Geometric moment invariants

Xu, Dong; Li, Hua

doi:10.1016/j.patcog.2007.05.001

Cited by 151 publications

(90 citation statements)

References 24 publications

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“…Finally, we compute three-dimensional moment invariants [16] that are not computational intensive and provide results stable to noise and distortion.…”

Section: Geometric Momentsmentioning

confidence: 99%

Evaluation of a Nonrigid Motion Compensation Technique Based on Spatiotemporal Features for Small Lesion Detection in Breast MRI

Steinbruecker

Meyer‐Baese

Schlossbauer³

et al. 2012

Advances in Artificial Neural Systems

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Motion-induced artifacts represent a major problem in detection and diagnosis of breast cancer in dynamic contrast-enhanced magnetic resonance imaging. The goal of this paper is to evaluate the performance of a new nonrigid motion correction algorithm based on the optical flow method. For each of the small lesions, we extracted morphological and dynamical features describing both global and local shape, and kinetics behavior. In this paper, we compare the performance of each extracted feature set under consideration of several 2D or 3D motion compensation parameters for the differential diagnosis of enhancing lesions in breast MRI. Based on several simulation results, we determined the optimal motion compensation parameters. Our results have shown that motion compensation can improve the classification results. The results suggest that the computerized analysis system based on the non-rigid motion compensation technique and spatiotemporal features has the potential to increase the diagnostic accuracy of MRI mammography for small lesions and can be used as a basis for computer-aided diagnosis of breast cancer with MR mammography.

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“…Finally, we compute three-dimensional moment invariants [16] that are not computational intensive and provide results stable to noise and distortion.…”

Section: Geometric Momentsmentioning

confidence: 99%

Evaluation of a Nonrigid Motion Compensation Technique Based on Spatiotemporal Features for Small Lesion Detection in Breast MRI

Steinbruecker

Meyer‐Baese

Schlossbauer³

et al. 2012

Advances in Artificial Neural Systems

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“…Cyganski and Orr [5] proposed a tensor method for derivation of rotation invariants from geometric moments. The method of geometric primitives of Xu and Li [6,7] yields the same results. Kazhdan [8] studied registration of objects differing by 3D rotation, Kakarala and Mao [9] used bispectrum for derivation of TRS invariants.…”

Section: Introductionmentioning

confidence: 80%

Recognition of Symmetric 3D Bodies

Suk

Flusser

2014

Symmetry

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The paper deals with the recognition of symmetric three-dimensional (3D) bodies that can be rotated and translated. We provide a complete list of all existing combinations of rotation and reflection symmetries in 3D. We define 3D complex moments by means of spherical harmonics, and the influence of individual symmetry groups on complex moment values is studied. Each particular symmetry pre-defines certain moment values. These moments can no longer differentiate between two objects of the same symmetry, which decreases the recognition power of the feature set. They should not be included when constructing the invariants. Translation and rotation invariants up to the fourth order are presented and their performance is studied on both artificial and real data.

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“…190 models are selected and categorized into 19 classes, each of which contains an equal number of models. Five representative matching methods are performed and compared with our approach: extended Gaussian images [25], spin images [26], D2 shape distribution [18], bending invariant signature [14], geometric moment invariants [68]. Two performance measures in [18] are used in our test: given an inquiry model in class C and a number K of top matches, precision is the ratio of the top K matches 5.…”

Section: Tree Skeleton Extraction and Classificationmentioning

confidence: 99%

Construction of Iso-Contours, Bisectors, and Voronoi Diagrams on Triangulated Surfaces

Liu

Chen

Tang

2011

IEEE Trans. Pattern Anal. Mach. Intell.

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Abstract-In the research of computer vision and machine perception, three-dimensional objects are usually represented by 2-manifold triangular meshes M. In this paper, we present practical and efficient algorithms to construct iso-contours, bisectors and Voronoi diagrams of point sites on M, based on an exact geodesic metric. Compared to Euclidean metric spaces, the Voronoi diagrams on M exhibit many special properties that fail all the existing Euclidean Voronoi algorithms. To provide practical algorithms for constructing geodesic-metric-based Voronoi diagrams on M, this paper studies the analytic structure of iso-contours, bisectors and Voronoi diagrams on M. After a necessary preprocessing of model M, practical algorithms are proposed for quickly obtaining full information about iso-contours, bisectors and Voronoi diagrams on M. The complexity of the construction algorithms is also analyzed. Finally three interesting applications, surface sampling and reconstruction, 3D skeleton extraction and point pattern analysis are presented that show the potential power of the proposed algorithms in pattern analysis.

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Geometric moment invariants

Cited by 151 publications

References 24 publications

Evaluation of a Nonrigid Motion Compensation Technique Based on Spatiotemporal Features for Small Lesion Detection in Breast MRI

Evaluation of a Nonrigid Motion Compensation Technique Based on Spatiotemporal Features for Small Lesion Detection in Breast MRI

Recognition of Symmetric 3D Bodies

Construction of Iso-Contours, Bisectors, and Voronoi Diagrams on Triangulated Surfaces

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