Range Kernel Research Articles

Scale‐adaptive Structure‐preserving Texture Filtering

AbstractThis paper proposes a scale‐adaptive filtering method to improve the performance of structure‐preserving texture filtering for image smoothing. With classical texture filters, it usually is challenging to smooth texture at multiple scales while preserving salient structures in an image. We address this issue in the concept of adaptive bilateral filtering, where the scales of Gaussian range kernels are allowed to vary from pixel to pixel. Based on direction‐wise statistics, our method distinguishes texture from structure effectively, identifies appropriate scope around a pixel to be smoothed and thus infers an optimal smoothing scale for it. Filtering an image with varying‐scale kernels, the image is smoothed according to the distribution of texture adaptively. With commendable experimental results, we show that, needing less iterations, our proposed scheme boosts texture filtering performance in terms of preserving the geometric structures of multiple scales even after aggressive smoothing of the original image.

Modified home range kernel density estimators that take environmental interactions into account

BackgroundKernel density estimation (KDE) is a major tool in the movement ecologist toolbox that is used to delineate where geo-tracked animals spend their time. Because KDE bandwidth optimizers are sensitive to temporal autocorrelation, statistically-robust alternatives have been advocated, first, data-thinning procedures, and more recently, autocorrelated kernel density estimation (AKDE). These yield asymptotically consistent, but very smoothed distributions, which may feature biologically unrealistic aspects such as spilling beyond impassable borders.MethodI introduce a semi-parametric variant of AKDE designed to extrapolate more realistic home range shapes by incorporating movement mechanisms into the bandwidth optimizer and into the base kernels. I implement a first approximative version based on the step selection framework. This method allows accommodating land cover selection, permeability of linear features, and attraction for select landscape features when delineating home ranges.ResultsIn a plains zebra (Equus quagga), the reluctance to cross a railway, the avoidance of dense woodland, and the preference for grassland when foraging created significant differences between the estimated home range contours by the new and by previous methods.ConclusionThere is a tradeoff to find between fully parametric density estimators, which can be very realistic but need to be provided with a good model and adequate environmental data, and non-parametric density estimators, which are more widely applicable and asymptotically consistent, but whose details are bandwidth-limited. The proposed semi-parametric approach attempts to strike this balance, but I outline a few areas of future improvement. I expect the approach to find its use in studies that compare extrapolated resource availability and interpolated resource use, in order to discover the movement mechanisms that we need to improve the extrapolations.

Fast bilateral filtering

The bilateral filter is a fundamental smoothing tool in image processing and computer vision due to its outstanding edge-preserving ability. However, the computational complexity depends on the size of the support of the spatial kernel. This drawback makes bilateral filtering time-consuming and significantly limits its applications. A novel strategy to turn the range kernel of the bilateral filter into a sum of exponential functions is proposed. As the convolution with the exponential function can be accelerated by the O ( 1 ) box filtering, the computational complexity of the bilateral thus becomes O ( 1 ) . Experimental results disclose that the proposed algorithm is competitive with the state-of-the-art algorithms in terms of filtering accuracy and computational efficiency.

Fast local SAR image despeckling by edge-avoiding wavelets

In this paper, a local despeckling algorithm based on a trous version of edge-avoiding wavelets for synthetic aperture radar images is proposed. Edge-avoiding wavelets provide the decomposition of the input image into several detail layers and a residual image which corresponds to the despeckled result by means of weighted a trous wavelet transform. The weight function is similar to the range kernel of the well-known bilateral filter and is determined by enhancing evaluation indexes. Visual and quantitative comparisons validate the performance of the proposed method in terms of both speckle reduction and edge preservation ability.

