437 results on '"Affine shape adaptation"'
Search Results
2. Greedy Learning of Deep Boltzmann Machine (GDBM)’s Variance and Search Algorithm for Efficient Image Retrieval
- Author
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Safa Jalil Jassim, Guangzhi Ma, Mudhafar Jalil Jassim Ghrabat, Zaid Ameen Abduljabbar, and Mustafa A. Al Sibahee
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Color histogram ,Jaccard index ,General Computer Science ,business.industry ,Computer science ,Feature extraction ,ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION ,General Engineering ,Boltzmann machine ,020206 networking & telecommunications ,Pattern recognition ,02 engineering and technology ,Affine shape adaptation ,Search algorithm ,Histogram ,0202 electrical engineering, electronic engineering, information engineering ,Median filter ,020201 artificial intelligence & image processing ,General Materials Science ,Artificial intelligence ,business ,Image retrieval - Abstract
Despite extensive research on content-based image retrieval, challenges such as low accuracy, incapability to handle complex queries and high time consumption persist. Initially, a preprocessing technique is introduced in this study, a technique that uses a median filter to remove noise to achieve improved accuracy and reliability. Then, Fourier and circularity descriptors are extract in an effective manner correspondent to the texture and affine shape adaptation features. In addition, various descriptors, such as color histogram, color moment, color autocorrelogram and color coherency vector, are extracted as the invariant color features. The multiple ant colony optimization (MACOBTC) approach is implemented with whole features to find relevant features. Finally, the relevant features are utilized for the greedy learning of deep Boltzmann machine classifier (GDBM). The proposed approach obtains effective performance and accurate results on four datasets and is analyzed with various parameters such as accuracy, precision, recall, Jaccard, Dice, and Kappa coefficients. The GDBM provides a 25% increase in accuracy compared with existing techniques, such as the a priori classification algorithm.
- Published
- 2019
3. Steady-State and Tracking Analyses of the Improved Proportionate Affine Projection Algorithm
- Author
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Yinxia Dong, Zongsheng Zheng, and Zhigang Liu
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Mathematical optimization ,Steady state (electronics) ,Computer science ,020206 networking & telecommunications ,02 engineering and technology ,Affine projection ,Tracking (particle physics) ,Affine projection algorithm ,Affine shape adaptation ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,Algorithm design ,Electrical and Electronic Engineering ,General expression ,Algorithm - Abstract
The performance analysis of the improved proportionate affine projection (IPAP) algorithm is performed in this brief. Based on the energy-conservation arguments, the steady-state analysis of the IPAP algorithm is performed, which provides a general expression of steady-state excess mean-square error for the proportionate-type affine projection algorithms. The tracking behavior is also studied and the step size that optimizes the tracking performance is provided. Simulation results confirm the accuracy of the proposed expressions under different operating scenarios.
- Published
- 2018
4. Learning Affine Hull Representations for Multi-Shot Person Re-Identification
- Author
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Richard J. Radke, Ziyan Wu, and Srikrishna Karanam
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business.industry ,Feature vector ,Pattern recognition ,02 engineering and technology ,010501 environmental sciences ,Machine learning ,computer.software_genre ,01 natural sciences ,Data modeling ,Affine shape adaptation ,Discriminative model ,Affine hull ,Metric (mathematics) ,0202 electrical engineering, electronic engineering, information engineering ,Media Technology ,Feature (machine learning) ,020201 artificial intelligence & image processing ,Affine transformation ,Artificial intelligence ,Electrical and Electronic Engineering ,business ,computer ,0105 earth and related environmental sciences ,Mathematics - Abstract
We consider the person re-identification problem, assuming the availability of a sequence of images for each person, commonly referred to as video-based or multi-shot re-identification. We approach this problem from the perspective of learning discriminative distance metric functions. While existing distance metric learning methods typically employ the average feature vector as the data exemplar, this discards the inherent structure of the data. To overcome this issue, we describe the image sequence data using affine hulls. We show that directly computing the distance between the closest points on these affine hulls as in existing recognition algorithms is not sufficiently discriminative in the context of person re-identification. To this end, we incorporate affine hull data modeling into the traditional distance metric learning framework, learning discriminative feature representations directly using affine hulls. We perform extensive experiments on several publicly available data sets to show that the proposed approach improves the performance of existing metric learning algorithms irrespective of the feature space employed to perform metric learning. Furthermore, we advance the state of the art on iLIDS-VID, PRID, and SAIVT, with absolute rank-1 performance improvements of 6.0%, 11.4%, and 6.0% respectively.
- Published
- 2018
5. An Efficient Four-Parameter Affine Motion Model for Video Coding
- Author
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Houqiang Li, Li Li, Lin Sixin, Huanbang Chen, Zhu Li, Dong Liu, Feng Wu, and Yang Haitao
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Motion compensation ,Harris affine region detector ,business.industry ,ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION ,030229 sport sciences ,02 engineering and technology ,Quarter-pixel motion ,Affine shape adaptation ,03 medical and health sciences ,0302 clinical medicine ,Motion field ,Motion estimation ,0202 electrical engineering, electronic engineering, information engineering ,Media Technology ,020201 artificial intelligence & image processing ,Computer vision ,Affine transformation ,Artificial intelligence ,Electrical and Electronic Engineering ,business ,Affine arithmetic ,ComputingMethodologies_COMPUTERGRAPHICS ,Mathematics - Abstract
In this paper, we study a simplified affine motion model-based coding framework to overcome the limitation of a translational motion model and maintain low-computational complexity. The proposed framework mainly has three key contributions. First, we propose to reduce the number of affine motion parameters from 6 to 4. The proposed four-parameter affine motion model can not only handle most of the complex motions in natural videos, but also save the bits for two parameters. Second, to efficiently encode the affine motion parameters, we propose two motion prediction modes, i.e., an advanced affine motion vector prediction scheme combined with a gradient-based fast affine motion estimation algorithm and an affine model merge scheme, where the latter attempts to reuse the affine motion parameters (instead of the motion vectors) of neighboring blocks. Third, we propose two fast affine motion compensation algorithms. One is the one-step sub-pixel interpolation that reduces the computations of each interpolation. The other is the interpolation-precision-based adaptive block size motion compensation that performs motion compensation at the block level rather than the pixel level to reduce the number of interpolation. Our proposed techniques have been implemented based on the state-of-the-art high-efficiency video coding standard, and the experimental results show that the proposed techniques altogether achieve, on average, 11.1% and 19.3% bits saving for random access and low-delay configurations, respectively, on typical video sequences that have rich rotation or zooming motions. Meanwhile, the computational complexity increases of both the encoder and the decoder are within an acceptable range.
- Published
- 2018
6. Medical image rigid registration using a novel binary feature descriptor and modified affine transform
- Author
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Praveen Kumar Reddy Yelampalli, Jagadish Nayak, and Vilas H. Gaidhane
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Computer science ,Local binary patterns ,business.industry ,Feature vector ,Feature extraction ,Image registration ,Pattern recognition ,02 engineering and technology ,030218 nuclear medicine & medical imaging ,Affine shape adaptation ,03 medical and health sciences ,0302 clinical medicine ,Image texture ,Feature (computer vision) ,Computer Science::Computer Vision and Pattern Recognition ,Signal Processing ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,Computer vision ,Computer Vision and Pattern Recognition ,Affine transformation ,Artificial intelligence ,Electrical and Electronic Engineering ,business ,Software - Abstract
Robust and reliable features with noise immunity, rotation-invariance, and low-dimensionality are the challenging aspects of pattern recognition. In this study, the authors presented a novel low-dimensional binary feature descriptor local diagonal Laplacian pattern (LDLP) for medical image registration. LDLP method is developed by defining the local relationship between a centre pixel and its diagonal neighbours and encoding it to a binary feature vector. The idea of centre-diagonal pixel correlation has drastically reduced the length of the feature vector without compromising the quality of local texture analysis. In the proposed work, first, the LDLP feature histograms of computed tomography (CT), magnetic resonance (MR), and ultrasound images are obtained. Further, these LDLP features of individual medical images are considered as target/fixed objects while their corresponding rotated and noisy features are considered as moving/floating objects to perform mono-modal rigid registration using an improved Procrustes analysis-based affine transform. The registration quality is examined by calculating the squared intensity error and the results are compared with the existing binary patterns such as local binary patterns, local tetra patterns, and local diagonal extrema patterns. The proposed LDLP feature descriptor-based rigid registration has attained relatively better performance in terms of registration accuracy and computational complexity.
