Showing papers on "Image gradient published in 2021"

Surface-Aware Blind Image Deblurring

Abstract: Blind image deblurring is a conundrum because there are infinitely many pairs of latent image and blur kernel. To get a stable and reasonable deblurred image, proper prior knowledge of the latent image and the blur kernel is urgently required. Different from the recent works on the statistical observations of the difference between the blurred image and the clean one, our method is built on the surface-aware strategy arising from the intrinsic geometrical consideration. This approach facilitates the blur kernel estimation due to the preserved sharp edges in the intermediate latent image. Extensive experiments demonstrate that our method outperforms the state-of-the-art methods on deblurring the text and natural images. Moreover, our method can achieve attractive results in some challenging cases, such as low-illumination images with large saturated regions and impulse noise. A direct extension of our method to the non-uniform deblurring problem also validates the effectiveness of the surface-aware prior.

All-optical neuromorphic binary convolution with a spiking VCSEL neuron for image gradient magnitudes

Abstract: All-optical binary convolution with a photonic spiking vertical-cavity surface-emitting laser (VCSEL) neuron is proposed and demonstrated experimentally for the first time, to the best of our knowledge. Optical inputs, extracted from digital images and temporally encoded using rectangular pulses, are injected in the VCSEL neuron, which delivers the convolution result in the number of fast (<100 ps long) spikes fired. Experimental and numerical results show that binary convolution is achieved successfully with a single spiking VCSEL neuron and that all-optical binary convolution can be used to calculate image gradient magnitudes to detect edge features and separate vertical and horizontal components in source images. We also show that this all-optical spiking binary convolution system is robust to noise and can operate with high-resolution images. Additionally, the proposed system offers important advantages such as ultrafast speed, high-energy efficiency, and simple hardware implementation, highlighting the potentials of spiking photonic VCSEL neurons for high-speed neuromorphic image processing systems and future photonic spiking convolutional neural networks.

SAR Image Speckle Reduction Based on Nonconvex Hybrid Total Variation Model

Abstract: Speckle noise inherent in synthetic aperture radar (SAR) images seriously affects the visual effect and brings great difficulties to the postprocessing of the SAR image. Due to the edge-preserving feature, total variation (TV) regularization-based techniques have been extensively utilized to reduce the speckle. However, the strong scatters in SAR image with radiometry several orders of magnitude larger than their surrounding regions limit the effectiveness of TV regularization. Meanwhile, the ${\ell _{1}}$ -norm first-order TV regularization sometimes causes staircase artifacts as it favors solutions that are piecewise constant, and it usually underestimates high-amplitude components of image gradient as the ${\ell _{1}}$ -norm uniformly penalizes the amplitude. To overcome these shortcomings, a new hybrid variation model, called Fisher–Tippett (FT) distribution- ${\ell _{p}}$ -norm first-and second-order hybrid TVs (HTpVs), is proposed to reduce the speckle after removing the strong scatters. Especially, the FT-HTpV inherits the advantages of the distribution based data fidelity term, the nonconvex regularization, and the higher order TV regularization. Therefore, it can effectively remove the speckle while preserving point scatters and edges and reducing staircase artifacts well. To efficiently solve the nonconvex minimization problem, an iterative framework with a nonmonotone-accelerated proximal gradient (nmAPG) method and a matrix-vector acceleration strategy are used. Extensive experiments on both the simulated and real SAR images demonstrate the effectiveness of the proposed method.

