Color quantization is an image processing operation that attempts to reduce the number of distinct colors used to represent an image without significant loss of quality. This operation is useful as an initial step to perform further processing on the image. The interest in this operation has led to several solution methods being proposed over the years. Within these methods several swarm-based methods have been used in recent years to solve the problem. This article discusses the application of one of these methods, called grey wolf optimization, to perform color quantization. This algorithm has generated good results when applied to a variety of optimization problems. Among the features that differentiate this algorithm from other swarm algorithms are its ability to converge toward better solutions, its speed, and the existence of a single control parameter. The article describes in detail how the grey wolf optimization method should be adapted to perform color quantization, so that it generates a quantized palette that allows the quantized image to be represented. In this case, each individual in the group represents a quantized palette, which is improved with the information provided by the group. The detailed description of the algorithm is complemented by an extensive testing section that compares the results of the proposed method to those of 16 others techniques. The results, based on the comparison of MSE, MAE, PSNR, SSIM, and runtime, show that grey wolf optimization can generate good quality images, better than most of the compared methods. • The Grey wolf optimization method is improved to apply it to color quantization. • The method is tested on 24 images commonly used in color quantization literature. • Extensive experiments and statistical analysis show that the proposal is effective. • It obtains better results than most of the 16 methods with which it is compared.

Abstract This article analyzes various color quantization methods using multiple image quality assessment indices. Experiments were conducted with ten color quantization methods and eight image quality indices on a dataset containing 100 RGB color images. The set of color quantization methods selected for this study includes well-known methods used by many researchers as a baseline against which to compare new methods. On the other hand, the image quality assessment indices selected are the following: mean squared error, mean absolute error, peak signal-to-noise ratio, structural similarity index, multi-scale structural similarity index, visual information fidelity index, universal image quality index, and spectral angle mapper index. The selected indices not only include the most popular indices in the color quantization literature but also more recent ones that have not yet been adopted in the aforementioned literature. The analysis of the results indicates that the conventional assessment indices used in the color quantization literature generate different results from those obtained by newer indices that take into account the visual characteristics of the images. Therefore, when comparing color quantization methods, it is recommended not to use a single index based solely on pixelwise comparisons, as is the case with most studies to date, but rather to use several indices that consider the various characteristics of the human visual system.

The papers in this special section focus on skin image analysis using deep learning applications. Skin is the largest organ of the human body, and is the first area of a patient assessed by clinical staff. The skin delivers numerous insights into a patient’s underlying health: for example, pale or blue skin suggests respiratory issues, unusually yellowish skin can signal hepatic issues, or certain rashes can be indicative of autoimmune issues. Dermatological complaints are the most prevalent reason that patients seek primary care, and images of the skin are the most easily captured form of medical image in healthcare. However, certain serious skin diseases are not reliably diagnosed by primary care. Out of all medical imaging datasets, skin images are the most similar to other standard computer vision datasets. However, significant and unique challenges still exist in this domain. In addition, there are remarkable visual similarities among skin diseases, and compared to other medical imaging domains, varying genetics, disease states, imaging equipment, and imaging conditions can significantly alter the appearance of the skin, making automated analysis in this domain highly challenging.

Facial phenotyping for medical prediagnosis has recently been successfully exploited as a novel way for the preclinical assessment of a range of rare genetic diseases, where facial biometrics is revealed to have rich links to underlying genetic or medical causes. In this paper, we aim to extend this facial prediagnosis technology for a more general disease, Parkinson's Diseases (PD), and proposed an Artificial-Intelligence-of-Things (AIoT) edge-oriented privacy-preserving facial prediagnosis framework to analyze the treatment of Deep Brain Stimulation (DBS) on PD patients. In the proposed framework, a novel edge-based privacy-preserving framework is proposed to implement private deep facial diagnosis as a service over an AIoT-oriented information theoretically secure multi-party communication scheme, while data privacy has been a primary concern toward a wider exploitation of Electronic Health and Medical Records (EHR/EMR) over cloud-based medical services. In our experiments with a collected facial dataset from PD patients, for the first time, we proved that facial patterns could be used to evaluate the facial difference of PD patients undergoing DBS treatment. We further implemented a privacy-preserving information theoretical secure deep facial prediagnosis framework that can achieve the same accuracy as the non-encrypted one, showing the potential of our facial prediagnosis as a trustworthy edge service for grading the severity of PD in patients.