- Published
- 2018
7. Algebraic Clustering of Affine Subspaces
- Author
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René Vidal and Manolis C. Tsakiris
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FOS: Computer and information sciences ,Computer Vision and Pattern Recognition (cs.CV) ,Computer Science - Computer Vision and Pattern Recognition ,02 engineering and technology ,Affine geometry ,Affine combination ,Artificial Intelligence ,Affine hull ,0202 electrical engineering, electronic engineering, information engineering ,Mathematics ,Discrete mathematics ,business.industry ,Applied Mathematics ,020206 networking & telecommunications ,Affine plane ,Affine shape adaptation ,Algebra ,Affine coordinate system ,ComputingMethodologies_PATTERNRECOGNITION ,Computational Theory and Mathematics ,Affine space ,020201 artificial intelligence & image processing ,Computer Vision and Pattern Recognition ,Affine transformation ,Artificial intelligence ,business ,Software - Abstract
Subspace clustering is an important problem in machine learning with many applications in computer vision and pattern recognition. Prior work has studied this problem using algebraic, iterative, statistical, low-rank and sparse representation techniques. While these methods have been applied to both linear and affine subspaces, theoretical results have only been established in the case of linear subspaces. For example, algebraic subspace clustering (ASC) is guaranteed to provide the correct clustering when the data points are in general position and the union of subspaces is transversal . In this paper we study in a rigorous fashion the properties of ASC in the case of affine subspaces. Using notions from algebraic geometry, we prove that the homogenization trick , which embeds points in a union of affine subspaces into points in a union of linear subspaces, preserves the general position of the points and the transversality of the union of subspaces in the embedded space, thus establishing the correctness of ASC for affine subspaces.
- Published
- 2018
8. On the Set of Points of Smoothness for the Value Function of Affine Optimal Control Problems
- Author
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Francesco Boarotto and Davide Barilari
- Subjects
0209 industrial biotechnology ,Smoothness ,Control and Optimization ,Dense set ,Control-affine systems ,Applied Mathematics ,010102 general mathematics ,Mathematical analysis ,02 engineering and technology ,Optimal control ,01 natural sciences ,Regularity ,Affine shape adaptation ,020901 industrial engineering & automation ,Affine combination ,Affine hull ,Bellman equation ,Value function ,Applied mathematics ,Affine transformation ,0101 mathematics ,Mathematics - Abstract
We study the regularity properties of the value function associated with an affine optimal control problem with quadratic cost plus a potential, for a fixed final time and initial point. Without assuming any condition on singular minimizers, we prove that the value function is continuous on an open and dense subset of the interior of the attainable set. As a byproduct we obtain that it is actually smooth on a possibly smaller set, still open and dense.
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- 2018
9. Locally strongly convex affine hyperspheres realizing Chen's equality
- Author
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Cece Li and Huiyang Xu
- Subjects
Pure mathematics ,Applied Mathematics ,010102 general mathematics ,Affine differential geometry ,01 natural sciences ,Affine plane ,010101 applied mathematics ,Affine coordinate system ,Affine geometry ,Affine shape adaptation ,Algebra ,Affine representation ,Affine hull ,Affine group ,Mathematics::Differential Geometry ,0101 mathematics ,Analysis ,Mathematics - Abstract
In affine differential geometry of hypersurface, C. Scharlach et al. found an inequality involving intrinsic and extrinsic curvatures, and classified elliptic and hyperbolic affine hyperspheres realizing the equality if an affine invariant 2-dimensional distribution D 2 is integrable. In this paper, we continue to study affine hyperspheres realizing the equality, including parabolic affine hyperspheres. As main results, firstly we classify parabolic affine hyperspheres realizing the equality if its scalar curvature is constant, or D 2 is integrable. Next, by introducing a well-defined 3-dimensional distribution D 3 when D 2 is not integrable, we complete the classification of locally strongly convex affine hyperspheres realizing the equality if D 3 is integrable. Finally, we pose a conjecture and a problem in order to determine all affine hyperspheres attaining the equality.
- Published
- 2017
10. An interior affine scaling cubic regularization algorithm for derivative-free optimization subject to bound constraints
- Author
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Detong Zhu and Xiaojin Huang
- Subjects
Mathematical optimization ,021103 operations research ,Applied Mathematics ,0211 other engineering and technologies ,Monotone cubic interpolation ,010103 numerical & computational mathematics ,02 engineering and technology ,01 natural sciences ,Polynomial interpolation ,Affine shape adaptation ,Affine coordinate system ,Computational Mathematics ,Affine combination ,Affine hull ,Derivative-free optimization ,Applied mathematics ,Affine transformation ,0101 mathematics ,Mathematics - Abstract
In this paper, we introduce an affine scaling cubic regularization algorithm for solving optimization problem without available derivatives subject to bound constraints employing a polynomial interpolation approach to handle the unavailable derivatives of the original objective function. We first define an affine scaling cubic model of the approximate objective function which is obtained by the polynomial interpolation approach with an affine scaling method. At each iteration a candidate search direction is determined by solving the affine scaling cubic regularization subproblem and the new iteration is strictly feasible by way of an interior backtracking technique. The global convergence and local superlinear convergence of the proposed algorithm are established under some mild conditions. Preliminary numerical results are reported to show the effectiveness of the proposed algorithm.
- Published
- 2017
11. An Affine Invariant Iterative Image Matching Approach for Matching Images with Different Views and Illumination
- Author
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Soundararajan K, Jayachandra Prasad T, and Rajasekhar D
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Matching (statistics) ,Computer science ,Image matching ,business.industry ,Template matching ,0211 other engineering and technologies ,General Engineering ,02 engineering and technology ,Topology ,Affine shape adaptation ,0202 electrical engineering, electronic engineering, information engineering ,Affine invariant ,020201 artificial intelligence & image processing ,Computer vision ,Artificial intelligence ,business ,021101 geological & geomatics engineering - Published
- 2017
12. On Para-Complex Affine Hyperspheres
- Author
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Zuzanna Szancer
- Subjects
010308 nuclear & particles physics ,Applied Mathematics ,Nuclear Theory ,010102 general mathematics ,01 natural sciences ,Affine plane ,Combinatorics ,Affine geometry ,Affine coordinate system ,Affine shape adaptation ,Mathematics (miscellaneous) ,Affine combination ,Affine hull ,0103 physical sciences ,Affine group ,Physics::Atomic and Molecular Clusters ,Physics::Atomic Physics ,Mathematics::Differential Geometry ,Affine transformation ,0101 mathematics ,Mathematics - Abstract
In this paper we introduce a notion of a para-complex affine hypersphere. We give a complete local classification of such hypersurfaces and give several examples. It turns out that every para-complex affine hypersphere can be constructed from (real) affine hyperspheres. As an application, we classify all 2-dimensional para-complex affine hyperspheres.
