Pattern Matching Under Affine Transformations

Dirilten,; Newman,

doi:10.1109/tc.1977.1674832

Cited by 37 publications

(14 citation statements)

References 5 publications

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“…There has been much work since, of which we shortly list the contributions that are most relevant for our work. About one decade after Hu, Dirilton et al [7] have introduced the notion of moment tensors. The moment tensor contractions to zeroth order are invariant under orthogonal transformations.…”

Section: Related Workmentioning

confidence: 99%

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Moment invariants for 3D flow fields via normalization

Bujack

Kasten

Hotz

et al. 2015

2015 IEEE Pacific Visualization Symposium (PacificVis)

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We generalize the framework of moments and introduce a definition of invariants for three-dimensional vector fields. To do so, we use the method of moment normalization that has been shown to be useful in the two dimensions. Using invariant moments, we show how to search for patterns in these fields independent from their position, orientation and scale. From the first order vector moment tensor, we construct a complete and independent set of descriptors. We test the invariants in queries on synthetic and real world flow fields.

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Section: Related Workmentioning

confidence: 99%

“…It has been introduced by Dirilton et al [7] and further explored by Suk et al [20] for the definition of 3D moment invariants for scalar fields. The basic idea is to arrange the moments of a given order such that they form a symmetric tensor of this order, exhibiting the typical transformation properties of a tensor.…”

mentioning

confidence: 99%

Moment invariants for 3D flow fields via normalization

Bujack

Kasten

Hotz

et al. 2015

2015 IEEE Pacific Visualization Symposium (PacificVis)

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“…His invariants have the desirable properties of being invariant under image scaling. Since then, Hu's publication has been extensively referenced in nearly all moment related researches for the past few decades, such as ship identification, aircraft identification, pattern matching and scene matching [2,3,4,5]. However, Hu's moment invariants are not derived from a family of orthogonal functions that implies the linear independence of the corresponding moments.…”

Section: Introductionmentioning

confidence: 99%

Scale Invariants of Three-Dimensional Legendre Moments

Ong

Chong

Besar

2006

TENCON 2006 - 2006 IEEE Region 10 Conference

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Three-dimensional digital images are gaining more attention in pattern recognition field. Mostly literatures, however, only focus on theoretical framework of twodimensional moment invariants, that are only implemented on two-dimensional images. Consequently, it reduces the invariance flexibility to support three-dimensional objects. In this paper, we introduce three-dimensional scale invariants ofLegendre moments. They are algebraically derived directlyfrom Legendrepolynomials. Simulated experiments using three-dimensional binary images are carried out to verify the validity ofproposed invariance.

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“…These invariants remain the same under image translation, rotation and scaling. A number of such moments invariants can be put into a feature vector and used for matching purposes as was done for instance in [44,45]. Recently, matching two shapes using moments was proposed in [46] in the context of affineinvariant shape-based segmentation.…”

Section: Parametric Representationsmentioning

confidence: 99%

“…The first row in Fig. (34) corresponds to the results obtained using the proposed registration model (44), while the results from the method in [5] are shown in the second row of the same figure. It is clear from this figure that, for this specific case, both methods lead to favorably comparable results with subtle dif-ferences.…”

Section: Numerical Implementationmentioning

confidence: 99%

Variational methods for shape and image registrations.

Fahmi

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Fahmi, Rachid 1971-, "Variational methods for shape and image registrations." (2008 Thank you for your endless love, support, and sacrifices.I love you more than anything else in this world.iii ACKNOWLEDGMENTS First of all, my deepest thanks are due to Almighty God, the merciful, the compassionate for all the blessings bestowed upon me. Estimating and analysis of deformation, either rigid or non-rigid, is an active area of research in various medical imaging and computer vision applications. Its importance stems from the inherent inter-and intra-variability in biological and biomedical object shapes and from the dynamic nature of the scenes usually dealt with in computer vision research. For instance, quantifying the growth of a tumor, recognizing a person's face, tracking a facial expression, or retrieving an object inside a data base require the estimation of some sort of motion or deformation undergone by the object of interest. To solve these problems, and other similar problems, registration comes into play. This is the process of bringing into correspondences two or more data sets. Depending on the application at hand, these data sets can be for instance gray scale/color images or objects' outlines. In the latter case, one talks about shape registration while in the former case, one talks about image/volume registration. In some situations, the combinations of different types of data can be used complementarily to establish point correspondences.One of most important image analysis tools that greatly benefits from the process of registration, and which will be addressed in this dissertation, is the image segmentation.This process consists of localizing objects in images. Several challenges are encountered in image segmentation, including noise, gray scale inhomogeneities, and occlusions. To cope with such issues, the shape information is often incorporated as a statistical model into the segmentation process. Building such statistical models requires a good and accurate v shape alignment approach. In addition, segmenting anatomical structures can be accurately solved through the registration of the input data set with a predefined anatomical atlas. Furthermore, it can deal with noisy, occluded and missing or corrupted data. The classical way of solving the shape-based segmentation problems within a level set framework is by directly solving the underlying Euler-Lagrange equations using a gradient descent scheme. This is very computationally expensive given the non-linear parabolic nature of the corresponding PDE's. To overcome these difficulties, a fast algorithm is designed and implemented to solve both the two-phase and the multi-phase shape-based segmentation problem. This algorithm exploits the fact that only the sign of the level set function, not its value, is needed to evolve the segmenting interface. The integration of multiple selective shape priors and the segmentation into multiple regions has never been addressed before.Third, a new image/volume non-rigid registration approach based on scale s...

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Pattern Matching Under Affine Transformations

Cited by 37 publications

References 5 publications

Moment invariants for 3D flow fields via normalization

Moment invariants for 3D flow fields via normalization

Scale Invariants of Three-Dimensional Legendre Moments

Variational methods for shape and image registrations.

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