Resolution Analysis of Grey Scale Image using Spherical Harmonics (SPH) Method

Gray Scale image colorization is an appealing area in the world of image processing. This work presents a simple process for colorizing gray image, using a colored image which is similar to this gray scale image but not the colorized version of the gray image. Here we convert both these images to a decorrelated color space YCbCr and then divide these images into small windows of equal size, then we calculate mean and standard deviation for data points based on luminance values in each of these windows to compute a luminance measure and we also extract texture features like energy, entropy, contrast, correlation and homogeneity based on correlation matrix for each of these windows. We apply proper weights to these texture features to calculate a texture similarity measure & then calculate a similarity measure based on the texture similarity measure and luminance measure for each of these windows in both the images. Then we compare each window in gray scale image with every other window in colored image using this similarity measure and find the best matching window. Then the chromatic properties of this colored window are transferred to the gray window pixel by pixel and colorization of gray scale image is achieved, which produces believable results.

Noise-proofing the doubly SH-projected coefficients for synthesizing images under environment lighting

Steganography is the art of the hidden data in such a way that it detection of hidden knowledge prevents. As the necessity of security and privacy increases, the need of the hiding secret data is ongoing. In this paper proposed an enhanced detection of the 1-2-4 LSB steganography and RSA cryptography in Gray Scale and Color images. For color images, we apply 1-2-4 LSB on component of the RGB, then encrypt information applying RSA technique. For Gray Images, we use LSB to then encrypt information and also detect edges of gray image. In the experimental outcomes, calculate PSNR and MSE. We calculate peak signal noise ratio for quality and brightness. This method makes sure that the information has been encrypted before hiding it into an input image. If in any case the cipher text got revealed from the input image, the middle person other than receiver can't access the information as it is in encrypted form.

SUMMARY This study aims to provide valuable scientific insights into various estimation techniques of geocentre motion (GCM) from the perspective of signal analysis, thereby enhancing Gravity Recovery and Climate Experiment (GRACE) users' understanding and application of GCM. Initially, it utilizes the satellite laser ranging (SLR) technique with the network shift approach to estimate over 30 yr of weekly GCM time-series from 1994 to 2024. Subsequently, we employ two approaches to estimate three types of monthly GCM time-series spanning more than 20 yr from 2002 to 2023: combining GRACE data with an ocean bottom pressure model (GRACE-OBP approach), the fingerprint approach (FPA), and the fingerprint approach with satellite altimetry data (FPA-SA, up to 2022). The former is referred to as SLR-based GCM estimates, while the latter, which uses GRACE Earth's gravity field models, is termed GRACE-based GCM estimates. Furthermore, this study pioneers the use of multichannel singular spectrum analysis (MSSA) for GCM analysis, especially focusing on the latest GRACE-based GCM estimates from the GRACE-OBP and FPA/FPA-SA approaches, marking the first comprehensive analysis of GCM estimated by various techniques. The results show that MSSA can effectively extract common signals from the three components of the GCM time-series. The seasonal components extracted from GRACE-based GCM estimates using MSSA are consistent with those from SLR-based GCM estimates, although the former exhibit slightly larger amplitudes of the annual and semi-annual signals. After correcting the atmosphere-ocean dealiasing, the amplitudes of the SLR-based estimates correspondingly decrease, remaining slightly larger but becoming closer to those of the GRACE-based estimates. However, a periodic signal with an approximate 160-d period is detectable in all GRACE-based GCM estimates, but it is absent in SLR-based GCM estimates. Further investigation using MSSA into higher degree spherical harmonic (SH) coefficients of the Earth's gravity field models reveals that these SH coefficients contain a 160-d periodic signal. This finding suggests that the signal detected in GRACE-based GCM estimates originates from systematic errors in these SH coefficients, offering new insights for improving the accuracy of GRACE Earth's gravity field solutions. Additionally, GRACE-based GCM estimates show significant secular non-zero trends, notably larger than those in SLR-based GCM estimates, which are not expected to exhibit any trends. However, the reliance of GRACE-based GCM estimates on geophysical models (e.g. glacier melting, glacial isostatic adjustment and hydrological models) limits the accuracy of their trends, underscoring the need for further validation. Overall, this study highlights new challenges regarding the accuracy of GRACE-based GCM estimates and emphasizes the necessity for further validation in mass change research.

Gray image coloring is utilized to increase the visual appeal of images such as old black and white photos, movies or scientific illustrations. Most of authors working in coloring of gray scale images have used primitive methods for coloring which are both inaccurate and limited. In this paper we propose a new technique for computer coloring gray scale images. This technique works for texture based images like natural scenes. It's based on segmenting the image into different regions according to their textures. Real colors of the image can then be obtained by classifying these textures to predefined texture classes. Recognition of these textures is performed by matching these textures with a training set stored in a special database. We validate the efficiency of our coloring system by coloring several sets of natural gray images with high quality real colors.