Optical Measurement of Highly Reflective Surfaces From a Single Exposure

Abstract: Three-dimensional structured light (SL) measurement of highly reflective surface is a challenge faced in industrial metrology. The high dynamic range (HDR) technique provides a solution by fusing images under multiple exposures; however, the process is highly time-consuming. This article reports a new SL-based method to measure parts with highly reflective surfaces from only a single exposure. A new quantitative metric is defined to optimally select camera exposure for capturing input single-exposure images. Different from existing image gradient or entropy-based metrics, the new metric incorporates both intensity modulation and overexposure. A skip pyramid context aggregation network (SP-CAN) is proposed to enhance the single exposure-captured images. Compared with existing image enhancement methods, SP-CAN effectively preserves detailed encoded phase information near edges and corners during enhancement. Experiments with various industrial parts demonstrated that the average time cost of the proposed method was 0.6 s, which was only one tenth of the HDR method (ten exposures), and the two methods achieved similar coverage rates (97.6 $\%$ versus 98.0 $\%$ ) and measurement accuracy (0.040 mm versus 0.038 mm).

Artificial Intelligence and Edge Computing-Enabled Web Spam Detection for Next Generation IoT Applications

Abstract: For next generation IoT applications, edge devices provides most of the computing resources close to the proximity of the end users. These devices having built-in intelligence using various AI techniques can take independent decisions in the environment where these are deployed. Motivated from these concerns, We suggest a cognitive intrusion security system to maintain the credibility of search engine results, which eliminates the advertising images from penetrating the image database of the web browser. The proposed framework provides edge intelligence for web data filteration and detects the web spam by considering three different layers, i.e., data collection services, edge computing services, and cloud services. The target is to detect the malicious images. Firstly, the features of an image such as mean, image gradient, entropy are fetched and then the retrieved data is processed in the proposed framework. Deep learning algorithms are used for the validation of the proposed system. By evaluating it on real-time collected dataset, it resulted in an accuracy of 98.77%.

On Biases in Displacement Estimation for Image Registration, with a Focus on Photomechanics

Abstract: Image registration under small displacements is the keystone of several image analysis tasks such as optical flow estimation, stereoscopic imaging, or full-field displacement estimation in photomechanics. A popular approach consists in locally modeling the displacement field between two images by a parametric transformation and performing least-squares estimation afterwards. This procedure is known as “digital image correlation” (DIC) in several domains as in photomechanics. The present article is part of this approach. First, the estimated displacement is shown to be impaired by biases related to the interpolation scheme needed to reach subpixel accuracy, the image gradient distribution, as well as the difference between the hypothesized parametric transformation and the true displacement. A quantitative estimation of the difference between the estimated value and the actual one is of importance in application domains such as stereoscopy or photomechanics, which have metrological concerns. Second, we question the extent to which these biases could be eliminated or reduced. We also present numerical assessments of our predictive formula in the context of photomechanics. Software codes are freely available to reproduce our results. Although this paper is focused on a particular application field, namely photomechanics, it is relevant to various scientific areas concerned by image registration.

SMAPGAN: Generative Adversarial Network-Based Semisupervised Styled Map Tile Generation Method

Abstract: Traditional online map tiles, which are widely used on the Internet, such as by Google Maps and Baidu Maps, are rendered from vector data. The timely updating of online map tiles from vector data, for which generation is time-consuming, is a difficult mission. Generating map tiles over time from remote sensing images is relatively simple and can be performed quickly without vector data. However, this approach used to be challenging or even impossible. Inspired by image-to-image translation (img2img) techniques based on generative adversarial networks (GANs), we proposed a semisupervised generation of styled map tiles based on the GANs (SMAPGAN) model to generate styled map tiles directly from remote sensing images. In this model, we designed a semisupervised learning strategy to pretrain SMAPGAN on rich unpaired samples and fine-tune it on limited paired samples in reality. We also designed the image gradient L1 loss and the image gradient structure loss to generate a styled map tile with global topological relationships and detailed edge curves for objects, which are important in cartography. Moreover, we proposed the edge structural similarity index (ESSI) as a metric to evaluate the quality of the topological consistency between the generated map tiles and ground truth. The experimental results show that SMAPGAN outperforms state-of-the-art (SOTA) works according to the mean squared error, the structural similarity index, and the ESSI. Also, SMAPGAN gained higher approval than SOTA in a human perceptual test on the visual realism of cartography. Our work shows that SMAPGAN is a new tool with excellent potential for producing styled map tiles. Our implementation of SMAPGAN is available at https://github.com/imcsq/SMAPGAN .

