Image Smoothing Research Articles

Optimized recursive approximate multipliers for edge detection and image smoothing applications

Optimized recursive approximate multipliers for edge detection and image smoothing applications

Simultaneous image denoising and completion through convolutional sparse representation and nonlocal self-similarity

Low rank matrix approximation (LRMA) has been widely studied due to its capability of approximating original image from the degraded image. According to the characteristics of degraded images, image denoising and image completion have become research objects. Existing methods are usually designed for a single task. In this paper, focusing on the task of simultaneous image denoising and completion, we propose a weighted low rank sparse representation model and the corresponding efficient algorithm based on LRMA. The proposed method integrates convolutional analysis sparse representation (ASR) and nonlocal statistical modeling to maintain local smoothness and nonlocal self-similarity (NLSM) of natural images. More importantly, we explore the alternating direction method of multipliers (ADMM) to solve the above inverse problem efficiently due to the complexity of simultaneous image denoising and completion. We conduct experiments on image completion for partial random samples and mask removal with different noise levels. Extensive experiments on four datasets, i.e., Set12, Kodak, McMaster, and CBSD68, show that the proposed method prevents the transmission of noise while completing images and has achieved better quantitative results and human visual quality compared to 17 methods. The proposed method achieves (1.9%, 1.8%, 4.2%, and 3.7%) gains in average PSNR and (4.2%, 2.9%, 6.7%, and 6.6%) gains in average SSIM over the sub-optimal method across the four datasets, respectively. We also demonstrate that our method can handle the challenging scenarios well. Source code is available at https://github.com/weimin581/demo_CSRNS.

ISRSL0: compressed sensing MRI with image smoothness regularized-smoothed \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:{\\ell}_{0}$$\\end{document} norm

The reconstruction of MR images has always been a challenging inverse problem in medical imaging. Acceleration of MR scanning is of great importance for clinical research and cutting-edge applications. One of the primary efforts to achieve this is using compressed sensing (CS) theory. The CS aims to reconstruct MR images using a small number of sampled data in k-space. The CS-MRI techniques face challenges, including the potential loss of fine structure and increased computational complexity. We introduce a novel framework based on a regularized sparse recovery problem and a sharpening step to improve the CS-MRI approaches regarding fine structure loss under high acceleration factors. This problem is solved via the Half Quadratic Splitting (HQS) approach. The inverse problem for reconstructing MR images is converted into two distinct sub-problems, each of which can be solved separately. One key feature of the proposed approach is the replacement of one sub-problem with a denoiser. This regularization assists the optimization of the Smoothed \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:{\\ell}_{0}$$\\end{document} (SL0) norm in escaping local minimums and enhances its precision. The proposed method consists of smoothing, feature modification, and Smoothed \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:{\\ell}_{0}$$\\end{document} cost function optimization. The proposed approach improves the SL0 algorithm for MRI reconstruction without complicating it. The convergence of the proposed approach is illustrated analytically. The experimental results show an acceptable performance of the proposed method compared to the network-based approaches.

Gaussian error loss function for image smoothing

Edge-preserving image smoothing plays an important role in the fields of image processing and computational photography, and is widely used for a variety of applications. The edge-preserving filters based on global optimization models have attracted widespread attention due to their nice smoothing quality. According to existing research, the edge-preserving capability is strongly correlated to the penalty function used for gradient regularization. By analyzing the edge-stopping function of existing penalties, we demonstrate that existing image smoothing models are not adequately edge-preserving. In this paper, based on a Gaussian error function (ERF), we propose a Gaussian error loss function (ERLF), which shows stronger edge-preserving capability. We embed the proposed loss function into a global optimization model for edge-preserving image smoothing. In addition, we propose an efficient solution based on additive half-quadratic minimization and Fourier-domain optimization that is capable of processing 720P color images (over 20 fps) in real-time on an NVIDIA RTX 3070 GPU. We have experimented with the proposed filter on a number of low-level vision tasks. Both quantitative and qualitative experimental results show that the proposed filter outperforms existing filters. Therefore, it can be practical for real applications.

Ultrasound image smoothing based on adaptive and non-adaptive filters.

