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1

Samad, Saleha, Anam Haq, and Shoab A. Khan. "Orientation Invariant Object Recognitions Using Geometric Moments Invariants and Color Histograms." International Journal of Computer and Electrical Engineering 7, no. 2 (2015): 101–8. http://dx.doi.org/10.17706/ijcee.2015.v7.876.

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2

NGUYEN, THU-TRANG, NINH-THUAN TRUONG, and VIET-HA NGUYEN. "VERIFYING JAVA OBJECT INVARIANTS AT RUNTIME." International Journal of Software Engineering and Knowledge Engineering 21, no. 04 (June 2011): 605–19. http://dx.doi.org/10.1142/s0218194011005281.

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Abstract (sommario):
An object invariant consisting of a set of properties that must hold for all instances of a class at any time is usually used in object-oriented design. However, verifying object invariants at runtime is always a challenging task in software verification. This paper proposes a method for verifying invariants of Java objects at runtime using AOP. Suppose that a software application is designed using UML models and its constraints are specified in OCL expressions, the software is then implemented, by default, using the UML design. They propose to construct verifiable aspects which are automatica
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3

Stejskal, Tomáš. "2D-Shape Analysis Using Shape Invariants." Applied Mechanics and Materials 613 (August 2014): 452–57. http://dx.doi.org/10.4028/www.scientific.net/amm.613.452.

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High efficiency detection of two-dimensional objects is achieved by an appropriate choice of object invariants. The aim is to show an example of the construction of an algorithm for rapid identification also for highly complex objects. The program structure works in a similar way as animal systems in nature. Differentiating runs from whole to details. They are used to shape invariants. The program algorithm is specifically used a surfaces invariant, which represents a whole. Then was used a boundary length invariant around the object. Finally, the chord distribution code was used, which repres
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4

Chang, Bor-Yuh Evan, K. Rustan, and M. Leino. "Inferring Object Invariants." Electronic Notes in Theoretical Computer Science 131 (May 2005): 63–74. http://dx.doi.org/10.1016/j.entcs.2005.01.023.

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5

Pagano, Christopher C., and Michael T. Turvey. "Eigenvectors of the Inertia Tensor and Perceiving the Orientations of Limbs and Objects." Journal of Applied Biomechanics 14, no. 4 (November 1998): 331–59. http://dx.doi.org/10.1123/jab.14.4.331.

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We report several experiments directed at the ability of humans to perceive the spatial orientation of occluded objects, to position an occluded limb relative to targets or directions in the environment, and to match the spatial orientations of occluded contralateral limbs. Results suggest that each of these abilities is lied to the inertial eigenvectors of each object or limb, which correspond to the object's or limb's principal axes of rotational inertia. Discussion focuses on the dynamic nature of proprioception, the importance of physical invariants for perception, and the relation of inva
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6

LASENBY, JOAN, and EDUARDO BAYRO-CORROCHANO. "ANALYSIS AND COMPUTATION OF PROJECTIVE INVARIANTS FROM MULTIPLE VIEWS IN THE GEOMETRIC ALGEBRA FRAMEWORKS." International Journal of Pattern Recognition and Artificial Intelligence 13, no. 08 (December 1999): 1105–21. http://dx.doi.org/10.1142/s0218001499000628.

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A central task of computer vision is to automatically recognize objects in real-world scenes. The parameters defining image and object spaces can vary due to lighting conditions, camera calibration and viewing positions. It is therefore desirable to look for geometric properties of the object which remain invariant under such changes. In this paper we present geometric algebra as a complete framework for the theory and computation of projective invariants formed from points and lines in computer vision. We will look at the formation of 3D projective invariants from multiple images, show how th
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7

Rivlin, Ehud, and Isaac Weiss. "Deformation Invariants in Object Recognition." Computer Vision and Image Understanding 65, no. 1 (January 1997): 95–108. http://dx.doi.org/10.1006/cviu.1996.0478.

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8

Weiss, Isaac. "Geometric invariants and object recognition." International Journal of Computer Vision 10, no. 3 (June 1993): 207–31. http://dx.doi.org/10.1007/bf01539536.

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9

Lu, Wei. "Image Retrieval Based on Contour and Relevance Feedback." Applied Mechanics and Materials 182-183 (June 2012): 1771–75. http://dx.doi.org/10.4028/www.scientific.net/amm.182-183.1771.