Speed Up Bilateral Filtering via Sparse Approximation on a Learned Cosine Dictionary

The edge-preserving bilateral filter (BF) is a widely used smoothing tool in many applications. However, its brute-force implementation depends on the size of the box window. The shortcoming causes BF time-consuming for the image processing task with a large window. To make the computational complexity irrelevant to the window size, sparse approximations of the filtering kernels are calculated on a learned cosine dictionary by two steps. First, all possible frequencies are learned (estimated) from the filtering kernel to compose a cosine dictionary. Then, the sparse approximation is conducted on the learned dictionary to seek the optimal cosine approximation for both the range and spatial kernels. By making use of the one-dimensional cosine approximation for the range kernel, the BF is transformed into spatial convolutions. Subsequently, by employing the two-dimensional cosine approximation for the spatial kernel, spatial convolutions are decomposed into box filters of which the computational complexity is O(1). To the best of our knowledge, our approach is the first method that adaptively constructs a cosine dictionary according to the input kernel. This merit guarantees the best filtering accuracy and efficiency. These advantages are corroborated by several carefully designed experiments.

A fast bilateral filtering algorithm based on rising cosine function

In order to speed up the bilateral filtering algorithm, a fast bilateral filtering algorithm based on raised cosine with compressibility factor (BRCF) is proposed. The BRCF uses a raised cosine function with a compression coefficient to replace Gaussian function as the range kernel function, and uses a limited number of linear convolution calculations to achieve bilateral filtering. Then, the improved BRCF (IBRCF) with a compression factor is proposed to accelerate the convergence rate of the raised cosine function. Compared to the published raised cosine algorithm, Taylor polynomial algorithm, and Gaussian polynomial algorithm, the computer simulation results show that the proposed IBRCF has a faster convergence rate with almost the same peak signal-to-noise ratio. After filtered seven images by various algorithms, the running time of the new IBRCF algorithm was confirmed to be less than 1/5 of Gaussian polynomial algorithm, while Gaussian polynomial algorithm was faster than the published raised cosine algorithm and Taylor polynomial algorithm. The mathematical proofs and algorithm flowcharts of the IBRCF algorithm are described in this paper in detail.

Fast Scale-Adaptive Bilateral Texture Smoothing

In the classical bilateral filter, a range kernel is used together with a spatial kernel for smoothing out fine details while simultaneously preserving edges. More recently, it has been demonstrated that even coarse textures can be smoothed using joint bilateral filtering. In this paper, we demonstrate that the superior texture filtering results can be obtained by adapting the spatial kernel at each pixel. To the best of our knowledge, spatial adaptation (of the bilateral filter) has not been explored for texture smoothing. The rationale behind adapting the spatial kernel is that one cannot smooth beyond a certain level using a fixed spatial kernel, no matter how we manipulate the range kernel. In fact, we should simply aggregate more pixels using a sufficiently wide spatial kernel to locally enhance the smoothing. Based on this reasoning, we propose to use the classical bilateral filter for texture smoothing, where we adapt the width of the spatial kernel at each pixel. We describe a simple and efficient gradient-based rule for the latter task. The attractive aspect is that we are able to develop a fast algorithm that can accelerate the computations by an order without visibly compromising the filtering quality. We demonstrate that our method outperforms classical bilateral filtering, joint bilateral filtering, and other filtering methods, and is competitive with the optimization methods. We also present some applications of texture smoothing using the proposed method.

Data driven particle size estimation of hematite grinding process using stochastic configuration network with robust technique

As a production quality index of hematite grinding process, particle size (PS) is hard to be measured in real time. To achieve the PS estimation, this paper proposes a novel data driven model of PS using stochastic configuration network (SCN) with robust technique, namely, robust SCN (RSCN). Firstly, this paper proves the universal approximation property of RSCN with weighted least squares technique. Secondly, three robust algorithms are presented by employing M-estimation with Huber loss function, M-estimation with interquartile range (IQR) and nonparametric kernel density estimation (NKDE) function respectively to set the penalty weight. Comparison experiments are first carried out based on the UCI standard data sets to verify the effectiveness of these methods, and then the data-driven PS model based on the robust algorithms are established and verified. Experimental results show that the RSCN has an excellent performance for the PS estimation.

