Discrete Tchebichef Moments Research Articles

Efficient watermarking algorithm for digital audio/speech signal

Ensuring conflicting requirements such as imperceptibility, payload capacity, and robustness, becomes a great challenge for a robust audio/speech watermarking algorithm. To achieve this, this paper proposes a blind and robust audio/speech watermarking algorithm that combines the discrete Tchebichef moment transform (DTMT), the chaotic system of the mixed linear–nonlinear coupled map lattices (MLNCML), and discrete wavelet transform (DWT). The watermark is encrypted by the MLNCML system, and then it is embedded in the norm of the Tchebichef moments of the low frequency components. DTMT and MLNCML are used to achieve high robustness, high payload capacity, and high security, while DWT is used to achieve a satisfactory level of imperceptibility. In addition, the adopted strategy has a blind nature, where no original audio/speech is needed in watermark extraction. Compared to other existing audio/speech watermarking algorithms, the proposed algorithm gives better results in terms of robustness and payload capacity while keeping the embedding effect non-perceptible and undetectable.

RETRACTED ARTICLE: Soft computing-based edge-enhanced dominant peak and discrete Tchebichef extraction for image segmentation and classification using DCML-IC

Texture analysis is a very predominant scope in the area of computer vision and associated fields. In this work, edge-enhanced dominant valley and discrete Tchebichef (EDV-DT) method is presented to eradicate noise and segment image into number of partitions with higher accuracy and lesser time. In EDV-DT method, an edge-enhancing anisotropic diffusion filtering technique is used to perform the preprocessing for MRI, CT and texture features. The adaptive anisotropic diffusion creates scale space and reduces the image noise without removing the texture image content (i.e., edges, lines) that is found to be essential for texture image segmentation. Followed by preprocessing, histogram dominant peak valley segmentation technique is applied to segment the localization of region of interest. Valleys in histogram for the preprocessed images help in segmenting the texture image into equal-sized texture regions. Finally, with the segmented images, discrete Tchebichef moment feature extraction is applied to extract relevant features from the segmented texture image for reducing the dimensionality. This in turn helps in improving the feature extraction rate. Further a deep convolution multinomial logarithmic-based image classification (DCML-IC) model is presented for predicting results via positive and negative fact classification. The proposed system provides the better prediction of accuracy and the prediction of time to compare the other existing methods.

Efficient compression of bio-signals by using Tchebichef moments and Artificial Bee Colony

In this paper, an algorithm is proposed for efficient compression of bio-signals based on discrete Tchebichef moments and Artificial Bee Colony (ABC). The Tchebichef moments are used to extract features of the bio-signals, then, the ABC algorithm is used to select of the optimum features which achieve the best bio-signal quality for a specific compression ratio (CR). The proposed algorithm has been tested by using different datasets of Electrocardiogram (ECG), Electroencephalogram (EEG), and Electromyogram (EMG). The optimum feature selection using ABC significantly improve the quality of the reconstructed bio-signals. Different numerical experiments are performed to compress different records of ECG, EEG and EMG bio-signals by using the proposed algorithm and the most recent existing methods. The performance of the proposed algorithm and the other existing methods are evaluated using different metrics such as CR, PRD, and peak signal to noise ratio (PSNR). The comparison has shown that, at the same CR, the proposed compression algorithm yields the best quality of the reconstructed signals over the other existing methods.

Dispersal ability determines the scaling properties of species abundance distributions: a case study using arthropods from the Azores

Species abundance distributions (SAD) are central to the description of diversity and have played a major role in the development of theories of biodiversity and biogeography. However, most work on species abundance distributions has focused on one single spatial scale. Here we used data on arthropods to test predictions obtained with computer simulations on whether dispersal ability influences the rate of change of SADs as a function of sample size. To characterize the change of the shape of the SADs we use the moments of the distributions: the skewness and the raw moments. In agreement with computer simulations, low dispersal ability species generate a hump for intermediate abundance classes earlier than the distributions of high dispersal ability species. Importantly, when plotted as function of sample size, the raw moments of the SADs of arthropods have a power law pattern similar to that observed for the SAD of tropical tree species, thus we conjecture that this might be a general pattern in ecology. The existence of this pattern allows us to extrapolate the moments and thus reconstruct the SAD for larger sample sizes using a procedure borrowed from the field of image analysis based on scaled discrete Tchebichef moments and polynomials.

