Range Kernel Research Articles

Bilateral regularized optimization model for edge-preserving image smoothing

Edge-preserving image smoothing is vital in the field of image processing and computational photography. The state-of-the-art filters based on optimization models have achieved promising performance. However, most of them fail to consider the spatial support in the regularization term, thus limiting the edge-preserving capabilities. In this paper, inspired by the bilateral filter, which consists of a range kernel and a spatial kernel. we propose to leverage bilateral kernel as a penalty function, and embed it into an optimization model for edge-preserving image smoothing. Furthermore, we propose to incorporate an edge-aware weighted scheme in the data term design, which further improves the edge-preserving capability. The bilateral function is non-convex and can be non-trivial to solve. In this paper, we propose a novel iterative solution based on fixed point iteration, where the main burden in each iteration is a bilateral filtering process. We have conducted extensive experiments to evaluate the proposed filter. Experiment results indicate that our filter benefits a variety of image processing tasks. Moreover, we propose an efficient approximation of the proposed filter, which is able to significantly accelerate the filtering process with neglectable sacrifice of smoothing quality.

Expanding Sparse Radar Depth Based on Joint Bilateral Filter for Radar-Guided Monocular Depth Estimation.

Radar data can provide additional depth information for monocular depth estimation. It provides a cost-effective solution and is robust in various weather conditions, particularly when compared with lidar. Given the sparse and limited vertical field of view of radar signals, existing methods employ either a vertical extension of radar points or the training of a preprocessing neural network to extend sparse radar points under lidar supervision. In this work, we present a novel radar expansion technique inspired by the joint bilateral filter, tailored for radar-guided monocular depth estimation. Our approach is motivated by the synergy of spatial and range kernels within the joint bilateral filter. Unlike traditional methods that assign a weighted average of nearby pixels to the current pixel, we expand sparse radar points by calculating a confidence score based on the values of spatial and range kernels. Additionally, we propose the use of a range-aware window size for radar expansion instead of a fixed window size in the image plane. Our proposed method effectively increases the number of radar points from an average of 39 points in a raw radar frame to an average of 100 K points. Notably, the expanded radar exhibits fewer intrinsic errors when compared with raw radar and previous methodologies. To validate our approach, we assess our proposed depth estimation model on the nuScenes dataset. Comparative evaluations with existing radar-guided depth estimation models demonstrate its state-of-the-art performance.

Fractional-Order Total Variation Geiger-Mode Avalanche Photodiode Lidar Range-Image Denoising Algorithm Based on Spatial Kernel Function and Range Kernel Function

A Geiger-mode avalanche photodiode (GM-APD) laser radar range image has much noise when the signal-to-background ratios (SBRs) are low, making it difficult to recover the real target scene. In this paper, based on the GM-APD lidar denoising model of fractional-order total variation (FOTV), the spatial relationship and similarity relationship between pixels are obtained by using a spatial kernel function and range kernel function to optimize the fractional differential operator, and a new FOTV GM-APD lidar range-image denoising algorithm is designed. The lost information and range anomalous noise are suppressed while the target details and contour information are preserved. The Monte Carlo simulation and experimental results show that, under the same SBRs and statistical frame number, the proposed algorithm improves the target restoration degree by at least 5.11% and the peak signal-to-noise ratio (PSNR) by at least 24.6%. The proposed approach can accomplish the denoising of GM-APD lidar range images when SBRs are low.

A target-free video structural motion estimation method based on multi-path optimization

The vibration data are quite important for structural health monitoring (SHM). This paper proposed a novel method, to adaptively estimate video motions of the structure in subpixel accuracy, without attaching any targets. The proposed method includes three steps. In the first step, to remove outliers and simultaneously preserve feature points, the Gaussian range kernel is used along with the Gaussian spatial kernel, and calculated by the polynomial fitting and recursive integrals computing. In the second step, to calculate video pixel motions varied with spatial coordinates in the region of interest (ROI) for testing, the ROI is divided into multiple grid cells. Motions in each grid cell are modeled as local spatially-variant homography matrices, and their spatial consistency are enhanced by a shape-preserving constraint. The third step is to enhance both spatial and temporal correlations of the calculated homography matrices, achieved by the data term and the smoothness term in both space and time domains. The superiority of the proposed method over traditional methods was validated in several case studies for analyzing structural motions. Among the comparisons, the proposed method can produce image denoising, camera motions, structural motions, and structural modal information in subpixel accuracy, and with the best accuracy.