To model adaptive and non-adaptive filters to ensure smooth ultrasound images. The comparative study was conducted at Al-Yarmouk Teaching Hospital, Al Mustansiriyah University, Baghdad, Iraq, in 2019, and comprised ultrasound images of kidney (303x208 pixel) and foetus (111x109 pixel). These images were smoothed based on 8 filters; 1 non-adaptive (median), and 7 adaptive enhanced filters (Gamma, Wiener, Lee, Frost, Kuan, Adaptive Lee and Adaptive Frost). They were applied to the images by windows measuring 3x3, 5x5, 7x7. The additive noise and the multiplicative noise factor were calculated using histogram to determine the noise type for each image. Statistical criteria included mean square error, normalised absolute error and signalto- noise ratio. The relationship between noise ratio and filter type showed that Wiener was the best filter and the best sliding window was 3x3. The worst filters were Gamma, EFrost and Kuan. The relationship between sliding window size and noise ratio for all the smoothing filters clearly identified the best filter for the type of noise.

A dictionary learning based unsupervised neural network for single image compressed sensing

In the field of Compressed Sensing (CS), the sparse representation of signals and the advancement of reconstruction algorithms are two critical challenges. However, conventional CS algorithms often fail to sufficiently exploit the structured sparsity present in images and suffer from poor reconstruction quality. Most deep learning-based CS methods are typically trained on large-scale datasets. Obtaining a sufficient number of training sets is challenging in many practical applications and there may be no training sets available at all in some cases. In this paper, a novel deep Dictionary Learning (DL) based unsupervised neural network for single image CS (dubbed DL-CSNet) is proposed. It is an effective trainless neural network that consists of three components and their corresponding loss functions: 1) a DL layer that consists of multi-layer perceptron (MLP) and convolution neural networks (CNN) for latent sparse features extraction with the L1-norm sparsity loss function; 2) an image smoothing layer with the Total Variation (TV) like image smoothing loss function; and 3) a CS acquisition layer for image compression, with the Mean Square Error (MSE) loss function between the original image compression and the reconstructed image compression. In particular, the proposed DL-CSNet is a lightweight and fast model that does not require datasets for training and exhibits a fast convergence speed, making it suitable for deployment in resource-constrained environments. Experiments have demonstrated that the proposed DL-CSNet achieves superior performance compared to traditional CS methods and other unsupervised state-of-the-art deep learning-based CS methods.

Stability and Preservation of Fuzzy Membership Functions in Adaptive Gaussian Derivative Filters

This paper examines the stability and preservation of fuzzy membership functions in Gaussian filters, particularly focusing on the Adaptive Gaussian Derivative (AGD) filter. Gaussian filters are essential for smoothing and noise reduction in image processing. The AGD filter, which adapts based on local image statistics, outperforms traditional methods. Key concepts like fuzzy sets, Boundary Input Boundary Output (BIBO) stability, and convolution are defined, and the mathematical formulation of the Gaussian and its derivative is presented. The AGD filter's BIBO stability ensures bounded outputs for bounded inputs, guaranteeing consistent behavior. It also preserves fuzzy membership function properties, maintaining convexity and boundedness through linearity and continuity. Frequency response analysis using Fourier Transform confirms the AGD filter retains the Gaussian shape in the frequency domain, preserving image smoothness. Theorems and proofs validate the AGD filter's stability and its capability to preserve fuzzy membership functions, ensuring reliable processing in applications such as medical image analysis. These properties make the AGD filter a robust tool for advanced image processing tasks.

Contrast-preserving image smoothing via the truncated first-order rational function

The main task of image smoothing is to remove the insignificant details of the input image while preserving salient structural edges. In the fields of computer vision and graphics, image smoothing techniques are of great practical importance. In this paper, we investigate a new nonconvex variational optimization model for contrast-preserving image smoothing based on the truncated first-order rational (TFOR) penalty function. We employ an iterative numerical method that utilizes the half-quadratic minimization to effectively solve the proposed model. To validate the effectiveness of the proposed method, we compare it with some related state-of-the-art methods. Experimental results are given to show that the proposed method performs well in preserving the image contrast while maintaining the important edges and structures. We apply the proposed method on various classic image processing tasks such as clip-art compression artifact removal, detail enhancement, image denoising, image abstraction, flash and no-flash image restoration, and guided depth map upsampling.

