1,206 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
- Subjects
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
- Subjects
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. Efficient planar affine canonicalization
- Author
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Pedro E. Lopez-de-Teruel, Lorenzo Fernandez-Maimo, and A. Ruiz
- Subjects
Image moment ,business.industry ,Pattern recognition ,02 engineering and technology ,010501 environmental sciences ,01 natural sciences ,Affine shape adaptation ,Affine combination ,Artificial Intelligence ,Signal Processing ,0202 electrical engineering, electronic engineering, information engineering ,Kurtosis ,Canonicalization ,020201 artificial intelligence & image processing ,Computer Vision and Pattern Recognition ,Artificial intelligence ,Affine transformation ,Invariant (mathematics) ,business ,Software ,0105 earth and related environmental sciences ,Mathematics ,Reference frame - Abstract
This paper presents a fast and accurate affine canonicalization method for planar shapes. This method improves on previous ones based on iterative optimization that produce multiple canonical versions. Canonicalization provides a common reference frame for shape comparison without the loss of discrimination ability often caused by invariant features. It also gives for free the alignment transformation between any pair of shapes. The proposed method is based on the properties of the joint angular distribution of marginal skewness and kurtosis, the so-called SK signature, which can be efficiently computed in closed form from the raw image moments. The experiments demonstrate that the method is robust to the non-affine distortions caused by natural perspective image conditions. Thus, it can be used as an automatic preprocessing step to add affine invariance in statistical pattern recognition applications.
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- 2017
11. ISAR cross-range scaling for non-uniform rotating targets using joint affine invariant normalization and weighted average method
- Author
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Fulin Su and Hongxin Yang
- Subjects
Normalization (statistics) ,Mathematical analysis ,0211 other engineering and technologies ,Scaling algorithm ,Angular velocity ,02 engineering and technology ,Combinatorics ,Affine shape adaptation ,Inverse synthetic aperture radar ,0202 electrical engineering, electronic engineering, information engineering ,Earth and Planetary Sciences (miscellaneous) ,Affine invariant ,020201 artificial intelligence & image processing ,Weighted average method ,Electrical and Electronic Engineering ,Scaling ,021101 geological & geomatics engineering ,Mathematics - Abstract
In this letter, we propose a novel cross-range scaling algorithm to estimate the effective rotational velocity (RV) of non-uniform rotating targets by using affine invariant normalization and weigh...
- Published
- 2017
12. A Hybrid Tactic Model Intended for Video Compression Using Global Affine Motion and Local Free-Form Transformation Parameters
- Author
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J. Dinesh Peter, D. Raveena Judie Dolly, and G. Josemin Bala
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Motion compensation ,Multidisciplinary ,business.industry ,ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION ,020206 networking & telecommunications ,02 engineering and technology ,Translation (geometry) ,Affine shape adaptation ,Transformation (function) ,Motion estimation ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,Computer vision ,Artificial intelligence ,Affine transformation ,business ,Group of pictures ,Data compression ,Mathematics - Abstract
Video compression marks its necessity when a huge sized video needs to be transmitted. The process starts with the identification of GoP (group of pictures), which depends on I- (intra), B- (bidirectional) and P- (predicted) frames determination. GoP is fixed, where consecutive frames are placed in an orderly manner based on the GoP size. Conventionally, B-frames lead to buffering of memory within the past and future frames consuming more computational time. Such issues are handled by an adaptive framework for determining frames based on matching criteria rather than fixed GoP. NSEW (North–South–East–West) affine translation (NAT) is proposed for replacing B with either I- or P-frame. The proposed framework involves video compression using affine motion-based free-form transformation and video decompression using warping methodologies for the purpose of compressing and decompressing the video sequence, based on the resulted I- and P-frames. B-spline transformation was also initiated at local level along with global affine transformation to improve the subjective quality of the decompressed video sequence. The methodology was investigated for the file size, computational time, peak-signal-to-noise ratio (PSNR) and Structural Similarity index (SSIM), which proved the superiority of the proposed technique. Further, the methodology was also investigated with optimizing the affine motion parameters (AMP) using nonlinear least squares, Broyden–Fletcher–Goldfarb–Shanno (BFGS) and limited-memory BFGS which yet again proved to be far more superior to conventional techniques with an average PSNR of 38.98 dB with LBFGS. To further improve the subjective quality, affine B-spline-based motion estimation using LBFGS was implemented and observed the average PSNR gain to be 42.03 dB.