Optimized Fourier Bilateral Filtering

We consider the problem of approximating a truncated Gaussian kernel using Fourier (trigonometric) functions. The computation-intensive bilateral filter can be expressed using fast convolutions by applying such an approximation to its range kernel, where the truncation in question is the dynamic range of the input image. The error from such an approximation depends on the period, the number of sinusoids, and the coefficient of each sinusoid. For a fixed period, we recently proposed a model for optimizing the coefficients using least-squares fitting. Following the Compressive Bilateral Filter (CBF), we demonstrate that the approximation can be improved by taking the period into account during the optimization. The accuracy of the resulting filtering is found to be at least as good as CBF, but significantly better for certain cases. The proposed approximation can also be used for non-Gaussian kernels, and it comes with guarantees on the filtering accuracy.

Fast Adaptive Bilateral Filtering.

In the classical bilateral filter, a fixed Gaussian range kernel is used along with a spatial kernel for edge-preserving smoothing. We consider a generalization of this filter, the so-called adaptive bilateral filter, where the center and width of the Gaussian range kernel are allowed to change from pixel to pixel. Though this variant was originally proposed for sharpening and noise removal, it can also be used for other applications, such as artifact removal and texture filtering. Similar to the bilateral filter, the brute-force implementation of its adaptive counterpart requires intense computations. While several fast algorithms have been proposed in the literature for bilateral filtering, most of them work only with a fixed range kernel. In this paper, we propose a fast algorithm for adaptive bilateral filtering, whose complexity does not scale with the spatial filter width. This is based on the observation that the concerned filtering can be performed purely in range space using an appropriately defined local histogram. We show that by replacing the histogram with a polynomial and the finite range-space sum with an integral, we can approximate the filter using analytic functions. In particular, an efficient algorithm is derived using the following innovations: the polynomial is fitted by matching its moments to those of the target histogram (this is done using fast convolutions), and the analytic functions are recursively computed using integration-by-parts. Our algorithm can accelerate the brute-force implementation by at least , without perceptible distortions in the visual quality. We demonstrate the effectiveness of our algorithm for sharpening, JPEG deblocking, and texture filtering.

Seasonal variability in vulnerability for Cassin's auklets (Ptychoramphus aleuticus) exposed to microplastic pollution in the Canadian Pacific region

Marine plastic pollution is an emerging global conservation challenge, potentially impacting organisms at all trophic levels. However, currently it is unclear to what extent plastic pollution is impacting marine organisms at the population, species or multispecies level. In this study, we explore seasonal exposure (i.e., vulnerability) of Cassin's Auklet (Ptychoramphus aleuticus) to plastic pollution with exposure models during boreal summer and winter seasons. Based on these models, we infer exposure at the population level for this species, in the Canadian Pacific region where approximately 75% of the global population of this species breeds. The models quantify plastic exposure by determining seasonal core foraging areas and plastic concentrations found in those same areas. Core foraging areas were determined using a Generalized Additive Model based on at-sea observation data (collected year round: 1990–2010) and 50% Home Range Kernels based on aerial telemetry data (May and June 1999–2001). Plastic concentrations within these core areas were interpolated based on seawater microplastic concentrations from the summer of 2012. We found that during the boreal summer, Cassin's Auklets were exposed to relatively low concentrations of plastics. During the winter, auklet distribution shifted towards the coast where plastic concentrations are considerably higher. Model derived seasonal variability in exposure was consistent with necropsy results from bird carcasses recovered during the winter of 2014, and from a multiyear study on chick provisioning during the summer. Local oceanography likely plays a role in determining seasonal shifts in both marine bird as well microplastic concentrations, and hence exposure. As well, individual sensitivity (i.e., dose-dependent effect) may vary with annual cycles. Currently, research is focusing on determining how sensitive individual birds are to microplastic concentrations, and our models will help translate sensitivity found at the individual level to potential impacts at population or species level.

Well-posedness of an evolution problem with nonlocal diffusion

We prove the well-posedness of a general evolution reaction–nonlocal diffusion problem under two sets of assumptions. In the first set, the main hypothesis is the Lipschitz continuity of the range kernel and the bounded variation of the spatial kernel and the initial datum. In the second set of assumptions, we relax the Lipschitz continuity of the range kernel to Hölder continuity, and assume monotonic behavior. In this case, the spatial kernel and the initial data can be just integrable functions. The main applications of this model are related to the fields of Image Processing and Population Dynamics.