Hybrid deep autoencoder network based adaptive cross guided bilateral filter for motion artifacts correction and denoising from MRI

ABSTRACT Removal of motion artifacts from medical images is essential, because the respiration by patient causes degradation in artifact removal. Therefore, getting an MRI without any artifacts and noise is challenging. Previous techniques failed to preserve the image quality during denoising, thereby affecting the classification accuracy. To overcome such challenges, two modules are considered in this work: classification and denoising. The classification process is successfully performed by Hybrid Deep autoencoder-convolutional neural network (DAE-CNN). It classifies the original images into motion artifacts, available and normal images. Then, the available artifacts are removed using cross guided bilateral filter (CGBF). The optimal parameters required to improve the CGBF performance are selected using the hybrid optimization algorithm. The filter’s performance relies on the optimal spatial and range kernels selection. Finally, the classification and denoising-based results are evaluated using the BRATS 2015 dataset and achieved 95.84% accuracy and PSNR – 46.4, which is better than existing methods.

Image downscaling via co-occurrence learning

Image downscaling is one of the widely used operations in image processing and computer graphics. It was recently demonstrated in the literature that kernel-based convolutional filters could be modified to develop efficient image downscaling algorithms. In this work, we present a new downscaling technique which is based on kernel-based image filtering concept. We propose to use pairwise co-occurrence similarity of the pixelpairs as the range kernel similarity in the filtering operation. The co-occurrence of the pixel-pair is learned directly from the input image. This co-occurrence learning is performed in a neighborhood based fashion all over the image. The proposed method can preserve the high-frequency structures, which were present in the input image, into the downscaled image. The idea is further extended to the case of fractions factor of downscaling. The resulting images retain visually-important details and do not suffer from edge-blurring artifact. We demonstrate the effectiveness of our proposed approach with extensive experiments on a large number of images downscaled with various downscaling factors.

Fast 3D kernel computation method for positron range correction in PET

Objective. The positron range is a fundamental, detector-independent physical limitation to spatial resolution in positron emission tomography (PET) as it causes a significant blurring of underlying activity distribution in the reconstructed images. A major challenge for positron range correction methods is to provide accurate range kernels that inherently incorporate the generally inhomogeneous stopping power, especially at tissue boundaries. In this work, we propose a novel approach to generate accurate three-dimensional (3D) blurring kernels both in homogenous and heterogeneous media to improve PET spatial resolution. Approach. In the proposed approach, positron energy deposition was approximately tracked along straight paths, depending on the positron stopping power of the underlying material. The positron stopping power was derived from the attenuation coefficient of 511 keV gamma photons according to the available PET attenuation maps. Thus, the history of energy deposition is taken into account within the range of kernels. Special emphasis was placed on facilitating the very fast computation of the positron annihilation probability in each voxel. Results. Positron path distributions of 18F in low-density polyurethane were in high agreement with Geant4 simulation at an annihilation probability larger than 10−2 ∼ 10−3 of the maximum annihilation probability. The Geant4 simulation was further validated with measured 18F depth profiles in these polyurethane phantoms. The tissue boundary of water with cortical bone and lung was correctly modeled. Residual artifacts from the numerical computations were in the range of 1%. The calculated annihilation probability in voxels shows an overall difference of less than 20% compared to the Geant4 simulation. Significance. The proposed method is expected to significantly improve spatial resolution for non-standard isotopes by providing sufficiently accurate range kernels, even in the case of significant tissue inhomogeneities.

Understanding spatially explicit capture–recapture parameters for informing invasive animal management

AbstractSpatially explicit capture–recapture modeling is used to estimate population density to enhance our ecological understanding and management of wildlife populations. The two primary parameters estimated in the capture process of these models are σ and g0. The σ parameter is the standard deviation of a bivariate normal home range kernel (indicating home range size), while g0 is the probability of capture by a device placed at the home range center. These parameters are being increasingly generalized and used in simulation models to predict the detection or capture rates of invasive animals to inform management strategies. Given the sensitivity of simulation model predictions to parameter values, we performed an analysis of preexisting GPS telemetry and trapping data of invasive brushtail possums (Trichosurus vulpecula) across New Zealand to address the following three questions. First, how does σ vary with population density, habitat, and age–sex class? Second, how is g0 influenced by home range size (i.e., σ) and trap type? Third, how does the predicted probability of capture or detection of individuals vary with σ, different trap types and trap densities? We used data from 180 possums across 18 sites to develop a Bayesian hierarchical model. Results showed that σ decreased with increasing population density and increasing area of productive grassland. There was a strong negative relationship between σ and g0, and g0 was highest for cage traps and lowest for raised leg‐hold traps. Despite the potential compensatory inverse effect of g0 with σ, the probability of capturing a randomly located possum by a large array of traps increased with increasing σ. Results show that selection of σ for predictive simulation modeling should begin with an estimated population density. The associated g0 should then be identified as a function of σ, and stochasticity should be incorporated to account for inter‐individual variability. The approach employed here provides a methodology for estimating density, σ, and g0 using trapping and telemetry data, and our results will help guide careful consideration of density, σ, and g0 to improve the accuracy of simulation studies across species.