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- 2017
13. Distortion calibrating method of measuring rail profile based on local affine invariant feature descriptor
- Author
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Jiuzhen Zeng, Ziji Ma, Tan Jin, Hongli Liu, Yanfu Li, and Chao Wang
- Subjects
business.industry ,Applied Mathematics ,GLOH ,020208 electrical & electronic engineering ,ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION ,Iterative closest point ,Rail profile ,02 engineering and technology ,Condensed Matter Physics ,Physics::Geophysics ,Affine shape adaptation ,Affine geometry ,0202 electrical engineering, electronic engineering, information engineering ,Calibration ,020201 artificial intelligence & image processing ,Computer vision ,Artificial intelligence ,Affine transformation ,Electrical and Electronic Engineering ,Invariant (mathematics) ,business ,Instrumentation ,Algorithm ,Mathematics - Abstract
Measuring rail profile in the presence of multiple degrees of freedom vibration is a very challenging task. This paper presents a novel method based on the local affine invariant feature descriptor to calibrate distorted profiles, which are obtained by traditional rail measurement system. It has three major modules: local affine invariant (LAI) feature descriptor, affine transformation estimation and parameters refinement. LAI feature descriptor is based on the affine geometry invariant and generated by calculating the proportions of different areas. Using the proposed LAI descriptor, we implement a three-stage profile calibration including matching, estimation, and refinement based on grouping and fast iterative closest point (FICP) algorithm. The performance of proposed LAI descriptor and calibrating method is tested by performing extensive experiments. The experimental results show that our LAI descriptor is highly descriptive and robust with respect to varying resolution and noise, and the LAI descriptor based calibration is effective and repeatable.
- Published
- 2017
14. Robust feature matching via support-line voting and affine-invariant ratios
- Author
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Qingwu Hu, Mingyao Ai, Jiayuan Li, and Ruofei Zhong
- Subjects
Image fusion ,Harris affine region detector ,business.industry ,ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION ,0211 other engineering and technologies ,Image registration ,Scale-invariant feature transform ,Pattern recognition ,02 engineering and technology ,RANSAC ,Atomic and Molecular Physics, and Optics ,Computer Science Applications ,Affine shape adaptation ,Computer Science::Computer Vision and Pattern Recognition ,Hessian affine region detector ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,Computer vision ,Affine transformation ,Artificial intelligence ,Computers in Earth Sciences ,business ,Engineering (miscellaneous) ,021101 geological & geomatics engineering ,Mathematics - Abstract
Robust image matching is crucial for many applications of remote sensing and photogrammetry, such as image fusion, image registration, and change detection. In this paper, we propose a robust feature matching method based on support-line voting and affine-invariant ratios. We first use popular feature matching algorithms, such as SIFT, to obtain a set of initial matches. A support-line descriptor based on multiple adaptive binning gradient histograms is subsequently applied in the support-line voting stage to filter outliers. In addition, we use affine-invariant ratios computed by a two-line structure to refine the matching results and estimate the local affine transformation. The local affine model is more robust to distortions caused by elevation differences than the global affine transformation, especially for high-resolution remote sensing images and UAV images. Thus, the proposed method is suitable for both rigid and non-rigid image matching problems. Finally, we extract as many high-precision correspondences as possible based on the local affine extension and build a grid-wise affine model for remote sensing image registration. We compare the proposed method with six state-of-the-art algorithms on several data sets and show that our method significantly outperforms the other methods. The proposed method achieves 94.46% average precision on 15 challenging remote sensing image pairs, while the second-best method, RANSAC, only achieves 70.3%. In addition, the number of detected correct matches of the proposed method is approximately four times the number of initial SIFT matches.