The papers in this special section focus on the emerging challenges for deep learningin the biomedical industry. Due to the proliferation of biomedical imaging modalities such as Photoacoustic Tomography, Computed Tomography (CT), Optical Microscopy and Tomography, Single Photon Emission Computed Tomography (SPECT), Magnetic Resonance (MR) Imaging, Ultrasound, Positron Emission Tomography (PET), Magnetic Particle Imaging, EE/MEG, Electron Tomography, and Atomic Force Microscopy, massive amounts of biomedical and health informatics data are being generated on a daily basis. How can we utilize such big data to build better health profiles and predictive models so that we can better diagnose and treat diseases and provide a better life for humans? In the past years, many successful learning methods such as deep learning were proposed to answer this crucial question, which has social, economic, as well as legal implications.

Melanoma is one of the deadliest types of skin cancer with increasing incidence. The most definitive diagnosis method is the histopathological examination of the tissue sample. In this paper, a melanoma detection algorithm is proposed based on decision-level fusion and a Hidden Markov Model (HMM), whose parameters are optimized using Expectation Maximization (EM) and asymmetric analysis. The texture heterogeneity of the samples is determined using asymmetric analysis. A fusion-based HMM classifier trained using EM is introduced. For this purpose, a novel texture feature is extracted based on two local binary patterns, namely local difference pattern (LDP) and statistical histogram features of the microscopic image. Extensive experiments demonstrate that the proposed melanoma detection algorithm yields a total error of less than 0.04%.

Colour quantisation is a common image processing technique to reduce the number of distinct colours in an image which are then represented by a colour palette. Selection of appropriate entries in this palette is challenging since the quality of the quantised image is directly dictated by the palette colours. In this paper, we propose a novel colour quantisation algorithm based on the human mental search (HMS) algorithm and subsequent refinement of the colour palette using k-means. HMS is a recent population-based metaheuristic algorithm that has been shown to yield good performance on a variety of optimisation problems. In the first stage, we use HMS to find a high-quality initial colour palette. In the second stage, this palette is refined using k-means to converge towards a local optimum and thus to further improve the quality of the quantised image. We evaluate our algorithm on a set of benchmark images and compare it to several conventional and soft computing-based colour quantisation algorithms to demonstrate excellent image quality, outperforming the other methods.

A wavelet network (WN) is a feed-forward neural network that uses wavelets as activation functions for the neurons in its hidden layer. By predetermining the wavelet positions and dilations, the WN can turn into a linear regression model. The common approach for the construction of these WN families is to use least-squares type algorithms. In this letter, we propose a novel approach by formulating a WN as a sparse linear regression problem, which we call a sparse wavelet network (SWN). In this WN, the problem of calculating the unknown inner parameters of the network becomes that of finding the sparse solution of an under-determined system of linear equations. Our sparse solution algorithm is a non-convex sparse relaxation approach inspired by smoothed L0 (SL0), a distinguished sparse recovery algorithm. The proposed SWN can be applied as a tool for the prediction and identification of dynamical systems.

No abstract available.

Dermoscopy image analysis (DIA) is a growing field, with works being published every week. This makes it difficult not only to keep track of all the contributions, but also for new researchers to identify relevant information and new directions to be explored. Several surveys have been written in the past decade, but these tend to cover all of the steps of a CAD system, which can be overwhelming. Moreover, in these works, each of the steps is briefly discussed due to lack of space. Among the different blocks of the CAD system, the most relevant is the one devoted to feature extraction. This is also the block where existing works exhibit the most variability. Therefore, we believe that it is important to review the state-of-the-art on this matter. This work thoroughly explores the several types of features that have been used in DIA. A discussion on their relevance and limitations, as well as suggestions for future research are provided.

Dermoscopy is a non-invasive skin imaging technique that permits visualization of features of pigmented melanocytic neoplasms that are not discernable by examination with the naked eye. While studies on the automated analysis of dermoscopy images date back to the late 1990s, because of various factors (lack of publicly available datasets, open-source software, computational power, etc.), the field progressed rather slowly in its first two decades. With the release of a large public dataset by the International Skin Imaging Collaboration in 2016, development of open-source software for convolutional neural networks, and the availability of inexpensive graphics processing units, dermoscopy image analysis has recently become a very active research field. In this paper, we present a brief overview of this exciting subfield of medical image analysis, primarily focusing on three aspects of it, namely, segmentation, feature extraction, and classification. We then provide future directions for researchers.