Guided Gaussian range kernel filtering based on similarity-aware window

We present a window-adaptive Gaussian guided filtering method to smooth images while preserving edge features. The key to our algorithm is designing a similarity-aware filtering window based on density clustering to protect the edge structure and introducing a small-scale Gaussian spatial kernel as the input of the Gaussian range kernel to construct a guided filter for image smoothing. Specifically, we first utilized the Gaussian spatial kernel filtering with a small spatial bandwidth to yield a guidance input. Then, the Mahalanobis metric was used to calculate the distance between the center point and the other pixels in the box filtering window, by which we employed the center density clustering algorithm to obtain a better nonbox region (i.e., similarity-aware window) in which each pixel was similar to the center point. Finally, based on the guidance input and the similarity-aware window, the guided Gaussian range filter performed better on image smoothing. Our proposed algorithm is simple and easy to implement. In particular, the window-aware technology effectively improved edge protection, and it can be widely used in image denoising, background smoothing, detexturing, detail enhancement, and edge extraction.

Adaptive Bilateral Texture Filter for Image Smoothing.

The biggest challenge of texture filtering is to smooth the strong gradient textures while maintaining the weak structures, which is difficult to achieve with current methods. Based on this, we propose a scale-adaptive texture filtering algorithm in this paper. First, the four-directional detection with gradient information is proposed for structure measurement. Second, the spatial kernel scale for each pixel is obtained based on the structure information; the larger spatial kernel is for pixels in textural regions to enhance the smoothness, while the smaller spatial kernel is for pixels on structures to maintain the edges. Finally, we adopt the Fourier approximation of range kernel, which reduces computational complexity without compromising the filtering visual quality. By subjective and objective analysis, our method outperforms the previous methods in eliminating the textures while preserving main structures and also has advantages in structure similarity and visual perception quality.

Mapping the \u201ccatscape\u201d formed by a population of pet cats with outdoor access

The domestic cat (Felis catus) is among the most popular companion animals and most abundant carnivores globally. It is also a pet with an immense ecological footprint because even non-feral and food-subsidized cats can be prolific predators. Whereas knowledge about the spatial behavior of individual domestic cats is growing, we still know little about how a local population of free-ranging pet cats occupies the landscape. Using a citizen science approach, we GPS-tagged 92 pet cats with outdoor access living in a residential area in southern Norway. The resulting position data allowed us to construct both individual home range kernels and a population-level utilization distribution. Our results reveal a dense predatory blanket that outdoor cats drape over and beyond the urban landscape. It is this population-level intensity surface—the “catscape”—that potential prey have to navigate. There were few gaps in the catscape within our residential study area and therefore few terrestrial refuges from potential cat predation. However, cats spent on average 79% of their outdoor time within 50 m to their owner’s home, which suggests that the primary impact is local and most acute for wildlife in the vicinity to homes with cats. We discuss the catscape as a conceptual and quantitative tool for better understanding and mitigating the environmental impact of domestic cats.

A Fast Two-Stage Bilateral Filter Using Constant Time O(1) Histogram Generation.

Bilateral Filtering (BF) is an effective edge-preserving smoothing technique in image processing. However, an inherent problem of BF for image denoising is that it is challenging to differentiate image noise and details with the range kernel, thus often preserving both noise and edges in denoising. This letter proposes a novel Dual-Histogram BF (DHBF) method that exploits an edge-preserving noise-reduced guidance image to compute the range kernel, removing isolated noisy pixels for better denoising results. Furthermore, we approximate the spatial kernel using mean filtering based on column histogram construction to achieve constant-time filtering regardless of the kernel radius’ size and achieve better smoothing. Experimental results on multiple benchmark datasets for denoising show that the proposed DHBF outperforms other state-of-the-art BF methods.