- Published
- 2017
15. 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
16. Affine scale space: an affine invariant image structure to promote the detection of correspondences from stereo images
- Author
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Biao Zhao
- Subjects
Harris affine region detector ,business.industry ,Cognitive Neuroscience ,Gaussian ,ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION ,020206 networking & telecommunications ,02 engineering and technology ,Computer Science Applications ,Scale space ,Affine shape adaptation ,symbols.namesake ,Artificial Intelligence ,Feature (computer vision) ,Computer Science::Computer Vision and Pattern Recognition ,0202 electrical engineering, electronic engineering, information engineering ,symbols ,020201 artificial intelligence & image processing ,Point (geometry) ,Computer vision ,Affine transformation ,Artificial intelligence ,business ,Representation (mathematics) ,Mathematics - Abstract
Calculating the geometry relationship by the positions of the correspondences from stereo images is a fundamental method to obtain the depth information. Such a method was quite widespread and popular thanks to its efficiency and easily accessed implementation. General speaking, the more density of the correspondences are, the more precisely the depth information can be calculated. Theoretically, a sufficient strengthened correspondences match algorithm can be utilized for depth information calculation under any circumstances. Unfortunately, the updated image feature detectors are all sensitive to the view point changes: with the rising of the stereo images' view angle, the number of matched features drastically reduced, resulting in the number of matched features not adequate to cover every details of the stereo images. This disadvantages of feature detections in practice hampers its application for the depth calibration. To tackle the sensitive of view point to stereo images, in this paper, we will propose an affine invariant affine scale space structure, which is more robust to detect the correspondences from stereo images. The purpose of affine scale space is to create a more general approach to the affine invariant image scale representation by modifying the corresponding Gaussian filters in order to cope with the specific change of view point. The affine adaptation of the scale space is to retain a linear relationship with the transiting of the view point. With linear relationship, the affine scale space can be established as a more general approach for the detection of correspondences from stereo images. With a better correspondences detection, a more precise depth information can be made.
- Published
- 2017
17. Partial affine system-based frames and dual frames
- Author
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Yu Tian and Yun-Zhang Li
- Subjects
Harris affine region detector ,General Mathematics ,010102 general mathematics ,General Engineering ,010103 numerical & computational mathematics ,01 natural sciences ,Affine plane ,Affine coordinate system ,Affine shape adaptation ,Affine combination ,Affine hull ,Affine group ,Affine transformation ,0101 mathematics ,Algorithm ,Mathematics - Abstract
In this paper, we introduce the notion of partial affine system that is a subset of an affine system. It has potential applications in signal analysis. A general affine system has been extensively studied; however, the partial one has not. The main focus of this paper is on partial affine system–based frames and dual frames. We obtain a necessary condition and a sufficient condition for a partial affine system to be a frame and present a characterization of partial affine system–based dual frames. Some examples are also provided.
- Published
- 2017
18. A theory of point-wise homography estimation
- Author
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Daniel Barath and Levente Hajder
- Subjects
Harris affine region detector ,Pixel ,business.industry ,Epipolar geometry ,020207 software engineering ,02 engineering and technology ,Affine coordinate system ,Affine shape adaptation ,Affine combination ,Artificial Intelligence ,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 ,business ,Software ,Mathematics ,Homography (computer vision) - Abstract
Estimating homography using only one affine correspondence.The proposed theory makes multi-homography estimation less ambiguous.Stochastic sampling can be omitted from robust homography estimation.Affine-covariant detectors are compared w.r.t. quality of estimated homographies.Equivalence of affine and perspective-invariances for known epipolar geometry. We propose a method, called HAF, to estimate planar homography from an affine correspondence satisfying the epipolar constraint in an image pair. An affine correspondence consists of a point pair and the related local affine transformation mapping the pixels infinitely close to the point locations from the first to the second images. As a minimal solver, it estimates the homography from only one correspondence, however, it is generalized for the over-determined case as well. The required local affinities are obtained by affine-covariant feature detectors accurately. As a side-effect of the tests, the state-of-the-art affine-covariant detectors are compared to each other w.r.t. the accuracy of the estimated point-wise homographies. The proposed method is validated both on the publicly available AdelaideRMF dataset and in a synthetic testing environment.