SRARDA: A lightweight adaptive residual dense attention generative adversarial network for image super-resolution

Image super-resolution (SR) is the task of inferring a high resolution (HR) image from one/multiple single low resolution (LR) input(s). Traditional networks are evaluated by pixel-level metrics such as Peak-Signal-to-Noise Ratio (PSNR) etc., which do not always align with human perception of image quality. They often produce excessively smooth images that lack high-frequency texture and appear unnatural. Therefore, in this paper, we propose a lightweight adaptive residual dense attention generative adversarial network (SRARDA) for image SR. Firstly, our generator adopts the residual in residual (RIR) structure but redesigns the basic module. By using dynamic residual connection (ARC) to dynamically adjust the importance of residual and main paths, we design a novel adaptive residual dense attention block (ARDAB) that enhances the feature extraction capability of the generator. In addition, we build a high-frequency filtering unit (HFU) to extract more high-frequency features from the LR space. Finally, to fully utilize the discriminator, we use WGAN to compute the difference between the HR image and the reconstructed image. Experiments demonstrate that SRARDA effectively addresses the issue of excessive smoothing in reconstructed images, while also enhancing visual quality.

Image dejittering on the perspective of spatially-varying mixed noise removal

Jittery image is visually abnormal in jags of edge and loss of coherence. The problem of image dejittering is challenging to resolve due to the ubiquitous blur and/or noise in jittery data. In this paper, we devote to the pixel-jitter (possibly blurry) image recovery on the perspective of spatially-varying mixed noise removal. By viewing jittery image as the corruption of ideal image with outliers and spatially-varying Gaussian noise, we proposed a two-phase (including filtering and diffusing phases) image dejittering approach. In the filtering phase, outliers posed by jitters around edges are inspected by median filters. In the diffusing phase, structure tensor based anisotropic diffusion is exploited to reduce the perturbations in piecewise smooth image regions. Upon the spectral decomposition of structure tensor, the variational model in diffusing phase can be solved by some state-of-the-art optimization methods. Numerical simulations on synthetic and real jittery data demonstrate the compelling performance of the proposed approach. The Matlab source codes of the proposed approach are available at the repositories of https://github.com/WenxingZhang.

Image reconstruction and bladder stimulation using electrical impedance tomography

Impedance tomography (EIT) is an imaging technique that harnesses differences in electrical conductivity to visualize the interior of objects. Despite limitations such as low resolution and nonlinearity of current distribution, its potential in medicine and industry is a source of fascination. The research in this work is a step towards unlocking this potential, focusing on improving the quality of EIT image reconstruction, particularly in bladder modeling. A key element is regularization techniques, including Laplace matrices and the iterative Gauss-Newton algorithm, which balance matching accuracy and image smoothness. In the practical part, simulations were conducted on dense and sparse meshes. Modeling the urinary bladder as a rotational ellipse significantly influences the interpretation of data by algorithms, a crucial factor for the accuracy of reconstruction. Various electrode configurations were also analyzed, revealing the impact of their arrangement on electrical properties and imaging quality. Iterative testing led to identifying optimal electrode placement and grid configuration, underscoring the importance of precise modeling for obtaining high-quality images. The results underscore the critical role of appropriately selecting the regularization parameter in minimizing reconstruction errors.

Image Denoising Using the Geodesics' Gramian of the Manifold Underlying Patch-Space

With the proliferation of sophisticated cameras in modern society, the demand for accurate and visually pleasing images is increasing. However, the quality of an image captured by a camera may be degraded by noise. Thus, some processing of images is required to filter out the noise without losing vital image features. Even though the current literature offers a variety of denoising methods, the fidelity and efficacy of their denoising are sometimes uncertain. Thus, here we propose a novel and computationally efficient image denoising method that is capable of producing accurate images. To preserve image smoothness, this method inputs patches partitioned from the image rather than pixels. Then, it performs denoising on the manifold underlying the patch-space rather than that in the image domain to better preserve the features across the whole image. We validate the performance of this method against benchmark image processing methods.

ICNoduleNet: Enhancing Pulmonary Nodule Detection Performance on Sharp Kernel CT Imaging.