- Published
- 2017
13. Convergence and Performance Analysis of the Affine Projection Algorithm with Direction Error
- Author
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Lei Si, DaMeng Dai, YongFeng Zhi, and FuQian Shi
- Subjects
Adaptive filter ,Combinatorics ,Affine shape adaptation ,Harris affine region detector ,Affine combination ,Applied Mathematics ,Convergence (routing) ,Applied mathematics ,Statistical analysis ,Electrical and Electronic Engineering ,Affine arithmetic ,Affine projection algorithm ,Mathematics - Published
- 2017
14. The Shape Interaction Matrix-Based Affine Invariant Mismatch Removal for Partial-Duplicate Image Search
- Author
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Zhouchen Lin, Hongbin Zha, and Yang Lin
- Subjects
Homogeneous coordinates ,business.industry ,Iterative method ,Feature extraction ,0102 computer and information sciences ,02 engineering and technology ,Real image ,01 natural sciences ,Computer Graphics and Computer-Aided Design ,Affine shape adaptation ,010201 computation theory & mathematics ,Robustness (computer science) ,Burstiness ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,Computer vision ,Artificial intelligence ,Affine transformation ,business ,Algorithm ,Software ,Mathematics - Abstract
Mismatch removal is a key step in many computer vision problems. In this paper, we handle the mismatch removal problem by adopting shape interaction matrix (SIM). Given the homogeneous coordinates of the two corresponding point sets, we first compute the SIMs of the two point sets. Then, we detect the mismatches by picking out the most different entries between the two SIMs. Even under strong affine transformations, outliers, noises, and burstiness, our method can still work well. Actually, this paper is the first non-iterative mismatch removal method that achieves affine invariance. Extensive results on synthetic 2D points matching data sets and real image matching data sets verify the effectiveness, efficiency, and robustness of our method in removing mismatches. Moreover, when applied to partial-duplicate image search, our method reaches higher retrieval precisions with shorter time cost compared with the state-of-the-art geometric verification methods.
- Published
- 2017
15. Performance Comparison of Different Affine Projection Algorithms for Noise Minimization from Speech Signals
- Author
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V. K. Gupta, Mahesh Chandra, and Deepak Gupta
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Computer Networks and Communications ,Computer science ,business.industry ,020209 energy ,0211 other engineering and technologies ,Pattern recognition ,02 engineering and technology ,Affine projection ,Affine shape adaptation ,Noise minimization ,Performance comparison ,021105 building & construction ,0202 electrical engineering, electronic engineering, information engineering ,Artificial intelligence ,business - Published
- 2017
16. Affine registration of point clouds based on point-to-plane approach
- Author
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Artyom Makovetskii, Vitaly Kober, Dmitrii Tihonkih, and Sergei Voronin
- Subjects
Harris affine region detector ,Plane (geometry) ,business.industry ,ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION ,Point cloud ,Iterative closest point ,Point set registration ,02 engineering and technology ,General Medicine ,01 natural sciences ,010309 optics ,Affine shape adaptation ,0103 physical sciences ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,Point (geometry) ,Computer vision ,Affine transformation ,Artificial intelligence ,business ,Mathematics - Abstract
The problem of aligning of 3D point data is the known registration task. The most popular registration algorithm is the Iterative Closest Point (ICP). This paper proposes a new algorithm for affine registration of point clouds by incorporating the affine transformation into the point-to-plane ICP algorithm. At each iterative step of the algorithm, a closed-form solution for the affine transformation is derived.
- Published
- 2017
17. Improvement of affine iterative closest point algorithm for partial registration
- Author
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Shaoyi Du, Jianmin Dong, and Zhongmin Cai
- Subjects
0209 industrial biotechnology ,Harris affine region detector ,Iterative method ,Iterative closest point ,Image registration ,02 engineering and technology ,Missing data ,Affine shape adaptation ,020901 industrial engineering & automation ,Outlier ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,Computer Vision and Pattern Recognition ,Affine transformation ,Algorithm ,Software ,Mathematics - Abstract
In this study, partial registration problem with outliers and missing data in the affine case is discussed. To solve this problem, a novel objective function is proposed based on bidirectional distance and trimmed strategy, and then a new affine trimmed iterative closest point algorithm is given. First, when bidirectional distance measurement is applied, the ill-posed partial registration problem in the affine case is prevented. Second, the overlapping percentage is solved by using trimmed strategy which uses as many correct overlapping points as possible. The authors' method computes the affine transformation, correspondence and overlapping percentage automatically at each iterative step. In this way, it handles partially overlapping registration with outliers and missing data in the affine case well. Experimental results demonstrate that their method is more robust and precise than the state-of-the-art algorithms. It also has good convergence and similar running time with traditional algorithms.
- Published
- 2016
18. Estimating affine-invariant structures on triangle meshes
- Author
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Thales Vieira, Maria Gorete Carreira Andrade, Dimas Martínez, and Thomas Lewiner
- Subjects
Discrete mathematics ,Pure mathematics ,General Engineering ,020207 software engineering ,02 engineering and technology ,Computer Graphics and Computer-Aided Design ,Affine plane ,Human-Computer Interaction ,Affine coordinate system ,Affine geometry ,Affine shape adaptation ,Affine combination ,Affine hull ,Affine group ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,Affine transformation ,Mathematics - Abstract
Affine invariant measures are powerful tools to develop robust shape descriptors that can be applied, for example, to shape matching, shape retrieval, or symmetry detection problems. In this work we introduce estimators for the affine structure of surfaces represented by triangle meshes, i.e. affine co-normal and normal vectors, affine curvature tensors, affine mean and Gaussian curvatures, and affine principal directions and curvatures. The proposed method estimates the affine normal using a finite differences scheme together with a least-squares approximation, followed by a weighted average strategy to approach discrete affine curvature tensors. When compared to the exact geometric measures of analytic models, experiments on regular meshes obtain small error, which decreases for finer meshes, and outperforms the state-of-the-art method in some cases. Experiments to evaluate affine invariance show that the difference between measures before and after equi-affine transformations remains small even after large deformations.
- Published
- 2016
19. Affine invariants of generalized polygons and matching under affine transformations
- Author
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Edgar Chávez, Ana C. Chávez Cáliz, and Jorge L. López-López
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Discrete mathematics ,Control and Optimization ,010102 general mathematics ,02 engineering and technology ,Computer Science::Computational Geometry ,Generalized polygon ,01 natural sciences ,Computer Science Applications ,Combinatorics ,Affine shape adaptation ,Computational Mathematics ,Affine combination ,Computational Theory and Mathematics ,Affine hull ,Polygon ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,Geometry and Topology ,Affine transformation ,0101 mathematics ,Invariant (mathematics) ,Complex number ,Mathematics - Abstract
A generalized polygon is an ordered set of vertices. This notion generalizes the concept of the boundary of a polygonal shape because self-intersections are allowed. In this paper we study the problem of matching generalized polygons under affine transformations. Our approach is based on invariants. Firstly we associate an ordered set of complex numbers with each polygon and construct a collection of complex scalar functions on the space of plane polygons. These invariant functions are defined as quotients of the so-called Fourier descriptors, also known as discrete Fourier transforms.Each one of these functions is invariant under similarity transformations; that is, the function associates the same complex number to similar polygons. Moreover, if two polygons are affine related (one of them is the image of the other under an affine transformation), the pseudo-hyperbolic distance between their associated values is a constant that depends only on the affine transformation involved, but independent of the polygons.More formally, given a collection { Z 1 , Z 2 , ź , Z m } of n-sided polygons in the plane and a query polygon W, we give algorithms to find all Z ź such that f ( Z ź ) = W + Δ W , where f is an unknown affine transformation and Δ W = ( Δ w 1 , ź , Δ w n ) with | Δ w k | ź ź , where ź is certain tolerance.