- Published
- 2017
19. Affine Invariant Description and Large-Margin Dimensionality Reduction for Target Detection in Optical Remote Sensing Images
- Author
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Hong Huo, Laiwen Zheng, Lihong Wan, and Tao Fang
- Subjects
Harris affine region detector ,business.industry ,Dimensionality reduction ,Feature extraction ,0211 other engineering and technologies ,Pattern recognition ,02 engineering and technology ,Geotechnical Engineering and Engineering Geology ,Object detection ,Interest point detection ,Affine shape adaptation ,Hessian affine region detector ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,Computer vision ,Affine transformation ,Artificial intelligence ,Electrical and Electronic Engineering ,business ,021101 geological & geomatics engineering ,Mathematics ,Remote sensing - Abstract
A novel target detection method based on affine invariant interest point detection, feature encoding, and large-margin dimensionality reduction (LDR) is proposed for optical remote sensing images. First, four types of interest point detectors are introduced, and their performance in extracting low-level affine invariant descriptors using affine shape estimation is compared. Such a description can deal with significant affine transformations, including viewpoints. Second, feature encoding, which extends bag-of-words (BOW) by encoding high-order statistics, is selected to generate mid-level representation. Finally, LDR based on the large-margin constraint and stochastic subgradient is introduced to make the high-dimensional mid-level representation applicable for target detection. The experiments on aircraft and vehicle detections illustrate the effectiveness of the affine invariant description and LDR (compared with principal component analysis) in improving the detection performance. The experiments also demonstrate the effectiveness of the proposed method compared with popular approaches including Gabor, HOG, LBP, BOW, and R-CNN.
- Published
- 2017
20. 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
21. 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
22. 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
23. A new two-microphone Gauss-Seidel pseudo affine projection algorithm for speech quality enhancement
- Author
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Mohamed Djendi
- Subjects
Microphone ,Noise reduction ,Speech quality ,Speech recognition ,020206 networking & telecommunications ,02 engineering and technology ,01 natural sciences ,Affine projection algorithm ,Speech enhancement ,Affine shape adaptation ,Affine combination ,Control and Systems Engineering ,0103 physical sciences ,Signal Processing ,0202 electrical engineering, electronic engineering, information engineering ,Gauss–Seidel method ,Electrical and Electronic Engineering ,010301 acoustics ,Algorithm ,Mathematics - Published
- 2017
24. 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
25. 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
- Subjects
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
26. Modified Locally Linear Embedding with Affine Transformation
- Author
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Gajendra Tyagi, Aashish Rao, Durg Singh Chauhan, Pardeep Kumar, and Kanika Mehta
- Subjects
Harris affine region detector ,Computer science ,020206 networking & telecommunications ,02 engineering and technology ,Affine coordinate system ,Affine shape adaptation ,Affine involution ,Affine combination ,Affine hull ,0202 electrical engineering, electronic engineering, information engineering ,Affine space ,020201 artificial intelligence & image processing ,Affine transformation ,Engineering (miscellaneous) ,Algorithm - Abstract
Dimensional reduction is a primary way to analyze and work with complex and large amount of multidimensional data by avoiding the effect of curse of dimensionality. This problem of constructing low dimensional embedding gains importance in number of fields like artificial intelligence, image processing, geographical research and lot more. In this paper, we introduce a modified locally linear embedding, an unsupervised learning algorithm that computes low dimensional data from complex high dimensional data using affine transformation and neighborhood preserving embedding. Unlike novel locally linear embedding, our method is affine invariant where each point is being represented by an affine combination of its neighboring points. At the end, we conduct the experiment to evaluate our proposed method and compare its performance with existing methods. Results show that our proposed method is unaffected by affine transformation, specifically shear while existing methods fail to produce correct results in case of shear.