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In this paper an algorithm is proposed to retrieve images based on contour moment invariants of image and relevance feedback. Firstly, the contour of each query image is extracted and its contour moment invariant is computed. Then according to Euclid Distance between the query image and each image in the image database, the most similar images to the query image can be found. Finally, the relevance feedback algorithm based on support vector machine (SVM) is applied to improve retrieval precision. Experimental results show that the algorithm is more accurate and efficient to retrieve images wit
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10

Shan, J. "Photogrammetric object description with projective invariants." ISPRS Journal of Photogrammetry and Remote Sensing 52, no. 5 (October 1997): 222–28. http://dx.doi.org/10.1016/s0924-2716(97)00015-4.

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11

Müller, Peter, Arnd Poetzsch-Heffter, and Gary T. Leavens. "Modular invariants for layered object structures." Science of Computer Programming 62, no. 3 (October 2006): 253–86. http://dx.doi.org/10.1016/j.scico.2006.03.001.

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12

Fahndrich, Manuel, and Songtao Xia. "Establishing object invariants with delayed types." ACM SIGPLAN Notices 42, no. 10 (October 21, 2007): 337–50. http://dx.doi.org/10.1145/1297105.1297052.

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13

Middelkoop, Ronald, Cornelis Huizing, Ruurd Kuiper, and Erik J. Luit. "Invariants for Non-Hierarchical Object Structures." Electronic Notes in Theoretical Computer Science 195 (January 2008): 211–29. http://dx.doi.org/10.1016/j.entcs.2007.08.034.

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14

Mercimek, Muharrem, Kayhan Gulez, and Tarik Veli Mumcu. "Real object recognition using moment invariants." Sadhana 30, no. 6 (December 2005): 765–75. http://dx.doi.org/10.1007/bf02716709.

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15

Yang, Jianwei, Ming Li, Zirun Chen, and Yunjie Chen. "Cutting Affine Moment Invariants." Mathematical Problems in Engineering 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/928161.

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The extraction of affine invariant features plays an important role in many fields of image processing. In this paper, the original image is transformed into new images to extract more affine invariant features. To construct new images, the original image is cut in two areas by a closed curve, which is called general contour (GC). GC is obtained by performing projections along lines with different polar angles. New image is obtained by changing gray value of pixels in inside area. The traditional affine moment invariants (AMIs) method is applied to the new image. Consequently, cutting affine m
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16

Barnett, Mike, Robert DeLine, Manuel Fähndrich, K. Rustan M. Leino, and Wolfram Schulte. "Verification of Object-Oriented Programs with Invariants." Journal of Object Technology 3, no. 6 (2004): 27. http://dx.doi.org/10.5381/jot.2004.3.6.a2.

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17

Alferez, R., and Yuan-Fang Wang. "Geometric and illumination invariants for object recognition." IEEE Transactions on Pattern Analysis and Machine Intelligence 21, no. 6 (June 1999): 505–36. http://dx.doi.org/10.1109/34.771318.

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18

Beis, J. S., and D. G. Lowe. "Indexing without invariants in 3D object recognition." IEEE Transactions on Pattern Analysis and Machine Intelligence 21, no. 10 (1999): 1000–1015. http://dx.doi.org/10.1109/34.799907.

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19

Nagao, Kenji, and W. Eric L. Grimson. "Using Photometric Invariants for 3D Object Recognition." Computer Vision and Image Understanding 71, no. 1 (July 1998): 74–93. http://dx.doi.org/10.1006/cviu.1997.0603.

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20

Reiss, Thomas H. "Object recognition using algebraic and differential invariants." Signal Processing 32, no. 3 (June 1993): 367–95. http://dx.doi.org/10.1016/0165-1684(93)90008-x.

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21

Vasseur, P., C. Pegard, E. Mouaddib, and L. Delahoche. "Indexing and alignment of 3-D objects using geometric quasi-invariants." Robotica 16, no. 6 (November 1998): 651–58. http://dx.doi.org/10.1017/s0263574798000575.

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In this paper, we are introducing a system which is able to recognize polyhedral objects in an indoor environment. Our system is intended to be implemented on autonomous mobile platforms in order to enable the localization or research of a precise item. The algorithm is based on the use of geometric quasi-invariants associated to every object. These geometric quasi-invariants correspond to the ratio of the lengths as well as the angle formed by the pair of segments which are in relationship and which are constituting the object. We present some experimental results gained on one of our platfor
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22

Mardia, K. V., Colin Goodall, and Alistair Walder. "Distributions of projective invariants and model-based machine vision." Advances in Applied Probability 28, no. 03 (September 1996): 641–61. http://dx.doi.org/10.1017/s0001867800046425.