Multimodal medical image fusion based on discrete Tchebichef moments and pulse coupled neural network

ABSTRACTMultimodal medical image fusion plays a vital role in clinical diagnoses and treatment planning. In many image fusion methods‐based pulse coupled neural network (PCNN), normalized coefficients are used to motivate the PCNN, and this makes the fused image blur, detail loss, and decreases contrast. Moreover, they are limited in dealing with medical images with different modalities. In this article, we present a new multimodal medical image fusion method based on discrete Tchebichef moments and pulse coupled neural network to overcome the aforementioned problems. First, medical images are divided into equal‐size blocks and the Tchebichef moments are calculated to characterize image shape, and energy of blocks is computed as the sum of squared non‐DC moment values. Then to retain edges and textures, the energy of Tchebichef moments for blocks is introduced to motivate the PCNN with adaptive linking strength. Finally, large firing times are selected as coefficients of the fused image. Experimental results show that the proposed scheme outperforms state‐of‐the‐art methods and it is more effective in processing medical images with different modalities. © 2017 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 27, 57–65, 2017

Evolutionary optimized discrete Tchebichef moments for image compression applications

Evolutionary optimized coefficients of discrete orthogonal Tchebichef moment transform (TMT) are utilized in this study to ameliorate the quality of the traditional moments-based image compression methods. Most of the existing methods compute moment-transform coefficients for the input image and then select the coefficients sequentially downward to a certain order based on the desired compression ratio. However, the proposed method divides the input image into nonoverlapping square blocks of specic size in order to circumvent the problem of numerical instability and then computes the TMT coefficients for each block. In this work, a real-coded genetic algorithm is employed to optimize the TMT coefficients of each block, which produces reconstructed images of better quality for the desired compression ratio. Here the optimization is carried out by minimizing the mean square error function. Standard test images of two different sizes (128 � 128 and 256 � 256) have been subjected to the proposed compression method for the block sizes (4 � 4 and 8 � 8) in order to assess its performance. The results reveal that the proposed real-coded genetic algorithm-based method outperforms others, namely the conventional sequential selection method and simple random optimization method, for the chosen input images in terms of the task of compression.

Fast Computation of Sliding Discrete Tchebichef Moments and Its Application in Duplicated Regions Detection

Computational load remains a major concern when processing signals by means of sliding transforms. In this paper, we present an efficient algorithm for the fast computation of one-dimensional and two-dimensional sliding discrete Tchebichef moments. To do so, we first establish the relationships that exist between the Tchebichef moments of two neighboring windows taking advantage of Tchebichef polynomials’ properties. We then propose an original way to fast compute the moments of one window by utilizing the moment values of its previous window. We further theoretically establish the complexity of our fast algorithm and illustrate its interest within the framework of digital forensics and more precisely the detection of duplicated regions in an audio signal or an image. Our algorithm is used to extract local features of such a signal tampering. Experimental results show that its complexity is independent of the window size, validating the theory. They also exhibit that our algorithm is suitable to digital forensics and beyond to any applications based on sliding Tchebichef moments.

No-Reference Image Blur Assessment Based on Discrete Orthogonal Moments.

Blur is a key determinant in the perception of image quality. Generally, blur causes spread of edges, which leads to shape changes in images. Discrete orthogonal moments have been widely studied as effective shape descriptors. Intuitively, blur can be represented using discrete moments since noticeable blur affects the magnitudes of moments of an image. With this consideration, this paper presents a blind image blur evaluation algorithm based on discrete Tchebichef moments. The gradient of a blurred image is first computed to account for the shape, which is more effective for blur representation. Then the gradient image is divided into equal-size blocks and the Tchebichef moments are calculated to characterize image shape. The energy of a block is computed as the sum of squared non-DC moment values. Finally, the proposed image blur score is defined as the variance-normalized moment energy, which is computed with the guidance of a visual saliency model to adapt to the characteristic of human visual system. The performance of the proposed method is evaluated on four public image quality databases. The experimental results demonstrate that our method can produce blur scores highly consistent with subjective evaluations. It also outperforms the state-of-the-art image blur metrics and several general-purpose no-reference quality metrics.

Quaternion Discrete Tchebichef Moments and Their Applications

The concept of the quaternion is useful for colour image processing and recognition. This paper introduces quaternion discrete Tchebichef moments (QTM), which use the traditional Tchebichef moments (TM) of each colour channel to describe colour images. A set of invariants that are invariant to translation and scale transformations is introduced for colour object recognition and image classification. A theoretical framework is provided for the recognition of colour face images by combining the proposed quaternion Tchebichef moment functions with the sparse representation classification (SRC) strategy for improving recognition despite partial occlusions. Simulation results on standard colour face databases demonstrate the effectiveness of the proposed algorithm, even when the images include Gaussian or pepper-and-salt noise.