- Published
- 2017
27. Affine registration of point clouds based on point-to-plane approach
- Author
-
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
28. Performance enhanced spatial video compression using global affine frame reconstruction
- Author
-
D. Raveena Judie Dolly, G. Josemin Bala, and J. Dinesh Peter
- Subjects
Motion compensation ,General Computer Science ,business.industry ,ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION ,Inter frame ,020206 networking & telecommunications ,02 engineering and technology ,Theoretical Computer Science ,Video compression picture types ,Affine shape adaptation ,Modeling and Simulation ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,Computer vision ,Affine transformation ,Artificial intelligence ,business ,Group of pictures ,Mathematics ,Block-matching algorithm ,Reference frame - Abstract
The modern era of information technology suffers a serious loss due to the lack of a cutting edge methodology for storing mega sized videos. It is at this juncture, video compression makes a mark for its necessity. There have been several research outcomes where almost all researchers have followed a particular methodology of adopting GoP (Group of pictures) for video compression, focusing on I (Intra), B (Bi-directional) & P (Predicted) frame determination. These frames remain fixed throughout the process of GoP regardless of the camera motion. Moreover, it also leads to buffering of memory within the past and future thereby consuming more computational time for B-frames. These vital issues are handled by an adaptive framework of determining frames based on a matching criteria rather than utilizing fixed GoP pattern. NSEW affine translation (NAT) is introduced for replacing B-frames with either I or P frame. The framework involves VCAME (Video Compression using Affine Motion Estimation) & VDAW (Video Decompression using Affine Warping) methodologies for compressing and decompressing a video sequence, based on the resulted I & P frames. The methodology was investigated over four vital parameters, the file size, computational time, SSIM (Structural Similarity Index) & PSNR (Peak Signal to Noise ratio), which proved the superiority of the proposed technique. Further, the methodology was also investigated with optimizing the affine motion parameters (AMP) using nonlinear least squares, BFGS (Broyden–Fletcher–Goldfarb–Shanno) and Limited-memory BFGS which yet again proved to be far more superior than conventional techniques yielding an average PSNR gain of 2.52 dB .
- Published
- 2017
29. Improvement of affine iterative closest point algorithm for partial registration
- Author
-
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
30. Geometric affine transformation estimation via correlation filter for visual tracking
- Author
-
Fanghui Liu, Jie Yang, and Tao Zhou
- Subjects
0209 industrial biotechnology ,Harris affine region detector ,business.industry ,Cognitive Neuroscience ,02 engineering and technology ,Computer Science Applications ,Affine shape adaptation ,Matrix (mathematics) ,020901 industrial engineering & automation ,Affine combination ,Artificial Intelligence ,Video tracking ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,Computer vision ,Multiple correlation ,Affine transformation ,Artificial intelligence ,business ,Rotation (mathematics) ,Mathematics - Abstract
Correlation filter achieves promising performance with high speed in visual tracking. However, conventional correlation filter based trackers cannot tackle affine transformation issues such as scale variation, rotation and skew. To address this problem, in this paper, we propose a part-based representation tracker via kernelized correlation filter (KCF) for visual tracking. A Spatial-Temporal Angle Matrix (STAM), severed as confidence metric, is proposed to select reliable patches from parts via multiple correlation filters. These stable patches are used to estimate a 2D affine transformation matrix of the target in a geometric method. Specially, the whole combination scheme for these stable patches is proposed to exploit sampling space in order to obtain numerous affine matrices and their corresponding candidates. The diversiform candidates would help to seek for the optimal candidate to represent the object's accurate affine transformation in a higher probability. Both qualitative and quantitative evaluations on VOT2014 challenge and Object Tracking Benchmark (OTB) show that the proposed tracking method achieves favorable performance compared with other state-of-the-art methods.
- Published
- 2016
31. Estimating affine-invariant structures on triangle meshes
- Author
-
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
32. Affine invariants of generalized polygons and matching under affine transformations
- Author
-
Edgar Chávez, Ana C. Chávez Cáliz, and Jorge L. López-López
- Subjects
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
33. Quantization of the affine group of a local field
- Author
-
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
34. An Affine Motion Model for Removing Rolling Shutter Distortions
- Author
-
Yue Sun, Gang Liu, and Yufen Sun
- Subjects
Harris affine region detector ,Artificial neural network ,business.industry ,Applied Mathematics ,Distortion (optics) ,ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION ,Rolling shutter ,020206 networking & telecommunications ,02 engineering and technology ,Backpropagation ,Affine shape adaptation ,Signal Processing ,0202 electrical engineering, electronic engineering, information engineering ,Piecewise ,020201 artificial intelligence & image processing ,Computer vision ,Artificial intelligence ,Affine transformation ,Electrical and Electronic Engineering ,business ,Mathematics - Abstract
Rolling shutter distortions degrade the quality of videos captured by hand-held cameras. This letter proposes an affine motion model for removing rolling shutter distortions. The model represents the image motion during image capture as a sequence of affine transformations and computes the composition of these affine transformations precisely. Because an affine transformation can be represented by a neural network with one layer of linear neurons, the motion model can be represented by a multilayer neural network of linear neurons. Thus, the backpropagation algorithm can be used to improve the efficiency of the optimization process that estimates the model parameters. The proposed model is calibration-free. It is more general than other rolling shutter motion models because it only assumes that the velocity of the image during image acquisition is piecewise constant. Experimental results demonstrate that the model is more accurate than two state-of-the-art models and that the model parameters can be estimated efficiently.