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In machine vision, objects are observed subject to an unknown projective transformation, and it is usual to use projective invariants for either testing for a false alarm or for classifying an object. For four collinear points, the cross-ratio is the simplest statistic which is invariant under projective transformations. We obtain the distribution of the cross-ratio under the Gaussian error model with different means. The case of identical means, which has appeared previously in the literature, is derived as a particular case. Various alternative forms of the cross-ratio density are obtained,
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23

Mardia, K. V., Colin Goodall, and Alistair Walder. "Distributions of projective invariants and model-based machine vision." Advances in Applied Probability 28, no. 3 (September 1996): 641–61. http://dx.doi.org/10.2307/1428174.

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Abstract (sommario):
In machine vision, objects are observed subject to an unknown projective transformation, and it is usual to use projective invariants for either testing for a false alarm or for classifying an object. For four collinear points, the cross-ratio is the simplest statistic which is invariant under projective transformations. We obtain the distribution of the cross-ratio under the Gaussian error model with different means. The case of identical means, which has appeared previously in the literature, is derived as a particular case. Various alternative forms of the cross-ratio density are obtained,
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24

Aouat, Saliha, and Slimane Larabi. "Object Retrieval Using the Quad-Tree Decomposition." Journal of Intelligent Systems 23, no. 1 (January 1, 2014): 33–47. http://dx.doi.org/10.1515/jisys-2013-0014.

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AbstractWe propose in this article an indexing and retrieval approach applied on outline shapes. Models of objects are stored in a database using the textual descriptors of their silhouettes. We extract from the textual description a set of efficient similarity measures to index the silhouettes. The extracted features are the geometric quasi-invariants that vary slightly with the small change in the viewpoint. We use a textual description and quasi-invariant features to minimize the storage space and to achieve an efficient indexing process. We also use the quad-tree structure to improve proce
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25

Mui, Yanping, Youzheng Zhang, and Guitao Cao. "Invariants of the Space Point Element Structure and Their Applications." Mathematical Problems in Engineering 2020 (October 19, 2020): 1–13. http://dx.doi.org/10.1155/2020/3295492.

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In this paper, a new geometric structure of projective invariants is proposed. Compared with the traditional invariant calculation method based on 3D reconstruction, this method is comparable in the reliability of invariant calculation. According to this method, the only thing needed to find out is the geometric relationship between 3D points and 2D points, and the invariant can be obtained by using a single frame image. In the method based on 3D reconstruction, the basic matrix of two images is estimated first, and then, the 3D projective invariants are calculated according to the basic matri
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26

Van Gool, Luc J., Theo Moons, Eric Pauwels, and Johan Wagemans. "Invariance from the Euclidean Geometer's Perspective." Perception 23, no. 5 (May 1994): 547–61. http://dx.doi.org/10.1068/p230547.

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It is remarkable how well the human visual system can cope with changing viewpoints when it comes to recognising shapes. The state of the art in machine vision is still quite remote from solving such tasks. Nevertheless, a surge in invariance-based research has led to the development of methods for solving recognition problems still considered hard until recently. A nonmathematical account explains the basic philosophy and trade-offs underlying this strand of research. The principles are explained for the relatively simple case of planar-object recognition under arbitrary viewpoints. Well-know
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27

JIN, CHENG. "GEOMETRIC INVARIANTS CONSTRUCTION FROM MULTIPLE VIEWS." International Journal of Modeling, Simulation, and Scientific Computing 02, no. 02 (June 2011): 195–206. http://dx.doi.org/10.1142/s1793962311000402.

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Geometric invariants have wide applications in computer vision and their precision has long been a hot topic. In most of the existing methods, three-dimensional (3D) invariants have been obtained by reconstruction of the object structure, where fundamental matrices between image pairs should be first established. Consequently, there are additional errors introduced during invariants construction and could be very time consuming. In this paper, a novel algorithm to calculate 3D projective invariants from multiple images has been proposed, without reconstructing the object structures explicitly.
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28

Ledger, Paul D., Ben A. Wilson, Alan A. S. Amad, and William R. B. Lionheart. "Identification of metallic objects using spectral magnetic polarizability tensor signatures: Object characterisation and invariants." International Journal for Numerical Methods in Engineering 122, no. 15 (May 25, 2021): 3941–84. http://dx.doi.org/10.1002/nme.6688.

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29

Benouini, Rachid, Imad Batioua, Ilham Elouariachi, Khalid Zenkouar, and Arsalane Zarghili. "Explicit Separable two dimensional Moment Invariants for object recognition." Procedia Computer Science 148 (2019): 409–17. http://dx.doi.org/10.1016/j.procs.2019.01.049.

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30

Khalil, Mahmoud I., and Mohamed M. Bayoumi. "Affine invariants for object recognition using the wavelet transform." Pattern Recognition Letters 23, no. 1-3 (January 2002): 57–72. http://dx.doi.org/10.1016/s0167-8655(01)00102-7.