Thoracic computed tomography (CT) currently plays the primary role in pulmonary nodule detection, where the reconstruction kernel significantly impacts performance in computer-aided pulmonary nodule detectors. The issue of kernel selection affecting performance has been overlooked in pulmonary nodule detection. This paper first introduces a novel pulmonary nodule detection dataset named Reconstruction Kernel Imaging for Pulmonary Nodule Detection (RKPN) for quantifying algorithm differences between the two imaging types. The dataset contains pairs of images taken from the same patient on the same date, featuring both smooth (B31f) and sharp kernel (B60f) reconstructions. All other imaging parameters and pulmonary nodule labels remain entirely consistent across these pairs. Extensive quantification reveals mainstream detectors perform better on smooth kernel imaging than on sharp kernel imaging. To address suboptimal detection on the sharp kernel imaging, we further propose an image conversion-based pulmonary nodule detector called ICNoduleNet. A lightweight 3D slice-channel converter (LSCC) module is introduced to convert sharp kernel images into smooth kernel images, which can sufficiently learn inter-slice and inter-channel feature information while avoiding introducing excessive parameters. We conduct thorough experiments that validate the effectiveness of ICNoduleNet, it takes sharp kernel images as input and can achieve comparable or even superior detection performance to the baseline that uses the smooth kernel images. The evaluation shows promising results and proves the effectiveness of ICNoduleNet.

Digital Image Noise Reduction Based on Proposed Smoothing and Sharpening Filters

In order to reduce noise in digital photographs, this paper provides a thorough analysis of sophisticated sharpness enhancement and image smoothing approaches. The research compares and contrasts different approaches, including well-known filters like Gaussian filter, Mean filter, Weighted Averaging filter, Laplacian filters, and Unsharp mask, with suggested strategies aimed at achieving optimal efficiency. The performance of these techniques is evaluated in several circumstances with speckle noise and Gaussian noise corrupted images. The results show how well the suggested strategy performs in terms of reducing noise, preserving image features, and improving overall image quality. The comparative advantage of the suggested technique over conventional filters is highlighted by comparative analysis. The study's conclusion offers information on the possible uses and future developments of these methods in practical image processing situations.

Discrete-Time Visual Servoing Control with Adaptive Image Feature Prediction Based on Manipulator Dynamics.

In this paper, a practical discrete-time control method with adaptive image feature prediction for the image-based visual servoing (IBVS) scheme is presented. In the discrete-time IBVS inner-loop/outer-loop control architecture, the time delay caused by image capture and computation is noticed. Considering the dynamic characteristics of a 6-DOF manipulator velocity input system, we propose a linear dynamic model to describe the motion of a robot end effector. Furthermore, for better estimation of image features and smoothing of the robot's velocity input, we propose an adaptive image feature prediction method that employs past image feature data and real robot velocity data to adopt the prediction parameters. The experimental results on a 6-DOF robotic arm demonstrate that the proposed method can ensure system stability and accelerate system convergence.

Reversible data hiding in encrypted image based on key-controlled balanced Huffman coding

To achieve privacy protection and effective management in cloud computing, and solve the problem of existing reversible data hiding in encrypted image (RDH-EI) algorithms being unable to resist existing various attacks, an RDH-EI algorithm based on key-controlled balanced Huffman coding (KBHC) is proposed. The novelty lies in KBHC and variable-length bit scrambling. KBHC possesses non-preset, balanced, and key-controlled characteristics, providing the proposed algorithm with high capacity and enhanced security. The non-preset allows coding tables to be adaptively generated based on prediction error maps, resulting in shorter encoded streams for higher embedding capacity. The balanced characteristic is achieved by adjusting the subtrees, so that the balance rate in the encoded stream is 0.014, and can also reach 0.065 for particularly smooth images, achieving uniform distribution of the encoded stream, thereby improving the ability to resist statistical analysis attacks. The random key controls the leaf nodes scrambling in the Huffman tree, which realizes the variability of the encoded stream and avoids the potential security risks caused by timestamp reconstruction, laying the foundation to achieve differential attack security. Variable-length bit scrambling determines the pseudo-random extension length and scrambling sequence by both the encryption key and coding table information, effectively resists brute force attacks and ensures up to 100 % difference rate between scrambling sequences generated in each run. Experimental results demonstrate that compared to several RDH-EI methods, the proposed algorithm achieves higher embedding capacity and security under acceptable complexity. The average embedding rate of three databases reaches 3.897 bpp, and the proposed algorithm effectively resists statistical analysis attacks, COA, KPA, and differential attack.