The multiscale directional neighborhood filter and its application to clutter removal in GPR data

We present a novel neighborhood filter (NF)-based clutter removal algorithm in ground-penetrating radar (GPR) images. Since NF uses only range kernel of the well-known bilateral filter, it is less complex and makes clutter removal method appropriate for real-time implementations. We extend NF to multiscale–multidirectional case: MDNF and then decompose the GPR image into approximation and detail subbands to capture the intrinsic geometrical structures that contain both target and clutter information. After directional decomposition, the clutter is eliminated by keeping the diagonal information for target component. Finally, the inverse transform is applied to the remaining subbands for reconstruction of clutter-free GPR image. Results of both simulated and real datasets validate the superiority of MDNF over the state-of-the-art methods, and it improves in the false alarm rate further by 5.5% at maximum detection performance.

Bilateral filter acceleration based on weighted variable projection

Due to the heavy computation cost, the bilateral filter cannot be applied to real-time applications. To deal with this problem, many range kernel approximation based acceleration schemes have been proposed. However, all these methods use predefined basis function and assign the same penalisation for all range values to fulfil range kernel approximation. These constraints block from further improving the filtering accuracy and speed. Employing weighted variable projection, a new acceleration method which achieves state-of-the-art performance is proposed. This is done by: (i) unleashing the constraint of using fixed basis function; (ii) exploiting the colour distribution information of the input image to perform a weighted approximation of the range kernel. Experiments demonstrate the superiority of the proposed method in gaining more accurate filtering results efficiently.

A Digital Image Denoising Algorithm Based on Gaussian Filtering and Bilateral Filtering

Bilateral filtering has been applied in the area of digital image processing widely, but in the high gradient region of the image, bilateral filtering may generate staircase effect. Bilateral filtering can be regarded as one particular form of local mode filtering, according to above analysis, an mixed image de-noising algorithm is proposed based on Gaussian filter and bilateral filtering. First of all, it uses Gaussian filter to filtrate the noise image and get the reference image, then to take both the reference image and noise image as the input for range kernel function of bilateral filter. The reference image can provide the image’s low frequency information, and noise image can provide image’s high frequency information. Through the competitive experiment on both the method in this paper and traditional bilateral filtering, the experimental result showed that the mixed de-noising algorithm can effectively overcome staircase effect, and the filtrated image was more smooth, its textural features was also more close to the original image, and it can achieve higher PSNR value, but the amount of calculation of above two algorithms are basically the same.

An ecophysiologically informed model of seed dispersal by orangutans: linking animal movement with gut passage across time and space.

Fauna-mediated ecosystem service provision (e.g. seed dispersal) can be difficult to quantify and predict because it is underpinned by the shifting niches of multiple interacting organisms. Such interactions are especially complex in tropical ecosystems, including endangered peat forests of Central Borneo, a biodiversity hot spot and home to the critically endangered orangutan (Pongo pygmaeus wurmbii). We combined studies of the digestive physiology of captive orangutans in Australia with detailed field studies of wild orangutans in the Natural Laboratory of Peat-Swamp Forest of Sabangau, Central Kalimantan, Indonesia. By measuring the gut transit time (TT) of indigestible seed mimics (beads) in captivity and applying this as a temporal constraint to movement data of wild orangutans, we developed a mechanistic, time-explicit spatial model to project the seed dispersal patterns by these large-bodied, arboreal frugivores. We followed seven orangutans and established home range kernels using Time Local Convex Hull (T-LoCoH) modelling. This allowed us to model individual orangutan movements and to adjust these models according to gut transit times to estimate seed dispersal kernels. Female movements were conservative (core ranges of 55 and 52 ha in the wet and dry seasons, respectively) and revisitation rates to the same location of n = 4 in each 24-h block. Male movements were more unpredictable, yielding fragmented core ranges and revisitation rates to the same location of only 1.2 times each 24 h; males also demonstrated large disjunctions where they moved rapidly over long distances and were frequently lost from view. Seed dispersal kernels were nested predictably within the core ranges of females, but not males. We used the T-LoCoH approach to analyse movement ecology, which offered a powerful tool to predict the primary deposition of seeds by orangutans, thereby providing a reliable method for making a priori predictions of seed dispersal dynamics by other frugivores in novel ecosystems.