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31

Gevers, T., and H. Stokman. "Robust histogram construction from color invariants for object recognition." IEEE Transactions on Pattern Analysis and Machine Intelligence 26, no. 1 (January 2004): 113–18. http://dx.doi.org/10.1109/tpami.2004.1261083.

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32

Michel, J., N. Nandhakumar, and V. Velten. "Thermophysical algebraic invariants from infrared imagery for object recognition." IEEE Transactions on Pattern Analysis and Machine Intelligence 19, no. 1 (1997): 41–51. http://dx.doi.org/10.1109/34.566809.

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33

Burel, Gilles, and Hugues Hénocq. "Three-dimensional invariants and their application to object recognition." Signal Processing 45, no. 1 (July 1995): 1–22. http://dx.doi.org/10.1016/0165-1684(95)00039-g.

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34

Bose, S. K., K. K. Biswas, and S. K. Gupta. "Model based object recognition — the role of affine invariants." Artificial Intelligence in Engineering 10, no. 3 (August 1996): 227–34. http://dx.doi.org/10.1016/0954-1810(95)00032-1.

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35

Guo, Liqiang, Ming Dai, and Ming Zhu. "Quaternion moment and its invariants for color object classification." Information Sciences 273 (July 2014): 132–43. http://dx.doi.org/10.1016/j.ins.2014.03.037.

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36

Naumann, David A. "On assertion-based encapsulation for object invariants and simulations." Formal Aspects of Computing 19, no. 2 (December 16, 2006): 205–24. http://dx.doi.org/10.1007/s00165-006-0020-5.

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37

Unel, Mustafa, Octavian Soldea, Erol Ozgur, and Alp Bassa. "3D object recognition using invariants of 2D projection curves." Pattern Analysis and Applications 13, no. 4 (May 22, 2010): 451–68. http://dx.doi.org/10.1007/s10044-010-0179-5.

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38

Stappers, P. J. "Forms Can Be Recognized from Dynamic Occlusion Alone." Perceptual and Motor Skills 68, no. 1 (February 1989): 243–51. http://dx.doi.org/10.2466/pms.1989.68.1.243.

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Direct and indirect theories of perception differ on whether form perception depends on higher order invariants or on features in the retinal image. The present paper describes a demonstration that an object can be recognized through a higher order pattern (dynamic occlusion) without any of the object's features being displayed. Stimuli consist of computer simulations of black wireframe objects moving in front of, and occluding, a random layout of point lights on a black background. In this way, no single videoframe of the stimuli displays any of the object's features, and motion of the amodal
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39

Wei, Hui, and Lei Wu. "A Line-Context Based Object Recognition Method." International Journal on Artificial Intelligence Tools 23, no. 06 (December 2014): 1460029. http://dx.doi.org/10.1142/s021821301460029x.

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The shape or contour of an object is usually stable and persistent, so it is a good basis for invariant recognition. For this purpose, two problems must be handled. The first is obtaining clean edges and the other is organizing those edges into a structured form so that they can be manipulated easily. We apply a bio-inspired orientation detection algorithm because it can output a fairly clean set of lines, and all lines are in the form of vectors instead of pixels. This line representation is efficient. We decompose them into several slope-depended layers and then create a hierarchical partiti
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40

CARLSSON, ERIK, GUNNAR CARLSSON, and VIN DE SILVA. "AN ALGEBRAIC TOPOLOGICAL METHOD FOR FEATURE IDENTIFICATION." International Journal of Computational Geometry & Applications 16, no. 04 (August 2006): 291–314. http://dx.doi.org/10.1142/s021819590600204x.

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We develop a mathematical framework for describing local features of a geometric object—such as the edges of a square or the apex of a cone—in terms of algebraic topological invariants. The main tool is the construction of a "tangent complex" for an arbitrary geometrical object, generalising the usual tangent bundle of a manifold. This framework can be used to develop algorithms for automatic feature location. We give several examples of applying such algorithms to geometric objects represented by point-cloud data sets.
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41

Liu Zhengjun, 刘正君, 李琦 Li Qi, and 王骐 Wang Qi. "Object Recognition of Ladar Range Image Using Combined Moment Invariants." Chinese Journal of Lasers 39, no. 6 (2012): 0609002. http://dx.doi.org/10.3788/cjl201239.0609002.

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42

Benouini, Rachid, Imad Batioua, Khalid Zenkouar, Said Najah, and Hassan Qjidaa. "Efficient 3D object classification by using direct Krawtchouk moment invariants." Multimedia Tools and Applications 77, no. 20 (April 12, 2018): 27517–42. http://dx.doi.org/10.1007/s11042-018-5937-1.