Scene analysis for robotic watercraft

The application of confusion and diffusion processes on the three individual components of an RGB image is not secure and efficient, so this problem needs to be addressed. In this paper, a novel RGB image cipher is proposed using chaotic systems, 15-puzzle artificial intelligence problem and DNA computing. First of all the given color image is decomposed into its red, green and blue gray scale images. Then these gray scale images are concatenated to make a single gray scale image. This single gray scale image is further divided into different blocks. A block level permutation (BLP) is proposed on this gray scale image by using the 15-puzzle problem. A pixel level permutation is applied to further randomize the image pixels. This confused image is then DNA encoded. Afterwards, a diffusion process is applied on this DNA encoded image. Lastly this DNA diffused image is converted back into the decimal. Further, this single gray scale image is broken into three gray scale images. These three images are combined to get the final color cipher image. To create the plaintext sensitivity, SHA 256 hash function has been used. Both the simulation and a comprehensive security analyses suggest the robustness and the impregnability of the proposed scheme which in turn signals towards the real world applicability of the scheme.

Direction of arrival (DOA) estimation for multi-channel speech enhancement is a challenging problem. In this context, this paper proposes a new method for joint DOA estimation using a low complexity convolutional neural network (CNN) architecture. The spherical harmonic (SH) coefficients of the received speech signal are obtained from the spherical harmonics decomposition (SHD). The magnitude and phase features are extracted from these SH coefficients and combined as a single feature for training the CNN. A single CNN model is trained using these combined features in contrast to two CNN models used in earlier work. Both azimuth and elevation are then obtained for estimation of DOA from this single CNN. Extensive simulations are also conducted for the performance evaluation of the proposed low complexity CNN model. It is observed that the proposed CNN model provides robust DOA estimates at the various signal to noise ratios (SNR) and reverberation times with reduced computational complexity. Performance evaluated in terms of the gross error (GE) and run-time complexity also provides interesting results motivating the use of the proposed model in practical applications.

3D Gaussian Splatting (3DGS) enables real-time, high-fidelity rendering but suffers from large model sizes, mainly due to the Spherical Harmonics (SH) coefficients used for view-dependent appearance modeling, whose parameter count scales quadratically <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(O(L²))</i> with the degree <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i>. This paper presents the first systematic study that reveals and leverages the intrinsic low-rank structure of SH coefficients in 3DGS. Unlike prior approaches that truncate spectral energy, the proposed low-rank paradigm compactly preserves spectral information, achieving high visual quality with substantially reduced storage. Two complementary approaches are introduced. (1) SHAC-PCA (Principal Component Analysis) is a plug-and-play post-hoc compressor that retains principal spectral variance for high-fidelity compression. (2) SHAC-LST (Learned Subset Transformation) is a training-integrated approach that decomposes Alternating Current (AC) of SH coefficients into low-dimensional subset coefficients and a shared transformation matrix, offering superior compression and even quality improvements through regularization. Both methods effectively reduce SH coefficients storage complexity to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O(L)</i>. Extensive experiments demonstrate that our approaches significantly reduce memory usage while maintaining or even improving rendering quality. The proposed techniques are highly versatile: SHAC-PCA can be applied to any pre-trained 3DGS model, while SHAC-LST supports end-to-end training or fine-tuning. Both methods are compatible with existing 3DGS compression pipelines, providing a practical and general solution for efficient compression of SH coefficients in 3DGS.

Timely sensing the abnormal condition of the bearings plays a crucial role in ensuring the normal and safe operation of the rotating machine. Most traditional bearing fault diagnosis methods are developed from machine learning, which might rely on the manual design features and prior knowledge of the faults. In this paper, based on the advantages of CNN model, a two-step fault diagnosis method developed from wavelet packet transform (WPT) and convolutional neural network (CNN) is proposed for fault diagnosis of bearings without any manual work. In the first step, the WPT is designed to obtain the wavelet packet coefficients from raw signals, which then are converted into the gray scale images by a designed data-to-image conversion method. In the second step, a CNN model is built to automatically extract the representative features from gray images and implement the fault classification. The performance of the proposed method is evaluated by a real rolling-bearing dataset. From the experimental study, it can be seen the proposed method presents a more superior fault diagnosis capability than other machine-learning-based methods.