- Published
- 2016
35. On affine translation surfaces in affine space
- Author
-
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
36. Reference‐omitted affine soft correspondence algorithm
- Author
-
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
37. Affine realizations with affine state processes for stochastic partial differential equations
- Author
-
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
38. Analysis of the Fitting Accuracy of the 3d Affine Transformation Applied to Cartosat-1 (IRS P5) Satellite Stereo Imagery
- Author
-
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
39. Statistical tracking behavior of affine projection algorithm for unity step size
- Author
-
Yongfeng Zhi, Zhen Wang, Xi Zheng, Jun Zhang, and Yunyi Yang
- Subjects
0209 industrial biotechnology ,Applied Mathematics ,System identification ,020206 networking & telecommunications ,02 engineering and technology ,Tracking (particle physics) ,Affine projection algorithm ,Adaptive filter ,Affine shape adaptation ,Computational Mathematics ,Noise ,020901 industrial engineering & automation ,Affine combination ,Control theory ,Convergence (routing) ,0202 electrical engineering, electronic engineering, information engineering ,Algorithm ,Mathematics - Abstract
Since unity step size could guarantee the fastest convergence and more detailed analysis for the affine projection (AP) algorithm, a statistical tracking behavior of AP algorithm is discussed in this paper. Deterministic recursive equations are derived for the mean weight error and mean-square error. All the possible correlations between the adaptive filtering coefficients and the past measurement noise are considered as well.
- Published
- 2016
40. Multiple View Geometry with Multiple Dynamic Affine Cameras
- Author
-
Cheng Wan and Jun Sato
- Subjects
Harris affine region detector ,Computer science ,business.industry ,General Chemistry ,Condensed Matter Physics ,Affine shape adaptation ,Computational Mathematics ,General Materials Science ,Computer vision ,Affine transformation ,Artificial intelligence ,Electrical and Electronic Engineering ,Multiple view ,business - Published
- 2016
41. Quantum image encryption based on generalized affine transform and logistic map
- Author
-
Nanrun Zhou, Xiang-Yang Tao, and Hao-Ran Liang
- Subjects
Harris affine region detector ,Computer science ,Statistical and Nonlinear Physics ,01 natural sciences ,010305 fluids & plasmas ,Theoretical Computer Science ,Electronic, Optical and Magnetic Materials ,Affine coordinate system ,Affine shape adaptation ,Affine combination ,Modeling and Simulation ,0103 physical sciences ,Signal Processing ,Quantum algorithm ,Affine transformation ,Electrical and Electronic Engineering ,Logistic map ,010306 general physics ,Algorithm ,Computer Science::Cryptography and Security ,Quantum computer - Abstract
Quantum circuits of the generalized affine transform are devised based on the novel enhanced quantum representation of digital images. A novel quantum image encryption algorithm combining the generalized affine transform with logistic map is suggested. The gray-level information of the quantum image is encrypted by the XOR operation with a key generator controlled by the logistic map, while the position information of the quantum image is encoded by the generalized affine transform. The encryption keys include the independent control parameters used in the generalized affine transform and the logistic map. Thus, the key space is large enough to frustrate the possible brute-force attack. Numerical simulations and analyses indicate that the proposed algorithm is realizable, robust and has a better performance than its classical counterpart in terms of computational complexity.