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43

Chukanov, Sergey N. "The Comparison of Diffeomorphic Images Based on the Construction of Persistent Homology." Modeling and Analysis of Information Systems 26, no. 3 (September 28, 2019): 450–68. http://dx.doi.org/10.18255/1818-1015-2019-3-450-468.

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Abstract (sommario):
An object shape analysis is a problem that is related to such areas as geometry, topology, image processing and machine learning. For analyzing the form, the deformation between the source and terminal form of the object is estimated. The most used form analysis model is the Large Deformation Diffeomorphic Metric Mapping (LDDMM) model. The LDDMM model can be supplemented with functional non-geometric information about objects (volume, color, formation time). The paper considers algorithms for constructing sets of barcodes for comparing diffeomorphic images, which are real values taken by persi
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44

Houdayer, Jérôme, and Frédéric Poitevin. "Reduction of small-angle scattering profiles to finite sets of structural invariants." Acta Crystallographica Section A Foundations and Advances 73, no. 4 (June 9, 2017): 317–32. http://dx.doi.org/10.1107/s205327331700451x.

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This paper shows how small-angle scattering (SAS) curves can be decomposed in a simple sum using a set of invariant parameters calledKnwhich are related to the shape of the object of study. TheseKn, together with a radiusR, give a complete theoretical description of the SAS curve. Adding an overall constant, these parameters are easily fitted against experimental data giving a concise comprehensive description of the data. The pair distance distribution function is also entirely described by this invariant set and theDmaxparameter can be measured. In addition to the understanding they bring, t
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45

DA CRUZ, WELLINGTON. "TOPOLOGICAL INVARIANTS AND ANYONIC PROPAGATORS." Modern Physics Letters A 14, no. 28 (September 14, 1999): 1933–36. http://dx.doi.org/10.1142/s0217732399002005.

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We obtain the Hausdorff dimension, h=2-2s, for particles with fractional spins in the interval, 0≤ s ≤0.5, such that the manifold is characterized by a topological invariant given by, [Formula: see text]. This object is related to fractal properties of the path swept out by fractional spin particles, the spin of these particles, and the genus (number of anyons) of the manifold. We prove that the anyonic propagator can be put into a path integral representation which gives us a continuous family of Lagrangians in a convenient gauge. The formulas for, h and [Formula: see text], were obtained tak
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46

Polishchuk, A. "K-theoretic exceptional collections at roots of unity." Journal of K-Theory 7, no. 1 (May 11, 2010): 169–201. http://dx.doi.org/10.1017/is010004018jkt112.

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AbstractUsing cyclotomic specializations of equivariant K-theory with respect to a torus action we derive congruences for discrete invariants of exceptional objects in derived categories of coherent sheaves on a class of varieties that includes Grassmannians and smooth quadrics. For example, we prove that if , where the ni's are powers of a fixed prime number p, then the rank of an exceptional object on X is congruent to ±1 modulo p.
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47

Shinagawa, Y. "Homotopic Image Pseudo-Invariants for Openset Object Recognition and Image Retrieval." IEEE Transactions on Pattern Analysis and Machine Intelligence 30, no. 11 (November 2008): 1891–901. http://dx.doi.org/10.1109/tpami.2008.143.

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48

Zhengwei Yang and F. S. Cohen. "Image registration and object recognition using affine invariants and convex hulls." IEEE Transactions on Image Processing 8, no. 7 (July 1999): 934–46. http://dx.doi.org/10.1109/83.772236.

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49

Song, Bong Seop, Kyoung Mu Lee, and Sang Uk Lee. "Model-Based Object Recognition Using Geometric Invariants of Points and Lines." Computer Vision and Image Understanding 84, no. 3 (December 2001): 361–83. http://dx.doi.org/10.1006/cviu.2001.0954.

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50

YANG, JIANWEI, LIANG ZHANG, and ZHENGDA LU. "THE MELLIN CENTRAL PROJECTION TRANSFORM." ANZIAM Journal 58, no. 3-4 (March 7, 2017): 256–64. http://dx.doi.org/10.1017/s1446181116000341.

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Abstract (sommario):
The central projection transform can be employed to extract invariant features by combining contour-based and region-based methods. However, the central projection transform only considers the accumulation of the pixels along the radial direction. Consequently, information along the radial direction is inevitably lost. In this paper, we propose the Mellin central projection transform to extract affine invariant features. The radial factor introduced by the Mellin transform, makes up for the loss of information along the radial direction by the central projection transform. The Mellin central p
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