Fast computation of separable two-dimensional discrete invariant moments for image classification

Hmimid, Abdeslam; Sayyouri, Mhamed; Qjidaa, Hassan

doi:10.1016/j.patcog.2014.08.020

Cited by 69 publications

(20 citation statements)

References 33 publications

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“…In the next step, each image of the training set was arbitrarily translated with (Δx, Δy) ∈ [− 45,45], subsequently letting φ i = 5 * i be a rotation angle vector with i being an integer and varying from 0 to 35, rotated by ϕ i , and scaled with a scaling factor of α = 0.5 + (2.5 * θ i )/ 360 ∈ [0. 5,3]. Therefore, we obtained a testing set, including 7200 (36 × 200) images in the experiment.…”

Section: Methodsmentioning

confidence: 99%

“…(4) Calculating the projection image in the horizontal direction of the binary image and obtaining the position for the troughs of the projection image, segmentation is performed for the whole image according to the trough point. (5) The projection operation in the vertical direction is the same as that in Step 4. (6) Finally, according to the segmentation position of the binary image, the target image can be separated from the background in the original image.…”

Section: Projection Approach For the Image Translation Invariancementioning

confidence: 99%

“…Moments and moment invariants are global descriptors for image feature extraction that have become a hot topic in the field of image analysis. In recent years, various moments have been widely used in image reconstruction [1,2], image detection [3,4], target classification [5], digital watermarking [6,7], image compression [8], and other applications [9,10]. The study of moments mainly focuses on three directions.…”

Section: Introductionmentioning

confidence: 99%

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Image analysis using modified exponent-Fourier moments

Cui

Xiao

et al. 2019

J Image Video Proc.

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Classic exponent-Fourier moments (EFMs) have been popularly used for image reconstruction and invariant classification. However, EFMs lack natively the translation and scaling-invariant; in addition, they exhibit two types of drawbacks, namely numerical instability and reconstruction error, which in turn influence their reconstruction capability and image classification accuracy. This study considers the challenge of defining modified EFMs (MEFMs), which are based on modified exponent polynomials. In our methods, the basis function of traditional EFMs is appropriately modified, and these modified basis functions are used to replace the original ones. The basis function of the proposed moments is composed of piecewise modified exponent polynomials modulated by a variable parameter exponential envelope. Various types of optimal-order moments can be established by slightly adjusting the bandwidth of the modified basis functions. Finally, we extend the rotation-invariant feature of previous works and propose a new method of scaling and rotation-invariant image recognition using the proposed moments in a log-polar coordinate domain. The translation invariance can then be achieved by an image projection operation, which is substituted for the traditional approach based on the calculation of image geometric moments. The experimental results demonstrate that the MEFMs perform better than traditional EFMs and other classic orthogonal moments including the latest image moments in terms of the image reconstruction capability and the invariant recognition accuracy of smoothing filters, in both noise-free and noisy conditions.

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Section: Methodsmentioning

confidence: 99%

Section: Projection Approach For the Image Translation Invariancementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Image analysis using modified exponent-Fourier moments

Cui

Xiao

et al. 2019

J Image Video Proc.

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“…The theory of moments has been widely used in several fields of image processing, such as image analysis [1][2][3][4][5], image watermarking [6,7], classification and pattern recognition [8][9][10], and video coding [11,12], with considerable and important results. Historically, Hu in 1962 has presented a set of geometric moment invariants [1], used particularly in pattern recognition.…”

Section: Introductionmentioning

confidence: 99%

“…The majority of continuous and discrete orthogonal moments in 2D space have separable basic functions. This property can be expressed as two separate terms by the product tensor of two classical orthogonal polynomials with one variable [10]. Zhu in [20] proposed a set of bivariate discrete and continuous orthogonal polynomials in order to define a series of new set of separable orthogonal moments.…”

Section: Introductionmentioning

confidence: 99%

Image analysis using new set of separable two-dimensional discrete orthogonal moments based on Racah polynomials

Batioua

Benouini

Zenkouar

et al. 2017

J Image Video Proc.

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In this paper, we propose three new separable two-dimensional discrete orthogonal moments baptized: RTM (Racah-Tchebichef moments), RKM (Racah-Krawtchouk moments), and RdHM (Racah-dual Hahn moments). We present a comparative study between our proposed separable two-dimensional discrete orthogonal moments and the classical ones, in terms of gray-level image reconstruction accuracy, including noisy and noise-free conditions. Furthermore, in this study, the local feature extraction capabilities of the proposed moments are described. Finally, a new set of RST (rotation, scaling, and translation) invariants, based on separable proposed moments, is introduced in this paper for the first time, and their description performances are highly tested as pattern features for image classification in comparison with the traditional moment invariants. The experimental results show that the new set of moments is potentially useful in the field of image analysis.

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