Detecting Stable Keypoints from Events through Image Gradient Prediction

Abstract: We present a method that detects stable keypoints from an event stream at high speed with a low memory footprint. Our key observation connects two points: It should be easier to reconstruct the image gradients rather than the image itself from the events, and the Harris corner detector, one of the most reliable keypoint detectors for short baseline regular images, depends on the image gradients, not the image. We therefore introduce a recurrent convolutional neural network to predict image gradients from events. As image gradients and events are correlated, this prediction task is relatively easy and we can keep this network very small. We train our network solely on synthetic data. Extracting Harris corners from these gradients is then very efficient. Moreover, in contrast to learned methods, we can change the hyperparameters of the detector without retraining. Our experiments confirm that predicting image gradients rather than images is much more efficient, and that our approach predicts stable corner points which are easier to track for a longer time compared to state-of-the-art event-based methods.

Gradient information distillation network for real-time single-image super-resolution

Abstract: In recent years, deep convolutional neural networks have played an increasingly important role in single-image super-resolution (SR). However, with the increase of the depth and width of networks, the super-resolution methods based on convolution neural networks are facing training difficulties, memory consumption, running slowness and other problems. Furthermore, most of the methods do not make full use of the image gradient information which leads to the loss of geometric structure information of the image. To solve these problems, we propose a gradient information distillation network in this paper. On the one hand, the advantages of fast and lightweight are maintained through information distillation. On the other hand, the SR performance is improved by gradient information. Our network has two branches named gradient information distillation branch (GIDB) and image information distillation branch. To combine features in both branches, we also introduce a residual feature transfer mechanism (RFT). Under the function of GIDB and RFT, our network can retain the rich geometric structure information which can make the edge details of the reconstructed image sharper. The experimental results show that our method is superior to the existing methods while well limits the parameters, computation and running time of the model. It provides the possibility for real-time image processing and mobile applications.

Real-time accurate eye center localization for low-resolution grayscale images

Abstract: Eye center localization is considered a crucial step for many human–computer interaction (HCI) real-time applications. Detecting the center of eye (COE), accurately and in real time, is very challenging due to the wide variation of poses, eye appearance and specular reflection, especially in low-resolution images. In this paper, an accurate real-time detection algorithm of the COE is proposed. The proposed approach depends on the image gradient to detect the COE. The computational complexity is minimized and the accuracy is improved by down sampling the face resolution and applying a rough-to-fine algorithms, to reduce the search area, in accordance with the Eye Region Of Interest (EROI) and the number of COE candidates, tested by the proposed algorithm. Also, the detection algorithm is applied on a limited number of pixels that represent the iris boundary of the COE candidates. The Look Up Tables (LUTs) are implemented to, initially, store the invariant elements of the proposed image gradient-based algorithm, to reduce the detection time. Before applying the proposed COE detection approach, a modified specular reflection method is used to improve the detection accuracy. The performance of the proposed algorithm has been evaluated by applying it to three benchmark databases: the BIOID, GI4E and Talking Face video datasets, at different face resolutions. Experimental results revealed that the accuracy of the proposed algorithm is up to 91.68% and 96.7% for BIOID and GI4E datasets, respectively, while the minimum achieved average detection time is 2.7 ms. The promising results highlight the potential of the proposed algorithm to be used in some eye gaze-based real-time applications. Comparing the proposed method with the most state-of-the-art approaches showed that the system outperforms most of them and has a comparable performance with the others, in terms of the COE localization accuracy and detection speed.

