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Affine Invariant

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Madhu Sudan – 1st expert on this subject based on the ideXlab platform

  • sparse Affine Invariant linear codes are locally testable
    Computational Complexity, 2017
    Co-Authors: Eli Bensasson, Noga Ronzewi, Madhu Sudan

    Abstract:

    We show that sparse AffineInvariant linear properties over arbitrary finite fields are locally testable with a constant number of queries. Given a finite field $${\mathbb{F}_q}$$Fq and an extension field $${\mathbb{F}_{q^n}}$$Fqn, a property is a set of functions mapping $${\mathbb{F}_{q^n}}$$Fqn to $${\mathbb{F}_q}$$Fq. The property is said to be AffineInvariant if it is Invariant under Affine transformations of $${\mathbb{F}_{q^n}}$$Fqn, linear if it is an $${\mathbb{F}_q}$$Fq -vector space, and sparse if its size is polynomial in the domain size. Our work completes a line of work initiated by Grigorescu et al. (2009) and followed by Kaufman & Lovett (2011). The latter showed such a result for the case when q was prime. Extending to non-prime cases turns out to be non-trivial, and our proof involves some detours into additive combinatorics, as well as a new calculus for building property testers for AffineInvariant linear properties.

  • FOCS – Sparse AffineInvariant Linear Codes Are Locally Testable
    2012 IEEE 53rd Annual Symposium on Foundations of Computer Science, 2012
    Co-Authors: Eli Ben-sasson, Noga Ron-zewi, Madhu Sudan

    Abstract:

    We show that sparse AffineInvariant linear properties over arbitrary finite fields are locally testable with a constant number of queries. Given a finite field $\F_q$ and an extension field $\F_{q^n}$, a property is a set of functions mapping $\F_{q^n}$ to $\F_q$. The property is said to be AffineInvariant if it is Invariant under Affine transformations of $\F_{q^n}$, and it is said to be sparse if its size is polynomial in the domain size. Our work completes a line of work initiated by Grigorescu et al. [RANDOM 2009] and followed by Kaufman and Lovett [FOCS 2011]. The latter showed such a result for the case when $q$ was prime. Extending to non-prime cases turns out to be non-trivial and our proof involves some detours into additive combinatorics, as well as a new calculus for building property testers for AffineInvariant linear properties.

  • Sparse AffineInvariant Linear Codes Are Locally Testable
    2012 IEEE 53rd Annual Symposium on Foundations of Computer Science, 2012
    Co-Authors: Eli Ben-sasson, Noga Ron-zewi, Madhu Sudan

    Abstract:

    We show that sparse AffineInvariant linear properties over arbitrary finite fields are locally testable with a constant number of queries. Given a finite field Fq and an extension field Fqn, a property is a set of functions mapping Fqn to Fq. The property is said to be AffineInvariant if it is Invariant under Affine transformations of Fqn, and it is said to be sparse if its size is polynomial in the domain size. Our work completes a line of work initiated by Grigorescu et al. [RANDOM 2009] and followed by Kaufman and Lovett [FOCS 2011]. The latter showed such a result for the case when q was prime. Extending to non-prime cases turns out to be non-trivial and our proof involves some detours into additive combinatorics, as well as a new calculus for building property testers for AffineInvariant linear properties.

Chun Hsiung Fang – 2nd expert on this subject based on the ideXlab platform

  • Synthesized Affine Invariant function for 2D shape recognition
    Pattern Recognition, 2007
    Co-Authors: Chun Hsiung Fang

    Abstract:

    By defining the weighted wavelet synthesis, the synthesized feature signals of an interesting shape are extracted to derive the innovative synthesized Affine Invariant function (SAIF). The synthesized feature signals hold the shape information with minimum loss by excluding simply the translation dependent and noise-contaminated bands. The SAIF is shown excellent in the invariance property and representative in describing the original shape for automated recognition. Experimental results demonstrate that automated shape recognition based on the SAIF achieves high correctness and significantly outperforms those using conventional wavelet Affine Invariant functions.

  • Synthesized Affine Invariant function for 2D shape recognition
    Pattern Recognition, 2007
    Co-Authors: Wei Song Lin, Chun Hsiung Fang

    Abstract:

    By defining the weighted wavelet synthesis, the synthesized feature signals of an interesting shape are extracted to derive the innovative synthesized Affine Invariant function (SAIF). The synthesized feature signals hold the shape information with minimum loss by excluding simply the translation dependent and noise-contaminated bands. The SAIF is shown excellent in the invariance property and representative in describing the original shape for automated recognition. Experimental results demonstrate that automated shape recognition based on the SAIF achieves high correctness and significantly outperforms those using conventional wavelet Affine Invariant functions. © 2006 Pattern Recognition Society.

Liang Cheng – 3rd expert on this subject based on the ideXlab platform

  • remote sensing image matching by integrating Affine Invariant feature extraction and ransac
    Computers & Electrical Engineering, 2012
    Co-Authors: Liang Cheng, Manchun Li, Yanming Chen, Kang Yang

    Abstract:

    A new technical framework for remote sensing image matching by integrating Affine Invariant feature extraction and RANSAC is presented. The novelty of this framework is an automatic optimization strategy for Affine Invariant feature matching based on RANSAC. An automatic way to determine the distance threshold of RANSAC is proposed, which is a key problem to implement this RANSAC-based automatic optimization. Since Affine Invariant feature matching technology has been successfully applied to remote sensing image matching, we design an experiment to compare the proposed framework (with optimization) with the standard Affine Invariant feature matching (without optimization). By using three pairs with different types of imagery, the experimental results indicate that the proposed framework can always get higher correctness of image matching in automatic way, compared to the standard Affine Invariant feature matching technology.

  • A new method for remote sensing image matching by integrating Affine Invariant feature extraction and RANSAC
    2010 3rd International Congress on Image and Signal Processing, 2010
    Co-Authors: Liang Cheng, Hao Hu, Yecheng Wang, Manchun Li

    Abstract:

    A new method on remote sensing image matching by integrating Affine Invariant feature extraction and RANSAC is presented. The novelty of this method is a strategy on automatic optimization for Affine Invariant feature matching based on RANSAC. An automatic way to determine the distance threshold of RANSAC is proposed, which is a key problem to implement this RANSAC-based automatic optimization. Since Affine Invariant feature matching technology has been successfully applied to remote sensing image matching, we design an experiment to compare the proposed method (with optimization) with the standard Affine Invariant feature matching (without optimization). By using two stereo pairs with different types of imagery, the experiment indicates that the proposed method can always get much matching score compared to the standard Affine Invariant feature matching method.

  • Robust Affine Invariant Feature Extraction for Image Matching
    IEEE Geoscience and Remote Sensing Letters, 2008
    Co-Authors: Liang Cheng, Jianya Gong, Xiaoxia Yang

    Abstract:

    A new approach is presented to extract more robust Affine Invariant features for image matching. The novelty of our approach is a hierarchical filtering strategy for Affine Invariant feature detection, which is based on information entropy and spatial dispersion quality constraints. The concept of spatial dispersion quality is introduced to quantify the spatial distribution of features. Moreover, an integrated algorithm combined by the filtering strategy, maximally stable extremal region (MSER) and scale Invariant feature transform, is introduced for Affine Invariant feature extraction. Since Mikolajczyk et al. identified that MSER is the best detector in many cases, we design an experiment to compare our approach (ED-MSER) with the standard MSER. By using two stereo pairs and an image sequence with different types of imagery, the experiment indicates that ED-MSER can always get much higher repeatability and matching score compared to the standard MSER and other algorithms, thus benefiting the subsequent image matching and many other applications.