Structure-aware adaptive bilateral texture filtering

The classical bilateral filter is designed for preserving the structure of the image by utilizing the range and spatial kernel. However, its straightforward application on texture smoothing is not viable as certain modifications are required in a bilateral filter to exploit it as a precise tool for texture smoothing. It is worth noting that with numerous rectifications, several methods have been developed over the last few decades that employ a bilateral filter as a precise tool for texture smoothing. Although these methods are precise in preserving significant structural information, a loss in the sharpness of the structures transpires simultaneously. Moreover, these methods do smooth texture efficiently but at the same time, they also blur some prominent structures. In this paper, we have designed a novel structure-aware bilateral filter that incorporates the structural information throughout texture smoothing. The filtering is executed on individual pixel from the scale map by employing the spatial kernel. The experimental section reveals the supremacy of the proposed method with respect to texture smoothing and structure preservation. We have also made an effort to demonstrate the proposed method's efficiency in several applications, namely, edge detection, detail enhancement, and texture transfer.

Two-Pass Bilateral Smooth Filtering for Remote Sensing Imagery

Bilateral filtering has been adopted for edge-preserving image smoothing and achieved the state-of-the-art performance. Most of the existing bilateral filters (BFs), however, focus on accelerating brute-force implementation but not on smoothing quality. In this letter, we propose a two-pass (TP) BF, TP-based BF, and an adaptive control scheme of range kernels for noise-invariant edge-preserving image smoothing. Specifically, the TP-based BF is composed of two bilateral filtering operations, which are, respectively, in charge of coarse context extraction and fine structure refinement. The control scheme of range kernels guides the TP bilateral mechanism to eliminate first high-frequency noisy pixels and then explore contribution between pixels from clean contexts. Experimental results on four aerial-imagery benchmark data sets show that our TP-based BF outperforms the existing BFs in terms of both feature- and gradient-aware measures.

Theoretical analysis and image reconstruction for multi-bit quanta image sensors

A new breed of photon-counting sensors, called quanta image sensor (QIS), enables the detection of light with precision represented by the number of photons arriving within a time period. However, most existing analysis results on QIS systems are formulated for the single-bit case only. Directly extending the existing single-bit analysis to the multi-bit case leads to the situation that the variance of the estimated exposure is greater than the Cramér-Rao bound (CRB). Also, the existing dynamic range analysis leads to a strange situation that the maximum exposure level is not a function of the spatiotemporal jot kernel size. This paper formally analyzes the properties of multi-bit QIS (MBQIS) systems. It derives the log likelihood function of the received photon counts in a spatiotemporal jot kernel, and introduces the concept of the probability of all jots being saturated. From the likelihood function result, we can obtain a maximum likelihood (ML) estimate for the exposure level and present an image construction algorithm, namely ML multi-bit (MLM). Since the estimate is ML based, the variance of the estimated exposure achieves the CRB asymptotically and the MLM is an asymptotically unbiased estimator. Also, based on the Fisher information concept, this paper derives the CRB on the variance of the estimated exposure. Hence the CRB given by this paper can be considered as a performance indicator for all algorithms. From the jot saturation analysis result, we can accurately formulate the relationship between dynamic range and spatiotemporal kernel size. Specifically, with our two analysis results, we can model the relationships between sensor design parameters and performance metrics (variance of the estimated exposure and the dynamic range). Since the two analysis results are independent of the construction algorithms used, they give us some guidelines to design a QIS system. In addition, this paper empirically studies the effect of the readout Gaussian noise. Finally, to demonstrate another application of the likelihood analysis result, we develop an enhanced version of MLM, namely MLM with denoising (MLMDN), based on the proposed likelihood function and the regularization concept.