Automated pollen identification using microscopic imaging and texture analysis

Pollen identification is required in different scenarios such as prevention of allergic reactions, climate analysis or apiculture. However, it is a time-consuming task since experts are required to recognize each pollen grain through the microscope. In this study, we performed an exhaustive assessment on the utility of texture analysis for automated characterisation of pollen samples. A database composed of 1800 brightfield microscopy images of pollen grains from 15 different taxa was used for this purpose. A pattern recognition-based methodology was adopted to perform pollen classification. Four different methods were evaluated for texture feature extraction from the pollen image: Haralick's gray-level co-occurrence matrices (GLCM), log-Gabor filters (LGF), local binary patterns (LBP) and discrete Tchebichef moments (DTM). Fisher's discriminant analysis and k-nearest neighbour were subsequently applied to perform dimensionality reduction and multivariate classification, respectively. Our results reveal that LGF and DTM, which are based on the spectral properties of the image, outperformed GLCM and LBP in the proposed classification problem. Furthermore, we found that the combination of all the texture features resulted in the highest performance, yielding an accuracy of 95%. Therefore, thorough texture characterisation could be considered in further implementations of automatic pollen recognition systems based on image processing techniques.

Psychovisual threshold on large Tchebichef moment for image compression

JPEG standard transforms an 8×8 image pixel into a requency domain. The discontinuities of the intensity image between adjacent image blocks cause the visual artifacts due to inter-block correlations in image reconstruction. The blocking artifacts appear by the pixel intensity value discontinuities which occur along block boundaries. This research proposes the psychovisual threshold on large Tchebichef moment to minimize the blocking artifacts. The psychovisual threshold is practically the best measure for the optimal amount of frequency image signals in the image coding. The psychovisual threshold is a basic element prior to generating quantization tables in image compression. The psychovisual threshold on the large Tchebichef moments has given significant improvements in the quality of image output. The experimental results show that the smooth psychovisual threshold on the large discrete Tchebichef moment produces high quality image output and largely free of any visual artifacts.

Texture classification using discrete Tchebichef moments

In this paper, a method to characterize texture images based on discrete Tchebichef moments is presented. A global signature vector is derived from the moment matrix by taking into account both the magnitudes of the moments and their order. The performance of our method in several texture classification problems was compared with that achieved through other standard approaches. These include Haralick's gray-level co-occurrence matrices, Gabor filters, and local binary patterns. An extensive texture classification study was carried out by selecting images with different contents from the Brodatz, Outex, and VisTex databases. The results show that the proposed method is able to capture the essential information about texture, showing comparable or even higher performance than conventional procedures. Thus, it can be considered as an effective and competitive technique for texture characterization.

Chinese Character Recognition by Tchebichef Moment Features

Abstract — Moment descriptors have long been applied in object recognition since the early years of the development of the moment theories. Nowadays, discrete orthogonal moments have been studied and proposed for they are superior to traditional continuous ones. In this paper, a set of moment features extracted from the discrete Tchebichef moments for Chinese character recognition is presented. A new method of evaluating the variance values of each moment feature is applied in this research. Tested on a set of 6,763 Chinese characters, our newly proposed Tchebichef moment features perform very well in distinguishing all Chinese character pairs that have similar structures. Index Terms — Discrete orthogonal moments, tchebichef moments, Chinese character recognition. I. I NTRODUCTION Since Hu [1] introduced the moment methods in 1961, moment descriptors have been widely used in image representation, pattern recognition, and object classification. One of the applications using moment features is the Chinese character recognition. Chinese characters are very different from many other languages in conveying information, while the structure of a character is a key to its meaning and pronunciation. Many feature extraction methods applied in the Chinese character recognition systems are based on the local features, such as strokes and feature points [2]-[5]. While the existing methods are quite efficient in general, there are some difficulties to distinguish two characters when they have very close structures. On the other hand, the moment method has the advantage of utilizing the global features of the Chinese characters, therefore, it can be used as a complementary scheme to overcome the obstacles confronted by other systems. Some Chinese character recognition systems based on the orthogonal moment descriptors have been reported [6]-[8]. Recently, the emergence of discrete orthogonal moments has substantially enriched the moment methods. Moments based on Tchebichef and Krawtchouk polynomials were introduced by Mukundan

Image reconstruction from continuous Gaussian–Hermite moments implemented by discrete algorithm

The problem of image reconstruction from its statistical moments is particularly interesting to researchers in the domain of image processing and pattern recognition. Compared to geometric moments, the orthogonal moments offer the ability to recover much more easily the image due to their orthogonality, which allows reducing greatly the complexity of computation in the phase of reconstruction. Since the 1980s, various orthogonal moments, such as Legendre moments, Zernike moments and discrete Tchebichef moments have been introduced early or late to image reconstruction. In this paper, another set of orthonormal moments, the Gaussian-Hermite moments, based on Hermite polynomials modulated by a Gaussian envelope, is proposed to be used for image reconstruction. Especially, the paper's focus is on the determination of the optimal scale parameter and the improvement of the reconstruction result by a post-processing which make Gaussian-Hermite moments be useful and comparable with other moments for image reconstruction. The algorithms for computing the values of the basis functions, moment computation and image reconstruction are also given in the paper, as well as a brief discussion on the computational complexity. The experimental results and error analysis by comparison with other moments show a good performance of this new approach.