Tone-mapping-operators (TMOs) provide a useful means for converting high dynamic range (HDR) images to low dynamic range (LDR) images so that they can be viewed on standard displays, but this may influence the visual quality of experience (QoE) of the end-user. There is a need to understand the impact of TMOs to inform the choice of TMO algorithms for different displays, especially for small-screen-devices (SSDs) such as those used in mobile phones. This is important, as mobile devices are becoming the primary means of consuming multimedia contents. However, few studies have been undertaken to assess the impact of TMOs and viewing devices (especially SSDs) on the visual QoE of the user when using. In this chapter, we evaluate subjectively and objectively, the commonly used TMOs in different displays and resolutions for colour and grey-scale HDR images. Our results show that viewing devices have an influence on the TMOs performance, suggesting the need for a careful choice of TMO to enhance the viewing-QoE of the end-user. As expected, the higher resolution, the better HDR-image quality. Surprisingly, there was no significant difference between the Mean of Opinion Score (MOS) scores for colour and grey-scale images in SSDs. The device and TMOs affect QoE for colour and grey HDR-image equally. We found Shannon entropy (SE) to be a good objective measure of quality for colour and grey HDR images, suggesting that entropy may find use in automated HDR quality control assessment schemes, while; HDR-VDP-2 is a good objective measure for colour HDR image only.

The increasing interest towards exploring small bodies in the Solar system has paved the way for the investigation of different gravity field models allowing robust orbit design and dynamical environment characterization. Among these, the spherical harmonics representation and the polyhedral gravity model are the most employed and studied—the former for historical reasons and the latter due to the fact that it is an exact and closed-form representation of the gravity field arising from a constant-density polyhedron. The exact algorithm computing the spherical harmonics coefficients from a given polyhedron is available in the literature. Unfortunately, little to no insight into the uncertainty in the spherical harmonics coefficients is provided alongside their computed value, as the polyhedron is customarily considered as a deterministically known solid. During orbit design, spacecraft operations and small body characterization, it is crucial to account for the uncertainty in the spherical harmonics coefficients and how it influences the overall mission architecture. This paper provides the analytical derivation of the partial derivatives of the transformation between the constant density polyhedron and the spherical harmonics coefficients with respect to the vertices of the polyhedron. This derivation allows for the quantification of the spherical harmonics coefficients’ uncertainties when a stochastic polyhedral shape is considered, i.e., a shape whose vertices do not have a deterministic position. As a result, the analytical expressions of the uncertainty in the gravity potential and acceleration are assembled to rigorously quantify the influence of a stochastic polyhedron on the surrounding dynamical environment. A brief explanation of the implementation procedure and the polyhedron vertices covariance matrix definition is provided to the reader. The final result of the paper is a set of numerical simulations validating the proposed model and demonstrating its capability to provide the uncertainties in the spherical harmonics coefficients, the gravity potential and acceleration arising from a stochastic polyhedral shape.

Biaxially texture magnesium oxide (MgO) films have been grown using ion beam assisted deposition (IBAD). IBAD-MgO films can easily to grow in the preferred direction and to form biaxial texture fast by the effect of ion beam assisted current, where the ability of preferred growth is directly controlled by the ion beam assisted current. An in situ reflection high energy electron diffraction (RHEED) has often been used to monitor the texture development of MgO film during the IBAD process. Here, we developed novel numerical analysis methods for RHEED patterns based on gray level. We constructed corresponding gray scale images and binary images from RHEED patterns. The area and brightness of selected diffraction spots, such as (004) diffraction spots, were measured based on the gray scale images. Further, rich information on the whole RHEED binary images, such as high-brightness pixels proportion of gray value higher than 50% gray level, can be obtained. Results from these qualitative analyses of RHEED patterns were coincided to the texture evolution obtained by phi scan rocking curves. This indicates these kinds of analysis methods based on gray level are effective for RHEED patterns.

Texture analysis (TA) of histological images has recently received attention as an automated method of characterizing liver fibrosis. The colored staining methods used to identify different tissue components reveal various patterns that contribute in different ways to the digital texture of the image. A histological digital image can be represented with various color spaces. The approximation processes of pixel values that are carried out while converting between different color spaces can affect image texture and subsequently could influence the performance of TA. Conventional TA is carried out on grey scale images, which are a luminance approximation to the original RGB (Red, Green, and Blue) space. Currently, grey scale is considered sufficient for characterization of fibrosis but this may not be the case for sophisticated assessment of fibrosis or when resolution conditions vary. This paper investigates the accuracy of TA results on three color spaces, conventional grey scale, RGB, and Hue-Saturation-Intensity (HSI), at different resolutions. The results demonstrate that RGB is the most accurate in texture classification of liver images, producing better results, most notably at low resolution. Furthermore, the green channel, which is dominated by collagen fiber deposition, appears to provide most of the features for characterizing fibrosis images. The HSI space demonstrated a high percentage error for the majority of texture methods at all resolutions, suggesting that this space is insufficient for fibrosis characterization. The grey scale space produced good results at high resolution; however, errors increased as resolution decreased.

The determination of the appropriate sampling rate for image data is often problematic because the traditional band-limited reconstruction approach for data sampled above the Nyquist frequency cannot be applied to sources which are not band-limited. High contrast edges play an important role in image content definition, and these sharp edges in an image source would theoretically require an unbounded spatial frequency range. The paper presents a theoretical argument supported by several examples for selecting a different minimum sampling frequency for grey scale and binary image acquisition. Implications with respect to image acquisition, image processing, and image compression are discussed. >