Image Preprocessing for Artistic Robotic Painting

Abstract: Artistic robotic painting implies creating a picture on canvas according to a brushstroke map preliminarily computed from a source image. To make the painting look closer to the human artwork, the source image should be preprocessed to render the effects usually created by artists. In this paper, we consider three preprocessing effects: aerial perspective, gamut compression and brushstroke coherence. We propose an algorithm for aerial perspective amplification based on principles of light scattering using a depth map, an algorithm for gamut compression using nonlinear hue transformation and an algorithm for image gradient filtering for obtaining a well-coherent brushstroke map with a reduced number of brushstrokes, required for practical robotic painting. The described algorithms allow interactive image correction and make the final rendering look closer to a manually painted artwork. To illustrate our proposals, we render several test images on a computer and paint a monochromatic image on canvas with a painting robot.

Approximate back-projection method for improving lateral resolution in circular-scanning-based photoacoustic tomography.

Abstract: Purpose In circular-scanning-based photoacoustic tomography (PAT), the effect of finite transducer aperture has not been effectively resolved. The goal of this paper is to propose a practical reconstruction method that accounts for the finite transducer aperture to improve the lateral resolution. Methods We for the first time propose to calculate the spatial temporal response (STR) of the employed finite-sized transducer in a forward model, and then compensate the time delay and the directional sensitivity of the transducer in the framework of the back-projection method. Both simulation and phantom experiments were carried out to evaluate the lateral resolution improvement with the proposed method. The performance of this new method for imaging complicated targets was also assessed by calculating the mean image gradient. Results Simulation results showed that with this new method the lateral resolution for off-center targets can be as good as that for the center targets. Phantom experimental results showed that this new method can improve the lateral resolution more than 2 times for a point target about 5 mm far from the rotation center. Phantom experimental results also showed that many blurred fine structures of a piece of leaf veins at the off-center regions were well restored with the new method, and the mean image gradient improved about 1.3 times. Conclusion The proposed new method can effectively account for the effect of finite transducer aperture for circular-scanning-based PAT in homogenous acoustic media. This new method also features for its robustness and computational efficiency, so that it is a worthy replacement to the conventional back-projection algorithm in circular-scanning-based PAT. This new method can be of great importance to the design of circular-scanning or spherical-scanning-based PAT systems.

Deep image enhancement for ill light imaging

Abstract: Imaging in the natural scene under ill lighting conditions (e.g., low light, back-lit, over-exposed front-lit, and any combinations of them) suffers from both over- and under-exposure at the same time, whereas processing of such images often results in over- and under-enhancement. A single small image sensor can hardly provide satisfactory quality for ill lighting conditions with ordinary optical lenses in capturing devices. Challenges arise in the maintenance of a visual smoothness between those regions, while color and contrast should be well preserved. The problem has been approached by various methods, including multiple sensors and handcrafted parameters, but extant model capacity is limited to only some specific scenes (i.e., lighting conditions). Motivated by these challenges, in this paper, we propose a deep image enhancement method for color images captured under ill lighting conditions. In this method, input images are first decomposed into reflection and illumination maps with the proposed layer distribution loss net, where the illumination blindness and structure degradation problem can be subsequently solved via these two components, respectively. The hidden degradation in reflection and illumination is tuned with a knowledge-based adaptive enhancement constraint designed for ill illuminated images. The model can maintain a balance of smoothness and contribute to solving the problem of noise besides over- and under-enhancement. The local consistency in illumination is achieved via a repairing operation performed in the proposed Repair-Net. The total variation operator is optimized to acquire local consistency, and the image gradient is guided with the proposed enhancement constraint. Finally, a product of updated reflection and illumination maps reconstructs an enhanced image. Experiments are organized under both very low exposure and ill illumination conditions, where a new dataset is also proposed. Results on both experiments show that our method has superior performance in preserving structural and textural details compared to other states of the art, which suggests that our method is more practical in future visual applications.