Image Segmentation Using Linked Mean-Shift Vectors and Global/Local Attributes

This paper proposes novel noniterative mean-shift-based image segmentation that uses global and local attributes. The existing mean-shift-based methods use a fixed range bandwidth, and hence their accuracy is dependent on the range spectrum of an image. To resolve this dependency, this paper proposes to modify the range kernel in the mean-shift process to be anisotropic. The modification is conducted using a global attribute defined as the range covariance matrix of the image. Further, to alleviate oversegmentation, the proposed method merges the segments having similar local attributes more aggressively than other segments. The local attribute for each segment is defined as the sum of the variances of the chromatic components. Finally, to expedite the processing, the proposed method uses a region adjacency graph (RAG) for the merging process, thus differing from the existing linked mean-shift-based methods. In the experiments on the Berkeley segmentation data set, the use of the global and local attributes improved segmentation accuracy; the proposed method outperformed the state-of-the-art linked mean-shift-based method by showing an improvement of 2.15%, 3.16%, 3.32%, and 1.90% in probability rand index, segmentation covering, variation of information, and F-measure, respectively. Further, compared with the benchmark method, which uses the dilating and merging scheme, the proposed method improved the speed of the merging process 42 times by applying the RAG.

A Fast Approximation of the Bilateral Filter using the Discrete Fourier Transform

The bilateral filter is a popular non-linear smoother that has applications in image processing, computer vision, and computational photography. The novelty of the filter is that a range kernel is used in tandem with a spatial kernel for performing edge-preserving smoothing, where both kernels are usually Gaussian. A direct implementation of the bilateral filter is computationally expensive, and several fast approximations have been proposed to address this problem. In particular, it was recently demonstrated in a series of papers that a fast and accurate approximation of the bilateral filter can be obtained by approximating the Gaussian range kernel using polynomials and trigonometric functions. By adopting some of the ideas from this line of work, we propose a fast algorithm based on the discrete Fourier transform of the samples of the range kernel. We develop a parallel C implementation of the resulting algorithm for Gaussian kernels, and analyze the effect of various extrinsic and intrinsic parameters on the approximation quality and the run time. A key component of the implementation are the recursive Gaussian filters of Deriche and Young.

Fast bilateral filtering using the Padé approximation

Due to the edge-preserving ability, the bilateral filter is considered as the fundamental tool in computer vision and computer graphics. However, its computational complexity has a close connection with the size of the box window. This drawback leads that the bilateral filter is inappropriate for the computational insensitive application. One way to accelerate the bilateral filter is to approximate the Gaussian range kernel by trigonometric functions and synthesise final results from a set of filtering results of fast convolutions. A novel approximation that can be applied to any range kernel is proposed. Specifically, first the Z transformation of the range kernel is obtained, then approximate the Z transformation of the range kernel using the Pade Approximation. Finally, inverse the transformation of the Pade approximation and obtain an exponential sum to approximate original range kernel, where the coefficients of the exponential basis are computed by solving a set of linear equations. Experiments show the method achieves state-of-the-art results in terms of accuracy and speed.

Entropy-based bilateral filtering with a new range kernel

Bilateral filter (BF) is a well-known edge-preserving image smoothing technique, which has been widely used in image denoising. The major drawback of BF is that its range kernel is sensitive to noise. To address this issue, we propose an entropy-based BF (EBF) with a new range kernel which contains a new range distance. The new range distance is robust to noise by exploiting the information from the denoised estimate and the corresponding method noise, i.e., the difference between the noisy image and its denoised estimate. Moreover, in order to consider the local statistics of images, local entropy is applied to adaptively guide the range parameter selections. This allows our method to adapt to the images with different characteristics. Experimental results demonstrate that the proposed EBF significantly outperforms the standard BF in terms of both quantitative metrics and subjective visual quality.