- Published
- 2016
20. Quantization of the affine group of a local field
- Author
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Victor Gayral, David Jondreville, Laboratoire de Mathématiques de Reims (LMR), Université de Reims Champagne-Ardenne (URCA)-Centre National de la Recherche Scientifique (CNRS), and Gayral, Victor
- Subjects
Pure mathematics ,[MATH.MATH-OA]Mathematics [math]/Operator Algebras [math.OA] ,FOS: Physical sciences ,[MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA] ,01 natural sciences ,[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR] ,Affine representation ,Affine hull ,0103 physical sciences ,Affine group ,FOS: Mathematics ,0101 mathematics ,Operator Algebras (math.OA) ,Mathematical Physics ,[MATH.MATH-GR] Mathematics [math]/Group Theory [math.GR] ,Mathematics ,[MATH.MATH-QA] Mathematics [math]/Quantum Algebra [math.QA] ,Applied Mathematics ,010102 general mathematics ,[MATH.MATH-FA] Mathematics [math]/Functional Analysis [math.FA] ,Mathematics - Operator Algebras ,Mathematical Physics (math-ph) ,Affine plane ,Functional Analysis (math.FA) ,Mathematics - Functional Analysis ,Affine shape adaptation ,Affine coordinate system ,Affine space ,[MATH.MATH-QA]Mathematics [math]/Quantum Algebra [math.QA] ,010307 mathematical physics ,Geometry and Topology ,[MATH.MATH-OA] Mathematics [math]/Operator Algebras [math.OA] ,Quotient group - Abstract
For a non Archimedean local field which is not of characteristic $2$, nor an extension of $\mathbb Q_2$, we construct a pseudo-differential calculus covariant under a unimodular subgroup of the affine group of the field. Our phase space is a quotient group of the covariance group. Our main result is a generalisation on that context of the Calder\'on-Vaillancourt estimate. Our construction can be thought as the non Archimedean version of Unterberger's Fuchs calculus and our methods are mainly based on Wigner functions and on coherent states transform., Comment: to appear in JFG
- Published
- 2018
21. On affine translation surfaces in affine space
- Author
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Dan Yang and Yu Fu
- Subjects
Applied Mathematics ,010102 general mathematics ,Mathematical analysis ,0102 computer and information sciences ,01 natural sciences ,Affine plane ,Affine geometry ,Affine coordinate system ,Affine shape adaptation ,Affine combination ,010201 computation theory & mathematics ,Affine hull ,Affine group ,Affine transformation ,0101 mathematics ,Analysis ,Mathematics - Abstract
In this work we give a systemic study of affine translation surfaces in affine 3-dimensional space. Specifically, we obtain the complete classification of minimal affine translation surfaces. Moreover, we consider affine translation surfaces with some natural geometric conditions, such as constant affine mean curvature and constant Gauss–Kronecker curvature. Some characterization results with these geometric conditions are also obtained.
- Published
- 2016
22. Reference‐omitted affine soft correspondence algorithm
- Author
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Jie Yang, Shengzheng Wang, Peng-peng Zhang, and Yu Qiao
- Subjects
Harris affine region detector ,Matching (graph theory) ,Iterative method ,020206 networking & telecommunications ,Scale (descriptive set theory) ,02 engineering and technology ,Set (abstract data type) ,Affine shape adaptation ,Signal Processing ,Outlier ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,Computer Vision and Pattern Recognition ,Affine transformation ,Electrical and Electronic Engineering ,Algorithm ,Software ,Mathematics - Abstract
In this study, an affine registration algorithm with reference-omitted scheme and soft correspondence is proposed. It is an iterative method with two-step matching process at each iteration, named as forward matching and backward matching. Due to the introduction of backward matching, two sets of points are alternately to be reference set, such that the selection of reference set is omitted. Failure caused by different reference sets can be corrected with the reference-omitted scheme, and even there is obvious difference in scale. Additionally, soft correspondence is applied to avoid estimating the initial transformations. The simulation and real experimental results show that the proposed method substantially outperforms the current affine registration methods, especially when the scale difference between two sets of points is obvious or there are outliers in one set.
- Published
- 2016
23. Affine realizations with affine state processes for stochastic partial differential equations
- Author
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Stefan Tappe
- Subjects
Statistics and Probability ,Applied Mathematics ,Probability (math.PR) ,010102 general mathematics ,Mathematical analysis ,Mathematical Finance (q-fin.MF) ,01 natural sciences ,FOS: Economics and business ,Affine shape adaptation ,Affine geometry ,Affine coordinate system ,010104 statistics & probability ,Affine combination ,Affine geometry of curves ,Quantitative Finance - Mathematical Finance ,Modeling and Simulation ,Affine hull ,Affine group ,FOS: Mathematics ,Applied mathematics ,Affine transformation ,0101 mathematics ,Mathematics - Probability ,60H15, 91G80 ,Mathematics - Abstract
The goal of this paper is to clarify when a stochastic partial differential equation with an affine realization admits affine state processes. This includes a characterization of the set of initial points of the realization. Several examples, as the HJMM equation from mathematical finance, illustrate our results., 27 pages
- Published
- 2016
24. Analysis of the Fitting Accuracy of the 3d Affine Transformation Applied to Cartosat-1 (IRS P5) Satellite Stereo Imagery
- Author
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Ali Azizi and Farzaneh Dadras Javan
- Subjects
Harris affine region detector ,business.industry ,Distortion (optics) ,Terrain ,Residual ,Affine shape adaptation ,Geography ,Photogrammetry ,Position (vector) ,Computer vision ,Affine transformation ,Artificial intelligence ,business ,Remote sensing - Abstract
Since few years ago it has been generally accepted without any dispute that the 3D affine transformation applied to high-resolution satellite imageries (HRSI), produces results as accurate as those obtained by the RPCs derived from rigorous photogrammetric model. However, as the higher order terms are absent in the affine transformation, the degree of success of this model obviously hinges upon the geometric nature of the imagery to be geo-rectified. In authors view, there are a latent confusion and misunderstanding in the minds of the photogrammetric practitioners as regards the potential of the 3D affine transformation as a replacement model for the geometric correction of the HRSI. The main intention of this paper is, therefore, to analyse the 3D affine transformation by concentrating more on its limitations. To obtain deeper insight into the nature of the 3D affine model, it is applied to images with larger field of view as well as the images of highly mountainous terrains. The geo-coding success of the affine model is then evaluated by comparing the object coordinates of a dense cloud of homologous points derived by the affine model with the object coordinates of the same points obtained by the standard terrain-independent rational functions. Extensive tests conducted over excessively mountainous as well as the hilly terrains indicate that there are clear distortion trends in the residual ground coordinates that cannot be fully absorbed into the 3D affine coefficients. The sources of these non-linear trends such as the satellite attitude and position variations, the terrain relief, the earth curvature and their impact on the final accuracy are analysed using the scatter patterns of the residual errors.
- Published
- 2016
25. Affine invariant shape projection distribution for shape matching using relaxation labelling
- Author
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Boli Xiong, Wei Wang, Xingwei Yan, Gangyao Kuang, and Yongmei Jiang
- Subjects
Harris affine region detector ,business.industry ,ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION ,020206 networking & telecommunications ,Point set registration ,02 engineering and technology ,Relaxation labelling ,Topology ,Affine coordinate system ,Affine shape adaptation ,Affine combination ,Active shape model ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,Computer Vision and Pattern Recognition ,Artificial intelligence ,Affine transformation ,business ,Algorithm ,Software ,ComputingMethodologies_COMPUTERGRAPHICS ,Mathematics - Abstract
Shape is considered to be one of the most promising tools to represent and recognise an object. In this study, an effective and rigorous shape matching algorithm is developed based on a new descriptor and relaxation labelling technique. For each contour point, the descriptor captures the distribution of all points within the shape region along the vector perpendicular to that from the centroid to the point. In addition to stable affine invariance, the descriptor is robust to noise since it makes use of all points in the shape region. The descriptor distance is used to initialise the contour point matching probability, and relaxation labelling technique is utilised to update the matching probability using a new compatibility coefficient function, which is defined based on the shape projection preserving characteristic. The experiments on synthetic and real remote sensing data are provided to test the performance of the authors’ proposed algorithm. Compared to other four state-of-the-art contour-based shape matching algorithms, their algorithm is more robust and capable of shape matching under affine transformations and noise.