Transformer based Refinement Network for Accurate Crack Detection

Abstract: The era of intelligent transportation systems is evolving, which amends the way to deploy smart vision systems. One prominent challenge is to maintain the quality of highway roads for the safety issues. The manual road crack inspection is laborious, time-consuming, and inaccurate. A robust and automatic crack detection is needed to overcome these issues. Many deep learning based automatic crack detections have been developed. However, the majority of models suffer from inaccurate boundary detection due to the irregular shapes of the edge. Thus, the edge detection plays an important role to detect the gradient of the images. This study focuses on the refinement process, in which the pre-computed crack detection is refined to enhance the detection result with more accurate boundaries. The proposed refinement involves the image gradient as an additional feature. The vision transformer is adopted as the core layer to refine the crack in patch-wise manner. The multi-head attention in the transformer enhances the ability of the refinement network to find the relation of each processed patch. Extensive experiments have shown that the proposed method is able to generate superior crack boundaries than that of the state-of-the-art methods.

Minimizing L1 over L2 norms on the gradient

Abstract: In this paper, we study the L1/L2 minimization on the gradient for imaging applications. Several recent works have demonstrated that L1/L2 is better than the L1 norm when approximating the L0 norm to promote sparsity. Consequently, we postulate that applying L1/L2 on the gradient is better than the classic total variation (the L1 norm on the gradient) to enforce the sparsity of the image gradient. To verify our hypothesis, we consider a constrained formulation to reveal empirical evidence on the superiority of L1/L2 over L1 when recovering piecewise constant signals from low-frequency measurements. Numerically, we design a specific splitting scheme, under which we can prove subsequential and global convergence for the alternating direction method of multipliers (ADMM) under certain conditions. Experimentally, we demonstrate visible improvements of L1/L2 over L1 and other nonconvex regularizations for image recovery from low-frequency measurements and two medical applications of MRI and CT reconstruction. All the numerical results show the efficiency of our proposed approach.

Deep Gradient Prior Regularized Robust Video Super-Resolution

Abstract: This paper proposes a robust multi-frame video super-resolution (SR) scheme to obtain high SR performance under large upscaling factors. Although the reference low-resolution frames can provide complementary information for the high-resolution frame, an effective regularizer is required to rectify the unreliable information from the reference frames. As the high-frequency information is mostly contained in the image gradient field, we propose to learn the gradient-mapping function between the high-resolution (HR) and the low-resolution (LR) image to regularize the fusion of multiple frames. In contrast to the existing spatial-domain networks, we train a deep gradient-mapping network to learn the horizontal and vertical gradients. We found that adding the low-frequency information (mainly from the LR image) to the gradient-learning network can boost the performance of the network. A forward and backward motion field prior is used to regularize the estimation of the motion flow between frames. For robust SR reconstruction, a weighting scheme is proposed to exclude the outlier data. Visual and quantitative evaluations on benchmark datasets demonstrate that our method is superior to many state-of-the-art methods and can recover better details with less artifacts.

Automatic Subsidence Troughs Detection in SAR Interferograms Using Circlet Transform

Abstract: This article presents the results of automatic detection of subsidence troughs in synthetic aperture radar (SAR) interferograms. The detection of subsidence troughs is based on the circlet transform, which is able to detect features with circular shapes. Compared to other methods of detecting circles, the circular transform takes into account the finite data frequency. Moreover, the search shape is not limited to a circle but identified on the basis of a certain width. This is especially important in the case of detection of subsidence troughs whose shapes may not be similar to circles or ellipses but to their fragments. The transformation works directly on the image gradient; it does not require further binary segmentation or edge detection as in the case of other methods, e.g., the Hough transform. The entire processing process can be automated to save time and increase reliability compared to traditional methods. The proposed automatic detection method was tested on a differential interferogram that was generated based on Sentinel-1A SAR images of the Upper Silesian Coal Basin area. The test carried out showed that the proposed method is 20% more effective in detecting troughs that than the method using Hough transform.

