We prove that these schemes preserve the positive semidefiniteness of a matrix field and are therefore appropriate for smoothing structure tensor fields. The use of diffusivity functions of total variation (TV) type allows us to construct nonlinear structure tensors without specifying additional parameters compared to the conventional structure tensor. The performance of nonlinear structure tensors is demonstrated in three fields where the classic structure tensor is frequently used: orientation estimation, optic flow computation, and corner detection. In all these cases the nonlinear structure tensors demonstrate their superiority over the classical linear one. Our experiments also show that for corner detection based on nonlinear structure tensors, anisotropic nonlinear tensors give the most precise localisation.

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Section: Introductionmentioning

confidence: 99%

Nonlinear structure tensors

Brox

Weickert

Burgeth

et al. 2006

Image and Vision Computing

Self Cite

219

139

View full text Add to dashboard Cite

show abstract

“…A simple but effective way to estimate the local orientation is by using the smoothed structure tensor (SST), a well-known tool in computer vision, which is given by the smoothed outer products of the image gradients [21]. Performing an eigenanalysis of the SST essentially corresponds to performing a principal component analysis (PCA) of the gradient vectors.…”

Section: Flow-based Difference-of-gaussians (Fdog)mentioning

confidence: 99%

XDoG: An eXtended difference-of-Gaussians compendium including advanced image stylization

Winnemöller

Kyprianidis

Olsen³

2012

Computers & Graphics

218

187

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Recent extensions to the standard difference-of-Gaussians (DoG) edge detection operator have rendered it less susceptible to noise and increased its aesthetic appeal. Despite these advances, the technical subtleties and stylistic potential of the DoG operator are often overlooked. This paper offers a detailed review of the DoG operator and its extensions, highlighting useful relationships to other image processing techniques. It also presents many new results spanning a variety of styles, including pencil-shading, pastel, hatching, and woodcut. Additionally, we demonstrate a range of subtle artistic effects, such as ghosting, speed-lines, negative edges, indication, and abstraction, all of which are obtained using an extended DoG formulation, or slight modifications thereof. In all cases, the visual quality achieved by the extended DoG operator is comparable to or better than those of systems dedicated to a single style.

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“…Mathematically, this condition can be measured analysing squared modules of vectors s, shown in Fig. 3, as follows (Brox et al 2006) The above can be reformulated as follows…”

Section: Finding Local Structures With the Structural Tensormentioning

confidence: 99%

“…The total error is obtained by integrating the square of (3) over all possible locations x in the neighbourhood , using a Gaussian soft averaging filter G σ (Brox et al 2006). That is…”

Section: Finding Local Structures With the Structural Tensormentioning

confidence: 99%

Hybrid ensemble of classifiers for logo and trademark symbols recognition

Cyganek

2014

Soft Comput

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The paper presents a hybrid ensemble of diverse classifiers for logo and trademark symbols recognition. The proposed ensemble is composed of four types of different member classifiers. The first one compares color distribution of the logo patterns and is responsible for sifting out images of different color distribution. The second of the classifiers is based on the structural tensor recognition of local phase histograms. A proposed modification in this module consists of tensor computation in the space of the morphological scale-space. Thanks to this, more discriminative histograms describing global shapes are obtained. Next in the chain, is a novel member classifier that joins the Hausdorff distance with the correspondence measure of the log-polar patches computed around the corner points. This sparse classifier allows reliable comparison of even highly deformed patterns. The last member classifier relies on the statistical affine moment invariants which describe global shapes. However, a real advantage is obtained by joining the aforementioned base classifiers into a hybrid ensemble of classifiers, as proposed in this paper. Thanks to this a more accurate response and generalizing properties are obtained at reasonable computational requirements. Experimental results show good recognition accuracy even for the highly deformed logo patterns, as well as fair generalization properties which support human search and logo assessment tasks.

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Adaptive Structure Tensors and their Applications

Cited by 76 publications

References 35 publications

Nonlinear structure tensors

Nonlinear structure tensors

XDoG: An eXtended difference-of-Gaussians compendium including advanced image stylization

Hybrid ensemble of classifiers for logo and trademark symbols recognition

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