Image analysis by Krawtchouk moments

A new set of orthogonal moments based on the discrete classical Krawtchouk polynomials is introduced. The Krawtchouk polynomials are scaled to ensure numerical stability, thus creating a set of weighted Krawtchouk polynomials. The set of proposed Krawtchouk moments is then derived from the weighted Krawtchouk polynomials. The orthogonality of the proposed moments ensures minimal information redundancy. No numerical approximation is involved in deriving the moments, since the weighted Krawtchouk polynomials are discrete. These properties make the Krawtchouk moments well suited as pattern features in the analysis of two-dimensional images. It is shown that the Krawtchouk moments can be employed to extract local features of an image, unlike other orthogonal moments, which generally capture the global features. The computational aspects of the moments using the recursive and symmetry properties are discussed. The theoretical framework is validated by an experiment on image reconstruction using Krawtchouk moments and the results are compared to that of Zernike, pseudo-Zernike, Legendre, and Tchebyscheff moments. Krawtchouk moment invariants are constructed using a linear combination of geometric moment invariants; an object recognition experiment shows Krawtchouk moment invariants perform significantly better than Hu's moment invariants in both noise-free and noisy conditions.     

Image analysis by Tchebichef moments

This paper introduces a new set of orthogonal moment functions based on the discrete Tchebichef polynomials. The Tchebichef moments can be effectively used as pattern features in the analysis of two-dimensional images. The implementation of the moments proposed in this paper does not involve any numerical approximation, since the basis set is orthogonal in the discrete domain of the image coordinate space. This property makes Tchebichef moments superior to the conventional orthogonal moments such as Legendre moments and Zernike moments, in terms of preserving the analytical properties needed to ensure information redundancy in a moment set. The paper also details the various computational aspects of Tchebichef moments and demonstrates their feature representation capability using the method of image reconstruction.     

Image analysis by Gaussian-Hermite moments

Orthogonal moments are powerful tools in pattern recognition and image processing applications. In this paper, the Gaussian-Hermite moments based on a set of orthonormal weighted Hermite polynomials are extensively studied. The rotation and translation invariants of Gaussian-Hermite moments are derived algebraically. It is proved that the construction forms of geometric moment invariants are valid for building the Gaussian-Hermite moment invariants. The paper also discusses the computational aspects of Gaussian-Hermite moment, including the recurrence relation and symmetrical property. Just as the other orthogonal moments, an image can be easily reconstructed from its Gaussian-Hermite moments thanks to the orthogonality of the basis functions. Some reconstruction tests with binary and gray-level images (without and with noise) were performed and the obtained results show that the reconstruction quality from Gaussian-Hermite moments is better than that from known Legendre, discrete Tchebichef and Krawtchouk moments. This means Gaussian-Hermite moment has higher image representation ability. The peculiarity of image reconstruction algorithm from Gaussian-Hermite moments is also discussed in the paper. The paper offers an example of classification using Gaussian-Hermite moment invariants as pattern feature and the result demonstrates that Gaussian-Hermite moment invariants perform significantly better than Hu's moment invariants under both noise-free and noisy conditions.     

Multiparameter discrete transforms based on discrete orthogonal polynomials and their application to image watermarking

Applications of discrete orthogonal polynomials (DOPs) in image processing have been recently emerging. In particular, Krawtchouk, Chebyshev, and Charlier DOPs have been applied as bases for image analysis in the frequency domain. However, fast realizations and fractional-type generalizations of DOP-based discrete transforms have been rarely addressed. In this paper, we introduce families of multiparameter discrete fractional transforms via orthogonal spectral decomposition based on Krawtchouk, Chebyshev, and Charlier DOPs. The eigenvalues are chosen arbitrarily in both unitary and non-unitary settings. All families of transforms, for varieties of eigenvalues, are applied in image watermarking. We also exploit recently introduced fast techniques to reduce complexity for the Krawtchouk case. Experimental results show the robustness of the proposed transforms against watermarking attacks.     