Refining tomography with generative neural networks trained from geodynamics

SUMMARY Inverse problems occur in many fields of geophysics, wherein surface observations are used to infer the internal structure of the Earth. Given the non-linearity and non-uniqueness inherent in these problems, a standard strategy is to incorporate a priori information regarding the unknown model. Sometimes a solution is obtained by imposing that the inverted model remains close to a reference model and with smooth lateral variations (e.g. a correlation length or a minimal wavelength are imposed). This approach forbids the presence of strong gradients or discontinuities in the recovered model. Admittedly, discontinuities, such as interfaces between layers, or shapes of geological provinces or of geological objects such as slabs can be a priori imposed or even suggested by the data themselves. This is however limited to a small set of possible constraints. For example, it would be very challenging and computationally expensive to perform a tomographic inversion where the subducting slabs would have possible top discontinuities with unknown shapes. The problem seems formidable because one cannot even imagine how to sample the prior space: is each specific slab continuous or broken into different portions having their own interfaces? No continuous set of parameters seems to describe all the possible interfaces that we could consider. To circumvent these questions, we propose to train a Generative Adversarial neural Network (GAN) to generate models from a geologically plausible prior distribution obtained from geodynamic simulations. In a Bayesian framework, a Markov chain Monte Carlo algorithm is used to sample the low-dimensional model space depicting the ensemble of potential geological models. This enables the integration of intricate a priori information, parametrized within a low-dimensional model space conducive to efficient sampling. The application of this approach is demonstrated in the context of a downscaling problem, where the objective is to infer small-scale geological structures from a smooth seismic tomographic image.

Image smoothing method based on global gradient sparsity and local relative gradient constraint optimization

Removing texture while preserving the main structure of an image is a challenging task. To address this, this paper propose an image smoothing method based on global gradient sparsity and local relative gradient constraints optimization. To reduce the interference of complex texture details, adopting a multi-directional difference constrained global gradient sparsity decomposition method, which provides a guidance image with weaker texture detail gradients. Meanwhile, using the luminance channel as a reference, edge-aware operator is constructed based on local gradient constraints. This operator weakens the gradients of repetitive and similar texture details, enabling it to obtain more accurate structural information for guiding global optimization of the image. By projecting multi-directional differences onto the horizontal and vertical directions, a mapping from multi-directional differences to bi-directional gradients is achieved. Additionally, to ensure the consistency of measurement results, a multi-directional gradient normalization method is designed. Through experiments, we demonstrate that our method exhibits significant advantages in preserving image edges compared to current advanced smoothing methods.

Brain Image Segmentation for Ultrascale Neuron Reconstruction via an Adaptive Dual-Task Learning Network.

Accurate morphological reconstruction of neurons in whole brain images is critical for brain science research. However, due to the wide range of whole brain imaging, uneven staining, and optical system fluctuations, there are significant differences in image properties between different regions of the ultrascale brain image, such as dramatically varying voxel intensities and inhomogeneous distribution of background noise, posing an enormous challenge to neuron reconstruction from whole brain images. In this paper, we propose an adaptive dual-task learning network (ADTL-Net) to quickly and accurately extract neuronal structures from ultrascale brain images. Specifically, this framework includes an External Features Classifier (EFC) and a Parameter Adaptive Segmentation Decoder (PASD), which share the same Multi-Scale Feature Encoder (MSFE). MSFE introduces an attention module named Channel Space Fusion Module (CSFM) to extract structure and intensity distribution features of neurons at different scales for addressing the problem of anisotropy in 3D space. Then, EFC is designed to classify these feature maps based on external features, such as foreground intensity distributions and image smoothness, and select specific PASD parameters to decode them of different classes to obtain accurate segmentation results. PASD contains multiple sets of parameters trained by different representative complex signal-to-noise distribution image blocks to handle various images more robustly. Experimental results prove that compared with other advanced segmentation methods for neuron reconstruction, the proposed method achieves state-of-the-art results in the task of neuron reconstruction from ultrascale brain images, with an improvement of about 49% in speed and 12% in F1 score.

Deep unsupervised nonconvex optimization for edge-preserving image smoothing

Deep unsupervised nonconvex optimization for edge-preserving image smoothing