Fast computation of Legendre and Zernike moments

Mukundan, Ramakrishnan; Ramakrishnan, K. R.

doi:10.1016/0031-3203(95)00011-n

Cited by 224 publications

(110 citation statements)

References 10 publications

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“…The same happens when images are modified to be centered, scaled or changed through linear transformations. These features make them more suitable for image analysis than other existing approaches like Legendre moments [6], though at the expense of a higher computational cost [7]. Figure 1 outlines the algorithm for computing Zernike moments of an order n and a repetition m following the equation 5, and assuming an N xN image size.…”

Section: A Mathematical Formulationmentioning

confidence: 99%

The LRPD test

RauchwergerLawrence

PaduaDavid

1995

SIGPLAN Not.

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Abstract-This work analyzes the most advanced features of the Kepler GPU by Nvidia, mainly dynamic parallelism for launching kernels internally from the GPU and thread scheduling via Hyper-Q. We illustrate several ways to exploit those features from a code which computes Zernike moments, using two different formulations: direct and iterative. This way, we compare how well they can deploy parallelism on the new generation of GPUs. The direct alternative tries to maximize parallelism, while the iterative one increases the operational intensity by reusing results coming from previous iterations. This has allowed us to increase the speed-up factor attained on Fermi architectures versus a code written in C and executed on a multicore CPU. We also succeed on identifying the critical workload which is required by a code to improve its execution on the new GPU platforms endowed with six more times computational cores, and quantify the overhead introduced by the new dynamic programming mechanisms in CUDA.

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Section: A Mathematical Formulationmentioning

confidence: 99%

The LRPD test

RauchwergerLawrence

PaduaDavid

1995

SIGPLAN Not.

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“…Unsurprisingly, these features caught the attention of the image processing community long ago 2,3 and many attempts have been made at reducing their computational cost in order to make them practical. [4][5][6] However, it has been only very recently that the availability of commodity parallel hardware and GPGPU (general-purpose GPU) programming tools have made possible to compute them at interactive frame rates. 7 The basic idea and structure of Zernike polynomials is not only valid in two dimensions, but theoretically also in higherdimensional spaces.…”

Section: Introductionmentioning

confidence: 99%

A parallel implementation of 3D Zernike moment analysis

2011

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Zernike polynomials are a well known set of functions that find many applications in image or pattern characterization because they allow to construct shape descriptors that are invariant against translations, rotations or scale changes. The concepts behind them can be extended to higher dimension spaces, making them also fit to describe volumetric data. They have been less used than their properties might suggest due to their high computational cost.We present a parallel implementation of 3D Zernike moments analysis, written in C with CUDA extensions, which makes it practical to employ Zernike descriptors in interactive applications, yielding a performance of several frames per second in voxel datasets about 200 3 in size.In our contribution, we describe the challenges of implementing 3D Zernike analysis in a general-purpose GPU. These include how to deal with numerical inaccuracies, due to the high precision demands of the algorithm, or how to deal with the high volume of input data so that it does not become a bottleneck for the system.

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“…Another related orthogonal moments, denoted as pseudo-Zernike moments [9], was derived based on the basis set of pseudo-Zernike polynomials. These orthogonal moments have been proved to be less sensitive to image noise as compared to geometric moments, and possess better feature representation ability [12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Translation and scale invariants of Tchebichef moments

Zhu

Xia

et al. 2007

Pattern Recognition

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Abstract⎯Discrete orthogonal moments such as Tchebichef moments have been successfully used in the field of image analysis. However, the invariance property of these moments has not been studied mainly due to the complexity of the problem. Conventionally, the translation and scale invariant functions of Tchebichef moments can be obtained either by normalizing the image or by expressing them as a linear combination of the corresponding invariants of geometric moments. In this paper, we present a new approach that is directly based on Tchebichef polynomials to derive the translation and scale invariants of Tchebichef moments. Both derived invariants are unchanged under image translation and scale transformation. The performance of the proposed descriptors is evaluated using a set of binary characters.Examples of using the Tchebichef moments invariants as pattern features for pattern classification are also provided.

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Fast computation of Legendre and Zernike moments

Cited by 224 publications

References 10 publications

The LRPD test

The LRPD test

A parallel implementation of 3D Zernike moment analysis

Translation and scale invariants of Tchebichef moments

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