3D scanning-based compression technique for digital hologram video

In this paper, we proposed an efficient coding method for digital hologram video using a three-dimensional (3D) scanning method and two-dimensional (2D) video compression technique. It consists of separation of the captured 3D image into R, G, and B color space components, localization by segmenting the fringe pattern in to M×N [pixel²], frequency-transform by 2D discrete cosine transform (2D DCT), 3D-scanning the segments to form a video sequence, classification of coefficients, and hybrid video coding with H.264/AVC, differential pulse code modulation (DPCM), and lossless coding method. The experimental results with this method showed that the proposed method has compression ratios of 8–16 times higher than the previous researches. Thus, we expect it to contribute to reduce the amount of digital hologram data for communication or storage.     

1D and 2D economical FIR filters generated by Chebyshev polynomials of the first kind

Christoffel–Darboux formula for Chebyshev continual orthogonal polynomials of the first kind is proposed to find a mathematical solution of approximation problem of a one-dimensional (1D) filter function in the z domain. Such an approach allows for the generation of a linear phase selective 1D low-pass digital finite impulse response (FIR) filter function in compact explicit form by using an analytical method. A new difference equation and structure of corresponding linear phase 1D low-pass digital FIR filter are given here. As an example, one extremely economic 1D FIR filter (with four adders and without multipliers) is designed by the proposed technique and its characteristics are presented. Global Christoffel–Darboux formula for orthonormal Chebyshev polynomials of the first kind and for two independent variables for generating linear phase symmetric two-dimensional (2D) FIR digital filter functions in a compact explicit representative form, by using an analytical method, is proposed in this paper. The formula can be most directly applied for mathematically solving the approximation problem of a filter function of even and odd order. Examples of a new class of extremely economic linear phase symmetric selective 2D FIR digital filters obtained by the proposed approximation technique are presented.     

On the reconstruction aspects of moment descriptors

The problem of reconstruction of an image from discrete and noisy data by the method of moments is examined. The set of orthogonal moments based on Legendre polynomials is employed. A general class of signal-dependent noise models is taken into account. An asymptotic expansion for the global reconstruction error is established. This reveals mutual relationships between a number of moments, the image smoothness, sampling rate, and noise model characteristics. The problem of an automatic (data-driven) section of an optimal number of moments is studied. This is accomplished with the help of cross-validation techniques     

On texture and image interpolation using Markov models

Markov-type models characterize the correlation among neighboring pixels in an image in many image processing applications. Specifically, a wide-sense Markov model, which is defined in terms of minimum linear mean-square error estimates, is applicable to image restoration, image compression, and texture classification and segmentation. In this work, we address first-order (auto-regressive) wide-sense Markov images with a separable autocorrelation function. We explore the effect of sampling in such images on their statistical features, such as histogram and the autocorrelation function. We show that the first-order wide-sense Markov property is preserved, and use this result to prove that, under mild conditions, the histogram of images that obey this model is invariant under sampling. Furthermore, we develop relations between the statistics of the image and its sampled version, in terms of moments and generating model noise characteristics. Motivated by these results, we propose a new method for texture interpolation, based on an orthogonal decomposition model for textures. In addition, we develop a novel fidelity criterion for texture reconstruction, which is based on the decomposition of an image texture into its deterministic and stochastic components. Experiments with natural texture images, as well as a subjective forced-choice test, demonstrate the advantages of the proposed interpolation method over presently available interpolation methods, both in terms of visual appearance and in terms of our novel fidelity criterion.     

Low-overhead video compression combining partial discrete cosine transform and compressed sensing in WMSNs