- Published
- 2016
26. Dense Correspondence using Multilevel Segmentation and Affine Transformation
- Author
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Seungryong Kim, Kihong Park, Sungil Choi, and Kwanghoon Sohn
- Subjects
Affine shape adaptation ,Computer science ,Scale-space segmentation ,Segmentation ,Affine transformation ,Topology ,Algorithm - Published
- 2016
27. Affine‐scale invariant feature transform and two‐dimensional principal component analysis: a novel framework for affine and scale invariant face recognition
- Author
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K. N. Balasubramanya Murthy, S Natarajan, Akshay Kumar. C, Vinay S. Shekhar, and A. Vinay
- Subjects
Harris affine region detector ,business.industry ,3D single-object recognition ,020206 networking & telecommunications ,Pattern recognition ,02 engineering and technology ,Facial recognition system ,Affine shape adaptation ,Hessian affine region detector ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,Computer vision ,Computer Vision and Pattern Recognition ,Artificial intelligence ,Affine transformation ,Invariant (mathematics) ,business ,Quaternion ,Software ,Mathematics - Abstract
Face recognition (FR) is one of the most effervescent fields of research with extensive applications that span numerous domains, and it stands resolutely as one of the most challenging problems in computer vision. The accuracy of FR systems is severely affected when two images under consideration for a match, vary in their scale and/or affine angles. The prevalent affine and scale invariant recognition systems have been predominantly developed only for objects, and hence in this study, the authors propose a novel approach for faces based on the affine-SIFT (ASIFT) and two-dimensional principal component analysis (2DPCA) techniques, to accomplish the formidable task of facial image recognition, invariant of scale and affine angles, i.e. the ability to simulate with enough accuracy, all the distortions caused by the differences in resolution and the variation of the camera optical axis direction. In the formulation of ASIFT-2DPCA, they investigate three different variants of 2DPCA: classical 2DPCA, quaternion 2DPCA and sparse 2DPCA to gauge as to which is more effective. The authors'experimentations will demonstrate that the proposed approach can robustly handle affine and scale variations, and hence provide better accuracy and matching performance than the state-of-the-art methodologies.
- Published
- 2016
28. Affine metrics of locally strictly convex surfaces in affine 4-space
- Author
-
Juan J. Nuño-Ballesteros and Luis Enrique Sánchez
- Subjects
Discrete mathematics ,Pure mathematics ,Mathematics::Complex Variables ,010102 general mathematics ,05 social sciences ,01 natural sciences ,Affine plane ,Affine coordinate system ,Affine shape adaptation ,Affine geometry ,Affine representation ,Affine hull ,0502 economics and business ,Affine group ,Mathematics::Differential Geometry ,Geometry and Topology ,Affine transformation ,0101 mathematics ,050203 business & management ,Mathematics - Abstract
We introduce a new family of affine metrics on a locally strictly convex surface M in affine 4-space. Then, we define the symmetric and antisymmetric equiaffine planes associated with each metric. We show that if M is immersed in a locally strictly convex hyperquadric, then the symmetric and the antisymmetric planes coincide and contain the affine normal of the hyperquadric. In particular, any surface immersed in a locally strictly convex hyperquadric is affine semiumbilical with respect to the symmetric or antisymmetric equiaffine planes.
- Published
- 2016
29. Affine Eikonal, Wavization and Wigner Function
- Author
-
Akihiro Ogura
- Subjects
010308 nuclear & particles physics ,05 social sciences ,01 natural sciences ,Affine shape adaptation ,Affine coordinate system ,Affine geometry ,Affine combination ,Affine geometry of curves ,Quantum mechanics ,0502 economics and business ,0103 physical sciences ,Affine group ,Wigner distribution function ,Affine transformation ,050203 business & management ,Mathematical physics ,Mathematics - Abstract
The aim in this paper is to construct an affine transformation using the classical physics analogy between the fields of optics and mechanics. Since optics and mechanics both have symplectic structures, the concept of optics can be replaced by that of mechanics and vice versa. We list the four types of eikonal (generating functions). We also introduce a unitary operator for the affine transformation. Using the unitary operator, the kernel (propagator) is calculated and the wavization (quantization) of the Gabor function is discussed. The dynamic properties of the affine transformed Wigner function are also discussed.
- Published
- 2016
30. On linear convergence of projected gradient method for a class of affine rank minimization problems
- Author
-
Su Zhang and Yuning Yang
- Subjects
0301 basic medicine ,Control and Optimization ,Matrix completion ,Applied Mathematics ,Strategy and Management ,010103 numerical & computational mathematics ,01 natural sciences ,Affine shape adaptation ,03 medical and health sciences ,030104 developmental biology ,Affine combination ,Rate of convergence ,Affine hull ,Applied mathematics ,Affine transformation ,0101 mathematics ,Business and International Management ,Gradient method ,Linear equation ,Mathematics - Abstract
The affine rank minimization problem is to find a low-rank matrix satisfying a set of linear equations, which includes the well-known matrix completion problem as a special case and draws much attention in recent years. In this paper, a new model for affine rank minimization problem is proposed. The new model not only enhances the robustness of affine rank minimization problem, but also leads to high nonconvexity. We show that if the classical projected gradient method is applied to solve our new model, the linear convergence rate can be established under some conditions. Some preliminary experiments have been conducted to show the efficiency and effectiveness of our method.
- Published
- 2016
31. FPGA based accelerated 3D affine transform for real-time image processing applications
- Author
-
Swapna Banerjee, Pulak Mondal, and Pradyut Kumar Biswal
- Subjects
General Computer Science ,Pixel ,Computer science ,business.industry ,ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION ,Parallel algorithm ,Top-hat transform ,Image registration ,Image processing ,02 engineering and technology ,030218 nuclear medicine & medical imaging ,Affine shape adaptation ,03 medical and health sciences ,0302 clinical medicine ,Control and Systems Engineering ,Digital image processing ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,Computer vision ,Affine transformation ,Artificial intelligence ,Electrical and Electronic Engineering ,business - Abstract
Display Omitted In the proposed algorithm, simultaneously 4 pixel/voxel locations can be transformed to compute AT of the entire image.The proposed architecture requires only relevant frames instead of all the frames simultaneously.The faster implementation of the affine transform is useful during image registration of the 3D bio-medical images. Affine Transform (AT) is widely used in high-speed image processing systems. This transform plays an important role in various high-speed image processing applications. AT, an important process during the intensity-based image registration, is applied iteratively during the registration. This is also used for the analysis of the interior of an organ and to get a better view of the organs from various angles in 3D coordinate system. Hence, for real-time medical image registration and visualization of the acquired volumetric images, acceleration of AT is very much sought for. In this paper, a parallel and pipelined architecture of the proposed AT algorithm has been presented. This will accelerate the transform process and reduce the processing time of medical image registration. The architecture is mapped in Field-Programmable Gate Array (FPGA) for prototyping and verification. The results show that the computational complexity of the proposed parallel algorithm is almost 4 times better than that of the conventional algorithm.