Facial Expression Recognition based on Image Gradient and Deep Convolutional Neural Network

Abstract: Facial Expression Recognition (FER) is one of the basic ways of interacting with machines and has been getting more attention in recent years. In this paper, a novel FER system based on a deep convolutional neural network (DCNN) is presented. Motivated by the powerful ability of DCNN to learn features and image classification, the goal of this research is to design a compatible and discriminative input for pre-trained AlexNet-DCNN. The proposed method consists of 4 steps: first, extracting three channels of the image including the original gray-level image, in addition to horizontal and vertical gradients of the image similar to the red, green, and blue color channels of an RGB image as the DCNN input. Second, data augmentation including scale, rotation, width shift, height shift, zoom, horizontal flip, and vertical flip of the images are prepared in addition to the original images for training the DCNN. Then, the AlexNet-DCNN model is applied to learn high-level features corresponding to different emotion classes. Finally, transfer learning is implemented on the proposed model and the presented model is fine-tuned on target datasets. The average recognition accuracy of 92.41% and 93.66% were achieved for JAFEE and CK+ datasets, respectively. Experimental results on two benchmark emotional datasets show promising performance of the proposed model that can improve the performance of current FER systems.

Grid Model-Based Global Color Correction for Multiple Image Mosaicking

Abstract: Color consistency optimization for multiple images is a challenging problem in image mosaicking. To facilitate the global color optimization, existing approaches mainly use less flexible models, e.g., linear or gamma function, to eliminate the color differences between multiple images. However, these models often struggle to eliminate the color differences that existed in the local areas and preserve the image gradient information. To solve this problem, we creatively propose a novel color-correction model, which comprised a series of local grid linear models. This model is simple, but it is flexible enough to approximate a variety of complicated local color variations. To obtain the optimal model parameters for each image globally, a specific cost function that considers both color consistency and gradient preservation is designed and solved. The aim of our approach is to generate a composite image with visually consistent color. The original color information may be destroyed. Thus, this approach is unsuitable for the quantitative remote sensing applications. The experimental results on several challenging data sets show that the proposed approach outperforms state-of-the-art approaches in both visual quality and quantitative metrics.

Efficient $\ell ^0$ Gradient-Based Super-Resolution for Simplified Image Segmentation

Abstract: We consider a variational model for single-image super-resolution based on the assumption that the gradient of the target image is sparse. We enforce this assumption by considering both an isotropic and an anisotropic $\ell ^0$ regularisation on the image gradient combined with a quadratic data fidelity, similarly as studied in [1] for signal recovery problems. For the numerical realisation of the model, we propose a novel efficient ADMM splitting algorithm whose substeps solutions are computed efficiently by means of hard-thresholding and standard conjugate-gradient solvers. We test our model on highly-degraded synthetic and real-world data and quantitatively compare our results with several sparsity-promoting variational approaches as well as with state-of-the-art deep-learning techniques. Our experiments show that thanks to the $\ell ^0$ smoothing on the gradient, the super-resolved images can be used to improve the accuracy of standard segmentation algorithms for applications like QR codes and cell detection and land-cover classification problems.

Plug-and-Play gradient-based denoisers applied to CT image enhancement

Abstract: Blur and noise corrupting Computed Tomography (CT) images can hide or distort small but important details, negatively affecting the diagnosis. In this paper, we present a novel gradient-based Plug-and-Play algorithm, constructed on the Half-Quadratic Splitting scheme, and we apply it to restore CT images. In particular, we consider different schemes encompassing external and internal denoisers as priors, defined on the image gradient domain. The internal prior is based on the Total Variation functional. The external denoiser is implemented by a deep Convolutional Neural Network (CNN) trained on the gradient domain (and not on the image one, as in state-of-the-art works). We also prove a general fixed-point convergence theorem under weak assumptions on both internal and external denoisers. The experiments confirm the effectiveness of the proposed framework in restoring blurred noisy CT images, both in simulated and real medical settings. The achieved enhancements in the restored images are really remarkable, if compared to the results of many state-of-the-art methods.

Fourth-Order Anisotropic Diffusion for Inpainting and Image Compression.

