Rotation invariants of vector fields from orthogonal moments

Yang, Bo; Kostková, Jitka; Flusser, Jan; Suk, Tomáš; Bujack, Roxana

doi:10.1016/j.patcog.2017.09.004

Cited by 31 publications

(18 citation statements)

References 27 publications

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“…The amplitudes of 9 moments of the rotated images and the original image when different values of

are taken are given in the tables above. Through comparison of the listed data, it is found that the amplitudes of the same FrPHFMs of all rotated images are approximately equal, indicating that the amplitudes of FrPHFMs are invariant to rotation [ 36 ].…”

Section: Experiments and Analysis Of Experimental Resultsmentioning

confidence: 99%

Invariant Image Representation Using Novel Fractional-Order Polar Harmonic Fourier Moments

Wang

Gao

Yang

et al. 2021

Sensors

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Continuous orthogonal moments, for which continuous functions are used as kernel functions, are invariant to rotation and scaling, and they have been greatly developed over the recent years. Among continuous orthogonal moments, polar harmonic Fourier moments (PHFMs) have superior performance and strong image description ability. In order to improve the performance of PHFMs in noise resistance and image reconstruction, PHFMs, which can only take integer numbers, are extended to fractional-order polar harmonic Fourier moments (FrPHFMs) in this paper. Firstly, the radial polynomials of integer-order PHFMs are modified to obtain fractional-order radial polynomials, and FrPHFMs are constructed based on the fractional-order radial polynomials; subsequently, the strong reconstruction ability, orthogonality, and geometric invariance of the proposed FrPHFMs are proven; and, finally, the performance of the proposed FrPHFMs is compared with that of integer-order PHFMs, fractional-order radial harmonic Fourier moments (FrRHFMs), fractional-order polar harmonic transforms (FrPHTs), and fractional-order Zernike moments (FrZMs). The experimental results show that the FrPHFMs constructed in this paper are superior to integer-order PHFMs and other fractional-order continuous orthogonal moments in terms of performance in image reconstruction and object recognition, as well as that the proposed FrPHFMs have strong image description ability and good stability.

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“…The amplitudes of 9 moments of the rotated images and the original image when different values of

Section: Experiments and Analysis Of Experimental Resultsmentioning

confidence: 99%

Invariant Image Representation Using Novel Fractional-Order Polar Harmonic Fourier Moments

Wang

Gao

Yang

et al. 2021

Sensors

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“…According to the above formula, the rotation angle φ could be estimated by the inverse trigonometric function. GFrEMs of any order could be used to estimate the rotation angle [35]. From Section 2.3, we know that the selection of t will lead to different focus areas.…”

Section: Rotation Angle Estimationmentioning

confidence: 99%

Accurate Computation of Fractional-Order Exponential Moments

Hao

et al. 2020

Security and Communication Networks

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Exponential moments (EMs) are important radial orthogonal moments, which have good image description ability and have less information redundancy compared with other orthogonal moments. Therefore, it has been used in various fields of image processing in recent years. However, EMs can only take integer order, which limits their reconstruction and antinoising attack performances. The promotion of fractional-order exponential moments (FrEMs) effectively alleviates the numerical instability problem of EMs; however, the numerical integration errors generated by the traditional calculation methods of FrEMs still affect the accuracy of FrEMs. Therefore, the Gaussian numerical integration (GNI) is used in this paper to propose an accurate calculation method of FrEMs, which effectively alleviates the numerical integration error. Extensive experiments are carried out in this paper to prove that the GNI method can significantly improve the performance of FrEMs in many aspects.

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“…Figure 68 shows an adaptive sampling technique based on importance to preserve features in the data [210,211,212]. Moments-based pattern detection can be used to find rotation-invariant patterns [213,214,215]. For algorithms, we have completed the initial R&D phase for our four mature algorithms (STDA04-5).…”

Section: Solution Strategymentioning

confidence: 99%

ECP Software Technology Capability Assessment Report

Heroux

McInnes

Thakur

et al. 2020

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The Exascale Computing Project (ECP) Software Technology (ST) Focus Area is responsible for developing critical software capabilities that will enable successful execution of ECP applications, and for providing key components of a productive and sustainable Exascale computing ecosystem that will position the US Department of Energy (DOE) and the broader high performance (HPC) community with a firm foundation for future extreme-scale computing capabilities.This ECP ST Capability Assessment Report (CAR) provides an overview and assessment of current ECP ST capabilities and activities, giving stakeholders and the broader HPC community information that can be used to assess ECP ST progress and plan their own efforts accordingly. ECP ST leaders commit to updating this document on regular basis (every six to 12 months). Highlights from this version of the report are presented here.What is new in CAR V2.0: CAR V2.0 contains the following updates relative to CAR V1.5.• We introduce the FY20-23 project structure. ECP ST now consists of 6 (up from 5) level-3 (L3) technical areas, introducing the NNSA ST L3 area, which brings into one L3 the ECP open source development efforts at NNSA labs that are of particular importance to the rest of ECP. The number of ECP ST level-4 (L4) subprojects has been reduced from 55 to 33. The strategic aggregation of projects into fewer and larger units enables us to better manage L4 subprojects consistently as a portfolio. See Section 1.2.• We describe new and enhanced project management processes and resources including our iterative planning process, new KPP-3 capability integration process, a product dictionary and dependency management database. These new project features and related dashboards enable more insight and better information to effectively manage efforts across ECP. See Section 2.• The two-page summaries of each ECP L4 projects have been updated to reflect recent progress and next steps. See Section 4.• The Extreme-scale Scientific Software Stack (E4S) is further described. The third release, which is also the first major public release Version 1.0, was November 18, 2019. E4S is the primary integration and delivery vehicle for ECP ST capabilities. See Section 2.1.1.• The ECP ST SDK effort has further refined its groupings. See Section 2.1.2.The Exascale Computing Project Software Technology (ECP ST) focus area represents the key bridge between Exascale systems and the scientists developing applications that will run on those platforms. ECP ST efforts contribute to 70 software products (Section 2.1.3) in six technical areas (Table 1). Since the publishing of CAR V1.5, we have introduced a product dictionary of official product names, which enables more rigorous mapping of ECP ST deliverables to stakeholders (Section 2.1.4).Programming Models & Runtimes: In addition to developing key enhancements to MPI and OpenMP for scalable systems with accelerated node architectures, we are working on performance portability layers (Kokkos and RAJA) and participating in OpenMP and OpenACC so...

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Rotation invariants of vector fields from orthogonal moments

Cited by 31 publications

References 27 publications

Invariant Image Representation Using Novel Fractional-Order Polar Harmonic Fourier Moments

Invariant Image Representation Using Novel Fractional-Order Polar Harmonic Fourier Moments

Accurate Computation of Fractional-Order Exponential Moments

ECP Software Technology Capability Assessment Report

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