- Published
- 2016
32. Invariant Sets for Switching Affine Systems Subject to Semi-Algebraic Constraints**Research supported by the Belgian Interuniversity Attraction Poles, and by the ARC grant 13/18-054 from Communaute´ francaise de Belgique - Actions de Recherche Concerteés. R.M. Jungers is a F.R.S.-FNRS Research Associate
- Author
-
Nikolaos Athanasopoulos and Raphaël M. Jungers
- Subjects
Discrete mathematics ,Convex hull ,0209 industrial biotechnology ,Invariant polynomial ,Linear system ,010103 numerical & computational mathematics ,02 engineering and technology ,01 natural sciences ,Affine shape adaptation ,Algebra ,020901 industrial engineering & automation ,Control and Systems Engineering ,Affine hull ,Affine transformation ,Invariant measure ,0101 mathematics ,Invariant (mathematics) ,Mathematics - Abstract
We study the problem of computing the maximal admissible positively invariant set for discrete time switching affine systems subject to basic semi-algebraic constraints. First, we obtain inner ϵ-approximations of the minimal invariant set. Second, following recent results for switching linear systems (Athanasopoulos and Jungers, 2016), we apply an algebraic lifting on the system and obtain a polyhedral representation of the constraint set. Working on this lifted state space offers two distinct advantages, namely (i) we can verify inclusion of an e-inflation of the minimal invariant set in the constraint set and (ii) under proper assumptions, we can characterize and compute the maximal admissible invariant set, which is also a basic semi-algebraic set. Consequently, we are able to identify and recover admissible invariant sets for switching affine systems even when only non-convex invariant sets exist. The underlying algorithms involve only linear operations and convex hull computations.
- Published
- 2016
33. 2D piecewise affine models approximate real continuous dynamics up to invariant sets**This work was supported in part by the projects GeMCo (ANR 2010 BLANC020101), RESET (Bioinformatique, ANR-11-BINF-0005), and by the LABEX SIGNALIFE (ANR-ll-LABX-0028-01)
- Author
-
Madalena Chaves and Jean-Luc Gouzé
- Subjects
0301 basic medicine ,0209 industrial biotechnology ,Mathematical analysis ,02 engineering and technology ,Piecewise linear function ,Affine coordinate system ,Affine shape adaptation ,03 medical and health sciences ,030104 developmental biology ,020901 industrial engineering & automation ,Affine combination ,Control and Systems Engineering ,Affine hull ,Affine group ,Piecewise ,Affine transformation ,Mathematics - Abstract
Piecewise affine models often provide a good approximation to describe continuous systems, but may involve a high degree of simplification. To compare solutions of the continuous and piecewise affine models, it is important to quantify the differences between solutions in each region of the state space. As an approach, we will use enveloping "bands" to characterize continuous activation or inhibition functions, and then describe the differences between continuous and piecewise affine solutions in terms of the width δ of these bands. As a case study, we will consider the negative feedback loop, a classical motif in two dimensions which results in oscillating behaviour. For this example, it is shown that the two types of models may differ only on a compact invariant set (the interior of a limit cycle), whose diameter is a function of the band width δ.
- Published
- 2016
34. Affine processes with compact state space
- Author
-
Martin Larsson and Paul Krühner
- Subjects
Statistics and Probability ,Pure mathematics ,affine processes ,compact state space ,Markov chains ,01 natural sciences ,010104 statistics & probability ,60J27 ,Affine combination ,Complex space ,60J25 ,Affine hull ,FOS: Mathematics ,0101 mathematics ,Mathematics ,Probability (math.PR) ,010102 general mathematics ,Affine plane ,Affine shape adaptation ,Affine coordinate system ,Hyperplane ,Affine space ,60J75 ,Statistics, Probability and Uncertainty ,Mathematics - Probability - Abstract
The behavior of affine processes, which are ubiquitous in a wide range of applications, depends crucially on the choice of state space. We study the case where the state space is compact, and prove in particular that (i) no diffusion is possible; (ii) jumps are possible and enforce a grid-like structure of the state space; (iii) jump components can feed into drift components, but not vice versa. Using our main structural theorem, we classify all bivariate affine processes with compact state space. Unlike the classical case, the characteristic function of an affine process with compact state space may vanish, even in very simple cases., Electronic Journal of Probability, 23, ISSN:1083-6489
- Published
- 2018
35. Computer Vision Meets Geometric Modeling: Multi-view Reconstruction of Surface Points and Normals Using Affine Correspondences
- Author
-
Levente Hajder and Ivan Eichhardt
- Subjects
Harris affine region detector ,business.industry ,QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány ,020207 software engineering ,02 engineering and technology ,Iterative reconstruction ,Object detection ,Affine shape adaptation ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,Computer vision ,Affine transformation ,Artificial intelligence ,business ,Geometric modeling ,Normal ,Surface reconstruction ,ComputingMethodologies_COMPUTERGRAPHICS ,Mathematics - Abstract
A novel surface normal estimator is introduced using affine-invariant features extracted and tracked across multiple views. Normal estimation is robustified and integrated into our reconstruction pipeline that has increased accuracy compared to the State-of-the-Art. Parameters of the views and the obtained spatial model, including surface normals, are refined by a novel bundle adjustment-like numerical optimization. The process is an alternation with a novel robust view-dependent consistency check for surface normals, removing normals inconsistent with the multiple-view track. Our algorithms are quantitatively validated on the reverse engineering of geometrical elements such as planes, spheres, or cylinders. It is shown here that the accuracy of the estimated surface properties is appropriate for object detection. The pipeline is also tested on the reconstruction of man-made and free-form objects.
- Published
- 2017
36. Second-Order Configuration of Local Features for Geometrically Stable Image Matching and Retrieval
- Author
-
Kunio Kashino and Xiaomeng Wu
- Subjects
business.industry ,Feature vector ,media_common.quotation_subject ,Pattern recognition ,Affine shape adaptation ,Interest point detection ,Discriminative model ,Voting ,Media Technology ,Artificial intelligence ,Electrical and Electronic Engineering ,Tuple ,business ,Image retrieval ,Scaling ,Mathematics ,media_common - Abstract
Local features offer high repeatability, which supports efficient matching between images, but they do not provide sufficient discriminative power. Imposing a geometric coherence constraint on local features improves the discriminative power but makes the matching sensitive to anisotropic transformations. We propose a novel feature representation approach to solve the latter problem. Each image is abstracted by a set of tuples of local features. We revisit affine shape adaptation and extend its conclusion to characterize the geometrically stable feature of each tuple. The representation thus provides higher repeatability with anisotropic scaling and shearing than found in previous research. We develop a simple matching model by voting in the geometrically stable feature space, where votes arise from tuple correspondences. To make the required index space linear as regards the number of features, we propose a second approach called a centrality-sensitive pyramid to select potentially meaningful tuples of local features on the basis of their spatial neighborhood information. It achieves faster neighborhood association and has a greater robustness to errors in interest point detection and description. We comprehensively evaluated our approach using Flickr Logos 32, Holiday, Oxford Buildings, and Flickr 100 K benchmarks. Extensive experiments and comparisons with advanced approaches demonstrate the superiority of our approach in image retrieval tasks.
- Published
- 2015
37. Forward Affine Point Set Matching Under Variational Bayesian Framework
- Author
-
Han-Bing Qu, Xi Chen, Song-Tao Wang, and Ming Yu
- Subjects
Mathematical optimization ,Matching (graph theory) ,Materials Science (miscellaneous) ,Covariance ,Directed acyclic graph ,General Business, Management and Accounting ,Industrial and Manufacturing Engineering ,Affine shape adaptation ,Affine combination ,Affine hull ,Graphical model ,Affine transformation ,Business and International Management ,General Agricultural and Biological Sciences ,Algorithm ,Mathematics - Abstract
In this work, the affine point set matching is formulated under a variational Bayesian framework and the model points are projected forward into the scene space by a linear transformation. A directed acyclic graph is presented to represent the relationship between the parameters, latent variables, model and scene point sets and an iterative approximate algorithm is proposed for the estimation of the posterior distributions over parameters. Furthermore, the anisotropic covariance is assumed on the transition variable and one Gaussian component is provided for the inference of outlier points. Experimental results demonstrate that the proposed algorithm achieves good performance in terms of both robustness and accuracy.