Wireless multimedia sensor network (WMSN) is a special wireless sensor network (WSN) made up of several multimedia sensor nodes, specially designed to retrieve multimedia content such as video and audio streams, still images, and scalar sensor data from the environment. Due to strict inherent limitations in terms of processing power, storage and bandwidth, data processing is a challenge in such network. Further, energy is one of the scarcest resources in WSN, especially in WMSN and therefore, saving energy is of utmost importance. Data compression is one of the solutions of such a problem. This paper proposes an energy saving video compression technique for WMSN by judicious combination of partial discrete cosine transform and compressed sensing. This amalgamation exploits the benefits of both the techniques towards fulfilling the objective of saving energy along with achieving desired peak signal to noise ratio (PSNR). When the transform technique ensures low-overhead compression, compressed sensing guarantees the reconstruction of the same video with lesser amount of measurements. Performance of the scheme is measured both qualitatively and quantitatively. In qualitative analysis, overhead of the scheme is measured in terms of storage, computation, and communication overheads and the results are compared with a number of existing schemes including the base scheme. The results show considerable reduction of all such overheads thereby justifying the appropriateness of the proposed scheme for resource-constrained networks like WMSNs. In quantitative analysis, for both ideal and packet loss environment, the scheme is simulated in Cooja, the Contiki network simulator to make it readily implementable in real life mote e.g. MICAz. When compared with the existing state-of-the-art schemes, it performs better not only in terms of 34.31% energy saving but also in getting an acceptable PSNR of 35–37 dB and SSIM of 0.85–0.88 in ideal environment. In packet loss environment, these values are 32.9–35.5 dB and 0.81–0.85 respectively implying acceptable reconstruction even in packet loss environment. Further, it requires the least storage of 51.2 KB. The observation on simulation results is also justified by statistical analysis.

     

Video hashing with secondary frames and invariant moments

Video hashing is a useful technique of many multimedia systems, such as video copy detection, video authentication, tampering localization, video retrieval, and anti-privacy search. In this paper, we propose a novel video hashing with secondary frames and invariant moments. An important contribution is the secondary frame construction with 3D discrete wavelet transform, which can reach initial data compression and robustness against noise and compression. In addition, since invariant moments are robust and discriminative features, hash generation based on invariant moments extracted from secondary frames can ensure good classification of the proposed video hashing. Extensive experiments on 8300 videos are conducted to validate efficiency of the proposed video hashing. The results show that the proposed video hashing can resist many digital operations and has good discrimination. Performance comparisons with some state-of-the-art algorithms illustrate that the proposed video hashing outperforms the compared algorithms in classification in terms of receiver operating characteristic results.     

Two-dimensional filter bank design for optimal reconstruction usinglimited subband information

In this correspondence, we propose design techniques for analysis and synthesis filters of 2-D perfect reconstruction filter banks (PRFB's) that perform optimal reconstruction when a reduced number of subband signals is used. Based on the minimization of the squared error between the original signal and some low-resolution representation of it, the 2-D filters are optimally adjusted to the statistics of the input images so that most of the signal's energy is concentrated in the first few subband components. This property makes the optimal PRFB's efficient for image compression and pattern representations at lower resolutions for classification purposes. By extending recently introduced ideas from frequency domain principal component analysis to two dimensions, we present results for general 2-D discrete nonstationary and stationary second-order processes, showing that the optimal filters are nonseparable. Particular attention is paid to separable random fields, proving that only the first and last filters of the optimal PRFB are separable in this case. Simulation results that illustrate the theoretical achievements are presented.     

Image compression optimized for 3D reconstruction by utilizing deep neural networks

Computer vision tasks are often expected to be executed on compressed images. Classical image compression standards like JPEG 2000 are widely used. However, they do not account for the specific end-task at hand. Motivated by works on recurrent neural network (RNN)-based image compression and three-dimensional (3D) reconstruction, we propose unified network architectures to solve both tasks jointly. These joint models provide image compression tailored for the specific task of 3D reconstruction. Images compressed by our proposed models, yield 3D reconstruction performance superior as compared to using JPEG 2000 compression. Our models significantly extend the range of compression rates for which 3D reconstruction is possible. We also show that this can be done highly efficiently at almost no additional cost to obtain compression on top of the computation already required for performing the 3D reconstruction task.     

An Energy Efficient Protocol to Mitigate Hot Spot Problem Using Unequal Clustering in WSN

Iris recognition under less constrained environment poses a challenge to be considered for high-security applications. In this paper, discrete orthogonal moment-based features including Tchebichef, Krawtchouk and Dual-Hahn are proposed which prove to be effective for both near-infrared and visible images. The local as well as global features are extracted from localized iris regions till 15th order with invariance (scale, rotation, translation and illumination) properties and tolerance to noise. The performance of the moment-based features is evaluated on four publicly available databases: CASIA-IrisV4-Interval, IITD.v1, UPOL and UBIRIS.v2. It is found that the proposed method gives encouraging results in terms of accuracy, equal error rate and decidability index as compared to the competing techniques available in the literature.     