- Published
- 2016
42. Shape Interpretation of Second-Order Moment Invariants
- Author
-
Dragiša Žunić and Joviša Žunić
- Subjects
Statistics and Probability ,Image moment ,Applied Mathematics ,Centroid ,02 engineering and technology ,Condensed Matter Physics ,Ellipse ,01 natural sciences ,Vertex (geometry) ,Combinatorics ,Affine shape adaptation ,Modeling and Simulation ,0103 physical sciences ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,Geometry and Topology ,Computer Vision and Pattern Recognition ,Affine transformation ,Invariant (mathematics) ,010303 astronomy & astrophysics ,Shape analysis (digital geometry) ,Mathematics - Abstract
This paper deals with the following problem: What can be said about the shape of an object if a certain invariant of it is known? Such a, herein called, shape invariant interpretation problem has not been studied/solved for the most of invariants, but also it is not known to which extent the shape interpretation of certain invariants does exist. In this paper, we consider a well-known second-order affine moment invariant. This invariant has been expressed recently Xu and Li (2008) as the average square area of triangles whose one vertex is the shape centroid while the remaining two vertices vary through the shape considered. The main results of the paper are (i) the ellipses are shapes which minimize such an average square triangle area, i.e., which minimize the affine invariant considered; (ii) this minimum is $$1/(16\pi ^2)$$1/(16?2) and is reached by the ellipses only. As by-products, we obtain several results including the expression of the second Hu moment invariant in terms of one shape compactness measure and one shape ellipticity measure. This expression further leads to the shape interpretation of the second Hu moment invariant, which is also given in the paper.
- Published
- 2016
43. Affine invariant shape projection distribution for shape matching using relaxation labelling
- Author
-
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
44. Dense Correspondence using Multilevel Segmentation and Affine Transformation
- Author
-
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
45. Affine‐scale invariant feature transform and two‐dimensional principal component analysis: a novel framework for affine and scale invariant face recognition
- Author
-
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
46. Dense Correspondence using Local Regions with Affine Transformations
- Author
-
Alfredo Reyes and Ismael Lopez
- Subjects
Harris affine region detector ,General Computer Science ,Orientation (computer vision) ,business.industry ,3D reconstruction ,ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION ,Scale-invariant feature transform ,02 engineering and technology ,Fault detection and isolation ,Affine shape adaptation ,Virtual image ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,Computer vision ,Affine transformation ,Artificial intelligence ,Electrical and Electronic Engineering ,business ,Mathematics - Abstract
The development of a virtual environments is desirable in many engineering applications for several reasons. For example, it can reduce the number of dangerous operations during the virtual inspection of mines, pipes for gas, water and sewer to inspect its current condition and identify possible failures. The proposal in this paper is an alternative solution to this problem obtaining a virtual image through the reconstruction of the inner pipe for assessment and fault detection. The proposed method employs regions with affine transformations used as dense correspondence, which are calculated through local correspondences, such as the detector/descriptor SIFT (Scale-invariant feature transform). The SIFT is required to obtain the position and orientation of the camera in the captured positions to get the structure of the scene through correspondences and to create a 3D reconstruction.
- Published
- 2016
47. 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
48. 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
49. 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
50. Digital Affine Shear Transforms: Fast Realization and Applications in Image/Video Processing
- Author
-
Xiaosheng Zhuang
- Subjects
Harris affine region detector ,business.industry ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,02 engineering and technology ,01 natural sciences ,Affine shape adaptation ,Affine coordinate system ,Affine combination ,Affine geometry of curves ,0202 electrical engineering, electronic engineering, information engineering ,Affine space ,020201 artificial intelligence & image processing ,Computer vision ,Affine transformation ,Artificial intelligence ,0101 mathematics ,business ,Algorithm ,Affine arithmetic ,Mathematics - Abstract
In this paper, we discuss the digitization and applications of smooth affine shear tight frames, a recently developed new class of directional multiscale representation systems. An affine wavelet tight frame is generated by isotropic dilations and translations of directional wavelet generators, while an affine shear tight frame is generated by anisotropic dilations, shears, and translations of shearlet generators. These two tight frames are actually connected in the sense that an affine shear tight frame can be obtained from an affine wavelet tight frame through subsampling. Consequently, an affine shear tight frame has an underlying filter bank from the MRA structure of its associated affine wavelet tight frame. We discuss the digitization of digital affine shear filter banks associated with the affine shear tight frames. Moreover, we provide the detailed algorithmic steps for both the forward and backward digital affine shear transforms. Analysis of the redundancy rate and computational complexity shows...
- Published
- 2016
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