- Published
- 2015
38. Metric corrections of the affine camera
- Author
-
Adrien Bartoli, Toby Collins, and Daniel Pizarro
- Subjects
ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION ,Topology ,Affine plane ,Affine geometry ,Affine shape adaptation ,Affine coordinate system ,Affine combination ,Camera auto-calibration ,Affine hull ,Signal Processing ,Computer Vision and Pattern Recognition ,Affine transformation ,Algorithm ,Software ,Mathematics - Abstract
A specific study of the orthographic, weak-perspective and paraperspective cameras.An algebraic procedure solving the affine correction problem for each camera model.A closed-form solution for each camera model.A full characterization of the affine corrections' generic ambiguities for each camera model.An experimental evaluation comparing the algebraic procedures to global polynomial optimization and an interior-point method. Given a general affine camera, we study the problem of finding the closest metric affine camera, where the latter is one of the orthographic, weak-perspective and paraperspective projection models. This problem typically arises in stratified Structure-from-Motion methods such as factorization-based methods. For each type of metric affine camera, we give a closed-form solution and its implementation through an algebraic procedure. Using our algebraic procedure, we can then provide a complete analysis of the problem's generic ambiguity space. This also gives the means to generate the other solutions if any.
- Published
- 2015
39. Steady State Analysis of Convex Combination of Affine Projection Adaptive Filters
- Author
-
Sivabalan Arumugam and S. Radhika
- Subjects
Affine shape adaptation ,Affine coordinate system ,Affine combination ,General Computer Science ,Affine hull ,Mathematical analysis ,General Engineering ,Applied mathematics ,Convex combination ,Affine transformation ,Conic optimization ,Dykstra's projection algorithm ,Mathematics - Published
- 2015
40. Variational Bayesian Approximation for Affine Point Set Matching
- Author
-
Han-Bing Qu, Hai-Jun Tao, Lin Xiang, and Jiaqiang Wang
- Subjects
Affine shape adaptation ,Mathematical optimization ,Harris affine region detector ,Affine combination ,Applied Mathematics ,Affine hull ,Bayesian network ,Point set registration ,Affine transformation ,Electrical and Electronic Engineering ,Directed acyclic graph ,Algorithm ,Mathematics - Abstract
In this paper, we propose a variational approach for the affine point set matching problems under the Bayesian probabilistic framework. A directed acyclic graph is provided for the representation of the joint probability over affine transformation, random variables and the point sets. Based on the directed graph, a variational iterative algorithm is derived to approximate the posteriors of the random variables and the anisotropic Gaussian mixtures are used for the estimation of the spurious outliers instead of the frequently-used uniform distribution. Experimental results demonstrate that our method achieves good performance in terms of both robustness and accuracy and is comparable to other state-of-the-art point registration algorithms especially in the case of complicated outliers.
- Published
- 2015
41. An invariant interest point detector under image affine transformation
- Author
-
Lining Sun, Rui Lin, Haibo Huang, and Rongchuan Sun
- Subjects
Affine shape adaptation ,Affine coordinate system ,Harris affine region detector ,Affine combination ,Hessian affine region detector ,Affine hull ,Metals and Alloys ,General Engineering ,Affine transformation ,Topology ,Algorithm ,Structure tensor ,Mathematics - Abstract
For vision-based mobile robot navigation, images of the same scene may undergo a general affine transformation in the case of significant viewpoint changes. So, a novel method for detecting affine invariant interest points is proposed to obtain the invariant local features, which is coined polynomial local orientation tensor (PLOT). The new detector is based on image local orientation tensor that is constructed from the polynomial expansion of image signal. Firstly, the properties of local orientation tensor of PLOT are analyzed, and a suitable tuning parameter of local orientation tensor is chosen so as to extract invariant features. The initial interest points are detected by local maxima search for the smaller eigenvalues of the orientation tensor. Then, an iterative procedure is used to allow the initial interest points to converge to affine invariant interest points and regions. The performances of this detector are evaluated on the repeatability criteria and recall versus 1-precision graphs, and then are compared with other existing approaches. Experimental results for PLOT show strong performance under affine transformation in the real-world conditions.
- Published
- 2015
42. A Note on the Structure of Affine Subspaces of L2(Rd)
- Author
-
Fengying Zhou and Xiaoyong Xu
- Subjects
Affine shape adaptation ,Affine coordinate system ,Combinatorics ,Affine combination ,Hyperplane ,Affine hull ,Affine group ,Affine space ,General Medicine ,Affine plane ,Mathematics - Abstract
This paper investigates the structure of general affine subspaces of L2(Rd) . For a d × d expansive matrix A, it shows that every affine subspace can be decomposed as an orthogonal sum of spaces each of which is generated by dilating some shift invariant space in this affine subspace, and every non-zero and non-reducing affine subspace is the orthogonal direct sum of a reducing subspace and a purely non-reducing subspace, and every affine subspace is the orthogonal direct sum of at most three purely non-reducing subspaces when |detA| = 2.
- Published
- 2015
43. Affine arc length polylines and curvature continuous uniform B-splines
- Author
-
Florian Käferböck
- Subjects
Aerospace Engineering ,Geometry ,Computer Science::Computational Geometry ,Computer Graphics and Computer-Aided Design ,Affine plane ,Affine geometry ,Affine coordinate system ,Affine shape adaptation ,Affine geometry of curves ,Affine curvature ,Modeling and Simulation ,Affine hull ,Automotive Engineering ,Affine transformation ,Mathematics - Abstract
We study the recently introduced notion of polylines that form a discrete version of planar curves in affine arc length parametrization, showing that they match the control polylines of curvature continuous uniform quadratic B-splines (with analogous results in R n ). It is demonstrated how inflection-free planar curves may be approximated by such affine arc length polylines in a way that the polyline is close to an affinely equidistant discretization of the curve and allows good approximations of the smooth affine curvature.
- Published
- 2014
44. Exemplar-Based Image Inpainting using an Affine Invariant Similarity Measure
- Author
-
Vadim V. Fedorov, Coloma Ballester, Gabriele Facciolo, Pablo Arias, DITIC, universitat Pompeu Fabra, Universitat Pompeu Fabra [Barcelona] (UPF), Centre de Mathématiques et de Leurs Applications (CMLA), École normale supérieure - Cachan (ENS Cachan)-Centre National de la Recherche Scientifique (CNRS), Departament de Tecnologies de la Informació i les Comunicacions, and Facciolo, Gabriele
- Subjects
Computer science ,[INFO.INFO-TS] Computer Science [cs]/Signal and Image Processing ,Inpainting ,ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION ,02 engineering and technology ,Similarity measure ,Topology ,Measure (mathematics) ,Image (mathematics) ,Set (abstract data type) ,[INFO.INFO-CV] Computer Science [cs]/Computer Vision and Pattern Recognition [cs.CV] ,[INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing ,0202 electrical engineering, electronic engineering, information engineering ,Computer vision ,ComputingMethodologies_COMPUTERGRAPHICS ,Harris affine region detector ,business.industry ,Affine Invariance ,[INFO.INFO-CV]Computer Science [cs]/Computer Vision and Pattern Recognition [cs.CV] ,020207 software engineering ,[INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation ,Affine shape adaptation ,Covalent Affinity ,Transformation (function) ,[INFO.INFO-TI] Computer Science [cs]/Image Processing [eess.IV] ,Source Patch ,[INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV] ,020201 artificial intelligence & image processing ,Artificial intelligence ,Inpainting Domain ,[INFO.INFO-MO] Computer Science [cs]/Modeling and Simulation ,business ,Exemplar-based Image Inpainting - Abstract
Comunicació presentada a 11th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2016), celebrat del 27 al 29 de febrer de 2016 a Roma, Itàlia. Patch-based approaches are used in state-of-the-art methods for image inpainting. This paper presents a new method for exemplar-based image inpainting using transformed patches. The transformation is determined for each patch in a fully automatic way from a surrounding texture content. We build upon a recent affine invariant patch similarity measure that performs an appropriate patch comparison by automatically adapting the size and shape of the patches. As a consequence, it intrinsically extends the set of available source patches to copy information from. We incorporate this measure into a variational formulation for inpainting and present a numerical algorithm for optimizing it. We show that our method can be applied to complete a perspectively distorted texture as well as to automatically inpaint one view of a scene using other view of the same scene as a source. We present experimental results both for gray and color images, and a comparison with some exemplar-based image inpainting methods. The first, second and fourth authors acknowledge partial support by the MINECO/FEDER project with reference TIN2015-70410-C2-1-R , the MICINN project with reference MTM2012- 30772, and by GRC reference 2014 SGR 1301, Generalitat de Catalunya. The second and third authors were partly founded by the Centre National dEtudes Spatiales (CNES, MISS Project), BPIFrance and R´egion Ile de France, in the framework of the FUI 18 Plein Phare project, the European Research Council (advanced grant Twelve Labours n246961), the Office of Naval research (ONR grant N00014-14-1-0023), and ANRDGA project ANR-12-ASTR-0035.