Putnam-Fuglede type theorem for class $ \mathcal{A}_k $ operators

<abstract> We will call $ U\in B(X) $ as an operator of class $ \mathcal{A}_k $ if for some integer $ k $, the following inequality is satisfied: <p class="disp_formula">$ \vert U^{k+1}\vert^{\frac{2}{k+1}}\geq \vert U\vert^{2}. $ In the present article, some basic spectral properties of this class are given, also the asymmetric Putnam-Fuglede theorem and the range kernel orthogonality for class $ \mathcal{A}_k $ operators are proved. </abstract>

Geographic information system based detection and quantification of boulders using HiRISE imagery: a case study in Jezero Crater

The objective of this study is to present a geographic information system based method for detecting and quantifying boulders (area, length, width, elevation, and transport distance) that couples image processing techniques with spatial analysis tools. This study focuses on a delta within Jezero Crater on Mars, the site of the upcoming Mars 2020 rover mission. Understanding the distribution of boulders and their properties is significant since they are critical for understanding surficial geology, sedimentology, and erosional/depositional processes on Mars. Additionally, boulders and large clasts pose a challenge to the traversability of terrain for both rovers and future human missions. A high-resolution imaging science experiment image of the Jezero delta was processed using a filtering/masking algorithm, which combines mean filtering, brightness interval masking, and range kernel filtering. User-determined conservative (no false-positive boulder pixels) and liberal (no false-negative pixels) brightness thresholds were used to generate boulder polygons and their minimum-bounding geometry. Using conservative parameters, 443,126 boulder-like features were identified, of which 153,582 (35%) were relevant boulders. For these boulders, the cumulative fractional area versus boulder width relationship flattens out as predicted in prior work, suggesting that approach is accurate, and further is simpler than existing approaches, and can identify boulders as small as 50 cm in diameter. The algorithm, which can be customized to various degrees of boulder rounding and works on images with different brightness and contrast levels and illumination angles, is applicable to boulder fields on Earth as well as Mars and other solar system bodies.

Structure-Aware Texture Filtering Based on Local Histogram Operator

Smoothing the multi-scale textures with strong gradient while maintaining the weak structures is still a challenging work for the existing texture filtering methods. In this paper, we propose a variant of the bilateral filter to address this issue. Unlike the classical bilateral filter, which usually uses a fixed range kernel for texture filtering, the variant uses an adaptive range kernel, that is, if a pixel is located near a structure, the range kernel assigned to the pixel is small, otherwise, the range kernel is large. This mechanism ensures the preservation of sharp edges. In order to perform structure measurement, we propose a local histogram operator, which can identify structures from textures by comparing the difference in color distribution between the left and right half neighboring windows centered on the pixel of interest. In addition, after once bilateral filtering, instead of multiple iterations, a novel anisotropic filter is designed to remove residual textures, which can avoid edge blurring to some extent. Experimental results demonstrate the effectiveness of our method by comparing it with the state-of-the-art methods in preserving weak structures as well as suppressing textures with strong gradient or varying scales.

Gaussian-Adaptive Bilateral Filter

Recent studies have demonstrated that a bilateral filter can increase the quality of edge-preserving image smoothing significantly. Different strategies or mechanisms have been used to eliminate the brute-force computation in bilateral filters. However, blindly decreasing the processing time of the bilateral filter cannot further ameliorate the effectiveness of filter. In addition, even when the processing speed of the filter is increased, inherent problem occurred in the Gaussian range kernel when facing a noise filtering input and its effect on edge-preserving image smoothing operation are barely discussed. In this letter, we propose a novel Gaussian-adaptive bilateral filter (GABF) to resolve the aforementioned problem. The basic idea is to acquire a low-pass guidance for the range kernel by a Gaussian spatial kernel. Such low-pass guidance lead to a clean Gaussian range kernel for later bilateral composite. The results of experiments conducted on several test datasets indicate that the proposed GABF outperforms most existing bilateral-filter-based methods.

Progressive denoising of seismic data via robust noise estimation in dual domains

Random noise attenuation plays an important role in seismic data processing. Most traditional methods suppress random noise either in the time-space domain or in the transformed domain, which may encounter difficulty in retaining the detailed structures. We have introduced the progressive denoising method to suppress random noise in seismic data. This method estimates random noise at each sample independently by imposing proper constraints on local windowed data in the time-space domain and then in the transformed domain, and the denoised results of the whole data set are gradually improved by many iterations. First, we apply an unnormalized bilateral kernel in time-space domain to reject large-amplitude signals; then, we apply a range kernel in the frequency-wavenumber domain to reject medium-amplitude signals; finally, we can obtain a total estimate of random noise by repeating these steps approximately 30 times. Numerical examples indicate that the progressive denoising method can achieve a better denoising result, compared with the two typical single-domain methods: the [Formula: see text]-[Formula: see text] deconvolution method and the curvelet domain thresholding method. As an edge-preserving method, the progressive denoising method can greatly reduce the random noise without harming the useful signals, especially to those high-frequency components, which would be crucial for high-resolution imaging and interpretations in the following stages.