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Journal articles on the topic 'Object invariants'

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Published: 4 June 2021

Last updated: 19 February 2022

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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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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 automatically generated from OCL constraints. These aspects can be woven into Java code to check whether object invariants are violated at runtime. Benefiting from AOP in separation of crosscutting concerns and weaving mechanisms, generated aspects can do the verification task whenever values of objects' attributes are changed. A Verification Aspect Generator (VAG) tool has been developed allowing the automatic generation of verifying aspects from the UML/OCL constraints.

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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 represent a detail of object recognition. The actual computational algorithms are not software-intensive and easy to debug. System uses the redundancy of uncertain information about the shape. In principle, chosen a certain balance between the confidence level of recognition and repetition of shape recognition by various methods.

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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 invariants to hypothesized frames of reference for proprioception and motor control. It is suggested that the detection of invariants revealed through movement is a major mechanism in kinesthetic perception involving intact limbs, neuropathic or anesthetized limbs, prosthetic devices, and hand-held tools and implements. The inertia tensor is identified as one such invariant.

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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 they can be formed from image coordinates and estimated tensors (F, fundamental matrix and T, trilinear tensor) and give results on simulated and real data.

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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 with monotonous background and clear object and meet the invariance on shift, rotation and scale transform of objects.

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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 moment invariants (CAMIs) are derived. Several experiments have been conducted to evaluate the proposed method. Experimental results show that CAMIs can be used in object classification tasks.

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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 platforms in our laboratory.

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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, e.g. under the Casey arccos transformation, and under an arctan transformation from the real projective line of cross-ratios to the unit circle. The cross-ratio distributions are novel to the probability literature; surprisingly various types of Cauchy distribution appear. To gain some analytical insight into the distribution, a simple linear-ratio is also introduced. We also give some results for the projective invariants of five coplanar points. We discuss the general moment properties of the cross-ratio, and consider some inference problems, including maximum likelihood estimation of the parameters.

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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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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, e.g. under the Casey arccos transformation, and under an arctan transformation from the real projective line of cross-ratios to the unit circle. The cross-ratio distributions are novel to the probability literature; surprisingly various types of Cauchy distribution appear. To gain some analytical insight into the distribution, a simple linear-ratio is also introduced. We also give some results for the projective invariants of five coplanar points. We discuss the general moment properties of the cross-ratio, and consider some inference problems, including maximum likelihood estimation of the parameters.

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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 processing time during indexing. Using both geometric features and quad-tree decomposition facilitates recognition and retrieval processes. Our approach is applied on the outline shapes of three-dimensional objects. Experiments conducted on two well-known databases show the efficiency of our method in real-world applications, especially for image indexing and retrieval.

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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 matrix. Therefore, in terms of algorithm complexity, the method proposed in this paper is superior to the traditional method. In this paper, we also study the projection transformation from a 3D point to a 2D point in space. According to this relationship, the geometric invariant relationships of other point structures can be easily derived, which have important applications in model-based object recognition. At the same time, the experimental results show that the eight-point structure invariants proposed in this paper can effectively describe the essential characteristics of the 3D structure of the target, without the influence of view, scaling, lighting, and other link factors, and have good stability and reliability.

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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-known Euclidean concepts form the basis of invariance in this case. Introducing constraints in addition to that of planarity may further simplify the invariants. On the other hand, there are problems for which no invariants exist.

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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. We have employed the geometric configuration of points and lines in general position to deduce the formulation of 3D invariants. It has been verified in our experiments that our proposed method is considerably accurate when compared with the ground truth, and more efficient when compared with reconstruction based methods.

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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 object in front of the light points is necessary for the form to become visible. The forms can also be recognized when isoluminous colours are used for background and point lights. Finally, it is noted that, if the observer can actively control the motion of the object, e.g., by moving a computer mouse, recognition is enhanced as in Gibson's (1962) experiment on active touch.

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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 partition tree to record their geometric distribution. Based on the similarity of trees, a rough classification of objects can be realized. However, for an accuracy recognition, we design a moment-based measure to describe the detail layout of lines in a layer and then re-describe image by Hu's moment invariants. The experimental results suggest that the representation efficiency enabled by simple cell's neural mechanism and application of multi-layered representation schema can simplify the complexity of the algorithm. This proves that line-context representation greatly eases subsequent shape-oriented recognition.

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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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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 persistent homology. A distinctive feature of the use of persistent homology with respect to methods of algebraic topology is to obtain more information about the shape of the object. An important direction of the application of persistent homology is the study invariants of big data. A method based on persistent cohomology is proposed that combines persistent homology technologies with embedded non-geometric information presented as functions of simplicial complexes. The proposed structure of extended barcodes using cohomology increases the effectiveness of persistent homology methods. A modification of the Wasserstein method for finding the distance between images by introducing non-geometric information was proposed. The possibility of the formation of barcodes of images invariant to transformations of rotation, shift and similarity is considered.

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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, these invariants can be used to reliably estimate structural moments beyond the radius of gyration, thereby rigorously expanding the actual set of model-free quantities one can extract from experimental SAS data, and possibly paving the way to designing new shape reconstruction strategies.

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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 taking into account the anyon model as a particle-flux system and by a qualitative inference of the topology.

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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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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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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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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:

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 projection transform can convert any object into a closed curve as a central projection transform, so the central projection transform is only a special case of the Mellin central projection transform. We prove that closed curves extracted from the original image and the affine transformed image by the Mellin central projection transform satisfy the same affine transform relationship. A method is provided for the extraction of affine invariants by employing the area of closed curves derived by the Mellin central projection transform. Experiments have been conducted on some printed Chinese characters and the results establish the invariance and robustness of the extracted features.

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