Orthogonal Polar V Transforms and application to shape retrieval

The traditional orthogonal moments (e.g., Zernike moments) are formulated with polynomials as their basis that often face the problem of computation difficulty especially with the high-order moments. In this paper, we present a novel set of transforms namely the Polar V Transforms (PVTs). We can use the PVTs not only to generate the rotation-invariant features but also to capture global and local information of images. Since the PVTs basis functions can keep a low order of polynomials, we can significantly speed-up the runtime for computing the kernels. The experimental results have demonstrated that our proposed method outperforms the previous methods in runtimes and achieves very good results in shape retrieval compared to the previous methods especially when the images with high degree of perspective distortions.     

Modeling the distribution of DCT coefficients for JPEG reconstruction

In the paper, the one moment (OM) method for the estimation of the shape parameter of generalized Gaussian distribution (GGD) is derived from the two moments method in the case when the moments converge in the limits to the same value. The one moment method reduces to the maximum likelihood (ML) method in the special case when the moment equals the shape parameter. The proposed method exhibits smaller complexity of calculations over ML keeping the same error.Assuming Laplacian distribution, there exists a method for optimally biasing the reconstruction levels for the quantized AC discrete cosine transform (DCT) coefficients using only the quantized ones available at the JPEG decoder [J.R. Price, M. Rabbani, Biased reconstruction for JPEG decoding, IEEE Signal Process. Lett. 6 (12) (1999) 297–299; R. Krupiński, J. Purczyński, First absolute moment and variance estimators used in JPEG reconstruction, IEEE Signal Process. Lett. 11 (8) (2004) 674–677].Many researchers stated that the subset of images can be modeled with GGD with the shape parameter lower than 1. By assuming a source signal with GGD with the exponent 0.5, equations in a closed form for the centroid reconstruction can be obtained as it cannot be done for a GGD model. The ML method of discrete GGD 0.5 is derived, which requires the estimation of only one parameter. For selected images, the values of PSNR coefficients are compared for both distributions.     

基于3维SPIHT编码的超光谱图像压缩

提出一种针对超光谱图像压缩的3维SPIHT编码算法.通过对超光谱图像进行3维小波变换,同时去除像素数据间的空间冗余和谱间冗余.针对变换后得到的小波系数,构造一种3维空间方向树结构,并用经3维扩展后的SPIHT算法(3D SPIHT算法)对小波系数进行量化编码.实验证明,基于3维小波变换的3维SPIHT编码算法在对超光谱图像压缩时,表现出了优良的率失真性能.并且算法复杂度适中,具有嵌入式特性.     

Compositional and Dimensional Control of 2D and Quasi‐2D Lead Halide Perovskites in Water

Blue light emitting two dimensional (2D) and quasi‐2D layered halide perovskites (LHPs) are gaining attention in solid‐state lighting applications but their fragile stability in humid condition is one of the most pressing issues for their practical applications. Though water is much greener and cost effective, organic solvents must be used during synthesis as well as the device fabrication process for these LHPs due to their water‐sensitivity/instability and consequently, water‐stable blue‐light emitting 2D and quasi‐2D LHPs have not been documented yet. Here, water‐mediated facile and cost‐effective syntheses, characterizations, and optical properties of 16 organic–inorganic hybrid compounds are reported including 2D (A′)₂PbX₄ (A′ = butylammonium, X = Cl/Br/I) (8 compounds), 3D perovskites (4), and quasi‐2D (A′)_pA_x?1B_xX_3x+1 LHPs (A = methylammonium) (4) in water. Here, both composition and dimension of LHPs are tuned in water, which has never been explored yet. Furthermore, the dual emissive nature is observed in quasi‐2D perovskites, where the intensity of two photoluminescence (PL) peaks are governed by 2D and 3D inorganic layers. The Pb(OH)₂‐coated 2D and quasi‐2D perovskites are highly stable in water even after several months. In addition, single particle imaging is performed to correlate structural–optical property of these LHPs.