Abstract: Edge-enhancing diffusion (EED) can reconstruct a close approximation of an original image from a small subset of its pixels. This makes it an attractive foundation for PDE based image compression. In this work, we generalize second-order EED to a fourth-order counterpart. It involves a fourth-order diffusion tensor that is constructed from the regularized image gradient in a similar way as in traditional second-order EED, permitting diffusion along edges, while applying a non-linear diffusivity function across them. We show that our fourth-order diffusion tensor formalism provides a unifying framework for all previous anisotropic fourth-order diffusion based methods, and that it provides additional flexibility. We achieve an efficient implementation using a fast semi-iterative scheme. Experimental results on natural and medical images suggest that our novel fourth-order method produces more accurate reconstructions compared to the existing second-order EED.

Weighted Hyper-Laplacian Prior with Overlapping Group Sparsity for Image Restoration under Cauchy Noise

Abstract: In this paper, we deal with the Cauchy image restoration problem under the maximum a posteriori framework. We propose a novel image prior, weighted hyper-Laplacian prior with overlapping group sparsity on the image gradient. This prior allows us to simultaneously promote the structural and pixel-level sparseness of the natural image gradient. The performance can be further improved by introducing the in-group-weights to balance the different scales of the components within each group. To tackle the corresponding optimization problem, we present a novel quadratic majorizer for majorization-minimization. We adopt the non-convex alternating direction method of multipliers as the main algorithm framework. The proposed regularizer can be reduced to the related variational regularizers including the total variation, the hyper-Laplacian, and the total variation with overlapping group sparsity. The comparative experiments with those existing gradient-based regularizers demonstrate the effectiveness of the proposed method in terms of PSNR and SSIM values.

Competitive Non-negative Representation with Image Gradient Orientations for Face Recognition

Abstract: Non-negative representation based classification (NRC) has achieved encouraging results in various pattern classification applications. Unfortunately, it still has some deficiencies. First, regularization term is absent in the objective function of NRC, which may produce an unstable solution and lead to misclassification. Second, NRC is not robust to occluded training samples. To address the above two problems, we propose a competitive NRC with image gradient orientations (IGO-CNRC) for face recognition. Concretely, first we introduce a competitive regularization term into the formulation of NRC and thereby present a competitive NRC (CNRC) method. To further increase the robustness to occluded training samples, we extract multiple-order image gradient orientations (IGOs) of samples and obtain the residuals under the framework of CNRC. Then these residuals are fused by the sum rule and the test sample is classified into the class that yields the least residual. Experimental results on standard face databases document the effectiveness of IGO-CNRC. The MATLAB code of IGO-CNRC is available at https://github.com/yinhefeng/IGO-CNRC

An image super-resolution reconstruction model based on fractional-order anisotropic diffusion equation.

Abstract: The image denoising model based on anisotropic diffusion equation often appears the staircase effect while image denoising, and the traditional super-resolution reconstruction algorithm can not effectively suppress the noise in the image in the case of blur and serious noise. To tackle this problem, a novel model is proposed in this paper. Based on the original diffusion equation, we propose a new method for calculating the adaptive fidelity term and its coefficients, which is based on the relationship between the image gradient and the diffusion function. It is realized that the diffusion speed can be slowed down by adaptively changing the coefficient of the fidelity term, and it is proved mathematically that the proposed fractional adaptive fidelity term will not change the existence and uniqueness of the solution of the original model. At the same time, washout filter is introduced as the control item of the model, and a new model of image super-resolution reconstruction and image denoising is constructed. In the proposed model, the order of fractional differential will be determined adaptively by the local variance of the image. And we give the numerical calculation method of the new model in the frequency domain by the method of Fourier transform. The experimental results show that the proposed algorithm can better prevent the staircase effect and achieve better visual effect. And by introducing washout filter to act as the control of the model, the stability of the system can be improved and the system can converge to a stable state quickly.