- Published
- 2017
45. Chaotic sliding dynamics for planar piecewise affine maps
- Author
-
Claudio A. Buzzi, Joao C. Medrado, and Paulo Ricardo da Silva
- Subjects
Piecewise linear function ,Affine shape adaptation ,Affine coordinate system ,Affine combination ,Affine geometry of curves ,Piecewise linear manifold ,Chaotic ,Piecewise ,Topology ,Mathematics - Abstract
In this work we adapt the theory of piecewise differential systems to the world of piecewise affine maps. Through this adaptation it is possible to define a sliding map in the sense of Filippov. We prove that there exists a choice for the pieces of the piecewise affine map, such that the associate sliding map possesses chaotic dynamics.
- Published
- 2017
46. On four-dimensional Einstein affine hyperspheres
- Author
-
Luc Vrancken, Zejun Hu, Haizhong Li, Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015 (LAMAV), and Centre National de la Recherche Scientifique (CNRS)-Université de Valenciennes et du Hainaut-Cambrésis (UVHC)-INSA Institut National des Sciences Appliquées Hauts-de-France (INSA Hauts-De-France)
- Subjects
Pure mathematics ,010102 general mathematics ,Mathematical analysis ,Einstein metric ,Affine hypersphere ,01 natural sciences ,Affine plane ,010101 applied mathematics ,Affine geometry ,Affine shape adaptation ,Affine coordinate system ,Affine combination ,Computational Theory and Mathematics ,Affine representation ,Affine hull ,Affine group ,Geometry and Topology ,0101 mathematics ,[MATH]Mathematics [math] ,Affine metric ,Analysis ,ComputingMilieux_MISCELLANEOUS ,Mathematics - Abstract
© 2016 Elsevier B.V. It is well-known that Vrancken–Li–Simon classified locally strongly convex affine hyperspheres in Rn+1 whose affine metric are of constant sectional curvatures, but on the other side it is still a difficult problem to classify n-dimensional locally strongly convex affine hyperspheres whose affine metrics are Einstein. In this paper, we have solved the problem in case n=4. publisher: Elsevier articletitle: On four-dimensional Einstein affine hyperspheres journaltitle: Differential Geometry and its Applications articlelink: http://dx.doi.org/10.1016/j.difgeo.2016.10.003 content_type: article copyright: © 2016 Elsevier B.V. All rights reserved. ispartof: Differential Geometry and its Applications vol:50 pages:20-33 status: published
- Published
- 2017
47. Affine focal points for locally strictly convex surfaces in 4-space
- Author
-
Marcelo José Saia, Juan J. Nuño-Ballesteros, and Luis F. Sánchez
- Subjects
Pure mathematics ,Applied Mathematics ,010102 general mathematics ,Mathematical analysis ,01 natural sciences ,Affine plane ,Affine geometry ,Affine coordinate system ,Affine shape adaptation ,Mathematics (miscellaneous) ,Affine combination ,Affine hull ,0103 physical sciences ,Affine group ,010307 mathematical physics ,Affine transformation ,0101 mathematics ,TEORIA DAS SINGULARIDADES ,Mathematics - Abstract
We consider locally strictly convex surfaces M in affine 4-space. By using the metric of the transversal vector field on M we introduce a new affine normal plane and the familly of affine distance functions on M. We show that the singularities of the family of affine distance functions appear at points on the affine normal plane and the affine focal points correspond to degenerate singularities of this family. Moreover we show that if M is immersed in a locally strictly convex hypersurface, then the affine normal plane contains the affine normal vector to the hypersurface and conclude that any surface immersed in a locally strictly convex hypersphere is affine semiumbilical.
- Published
- 2017
48. An improved affine projection algorithm for active noise cancellation
- Author
-
Yunzhuo Sun, Mingjiang Wang, Congyan Zhang, and Yufei Han
- Subjects
Affine shape adaptation ,Variable (computer science) ,Rate of convergence ,Ramer–Douglas–Peucker algorithm ,Control theory ,Convergence (routing) ,Projection (set theory) ,Algorithm ,Signal ,Active noise control ,Mathematics - Abstract
Affine projection algorithm is a signal reuse algorithm, and it has a good convergence rate compared to other traditional adaptive filtering algorithm. There are two factors that affect the performance of the algorithm, which are step factor and the projection length. In the paper, we propose a new variable step size affine projection algorithm (VSS-APA). It dynamically changes the step size according to certain rules, so that it can get smaller steady-state error and faster convergence speed. Simulation results can prove that its performance is superior to the traditional affine projection algorithm and in the active noise control (ANC) applications, the new algorithm can get very good results.
- Published
- 2017
49. Recursive estimation in piecewise affine systems using parameter identifiers and concurrent learning
- Author
-
Martin Buss and Stefan Kersting
- Subjects
0209 industrial biotechnology ,Estimation theory ,02 engineering and technology ,Computer Science Applications ,ddc ,Affine shape adaptation ,Piecewise linear function ,020901 industrial engineering & automation ,Rate of convergence ,Control and Systems Engineering ,Control theory ,Hybrid system ,Convergence (routing) ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,Linear independence ,Affine transformation ,Mathematics - Abstract
Piecewise affine systems constitute a popular framework for the approximation of non-linear systems and the modelling of hybrid systems. This paper addresses the recursive subsystem estimation in continuous-time piecewise affine systems. Parameter identifiers are extended from continuous-time state-space models to piecewise linear and piecewise affine systems. The convergence rate of the presented identifiers is improved further using concurrent learning, which makes concurrent use of current and recorded measurements. In concurrent learning, assumptions on persistence of excitation are replaced by the less restrictive linear independence of the recorded data. The introduction of memory, however, reduces the tracking ability of concurrent learning because errors in the recorded measurements prevent convergence to the true parameters. In order to overcome this limitation, an algorithm is proposed to detect and remove erroneous measurements at run-time and thereby restore the tracking ability. Detai...
- Published
- 2017
50. Quantitative Comparison of Affine Invariant Feature Matching
- Author
-
Levente Hajder, Zoltán Pusztai, Imai, F, Tremeau, A, and Braz, J
- Subjects
Affine shape adaptation ,Affine coordinate system ,Harris affine region detector ,Pure mathematics ,Affine combination ,Affine geometry of curves ,Computer science ,Hessian affine region detector ,Affine hull ,QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány ,Affine transformation - Published
- 2017
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