The papers in this special section focus on the use of image analysis to detect Melanoma. Melanoma is deadliest form of skin cancer, with roughly 91,000 new cases reported every year in the US and more than 9,000 deaths. Unlike many other cancer types, the incidence rate of melanoma has been steadily increasing in the past several decades. Early diagnosis is crucial since melanoma can be cured with a simple excision, if detected early. The goals of this special issue are to summarize the state-ofthe- art in the automated analysis of skin lesion images and to provide future directions for this exciting subfield of medical image analysis. The intended audience includes researchers and practicing clinicians, who are increasingly using digital analytic tools.

Color quantization is an important operation with many applications in computer graphics and image processing and analysis. Clustering algorithms have been extensively applied to this problem. However, despite its popularity as a general purpose clustering algorithm, k-means has not received much attention in the colour quantization literature because of its high computational requirements and sensitivity to initialization. In this paper, we propose a novel color quantization method based on the k-means algorithm. The proposed method utilizes adaptive initialization, deterministic sub-sampling and efficient coreset construction to attain high speed and high quality quantization. Experiments on a set of benchmark images demonstrate the proposed method to be significantly faster than k-means while delivering nearly identical results.

A new computer‐aided diagnosis (CAD) system for detecting malignant melanoma from dermoscopy images based on a fixed grid wavelet network (FGWN) is proposed. This novel approach is unique in at least three ways: (i) the FGWN is a fixed WN which does not require gradient‐type algorithms for its construction, (ii) the construction of FGWN is based on a new regressor selection technique: D‐optimality orthogonal matching pursuit (DOOMP), and (iii) the entire CAD system relies on the proposed FGWN. These characteristics enhance the integrity and reliability of the results obtained from different stages of automatic melanoma diagnosis. The DOOMP algorithm optimises the network model approximation ability rapidly while improving the model adequacy and robustness. This FGWN is then used to build a CAD system, which performs image enhancement, segmentation, and classification. To classify the images, in the first stage, 441 features with respect to colour, texture, and shape of each lesion are extracted. By means of feature selection, these 441 features are then reduced to 10. The proposed CAD system achieved an accuracy of 91.82%, sensitivity of 92.61%, specificity of 91%, and area under the curve value of 0.944 on a challenging set of 1039 dermoscopy images.

In this paper, we propose a simple and effective preprocessing method for melanoma classification by considering cytological properties of melanomas, in particular the alignment of the major axis of the tumor in the same direction. We evaluate our method with a set of 1,760 dermoscopic images (329 of melanomas and 1,431 of nevi) and a simple convolutional neural network (CNN) classifier with five-fold cross validation. The proposed tumor alignment method improves the classification performance by 5.8% in terms of the area under the ROC curve (AUC). In addition, it proves to be 2.1% better in term of AUC when compared with the same configured CNN trained using images that are nine times larger. Our results also show that considering the intrinsic features of the classification target is important even when the classifier has a capability to obtain effective features automatically through its learning process.

Although visual surveillance has emerged as an effective technology for public security, privacy has become an issue of great concern in the transmission and distribution of surveillance videos. For example, personal facial images should not be browsed without permission. To cope with this issue, face image scrambling has emerged as a simple solution for privacy-related applications. Consequently, online facial biometric verification needs to be carried out in the scrambled domain, thus bringing a new challenge to face classification. In this paper, we investigate face verification issues in the scrambled domain and propose a novel scheme to handle this challenge. In our proposed method, to make feature extraction from scrambled face images robust, a biased random subspace sampling scheme is applied to construct fuzzy decision trees from randomly selected features, and fuzzy forest decision using fuzzy memberships is then obtained from combining all fuzzy tree decisions. In our experiment, we first estimated the optimal parameters for the construction of the random forest and, then, applied the optimized model to the benchmark tests using three publically available face datasets. The experimental results validated that our proposed scheme can robustly cope with the challenging tests in the scrambled domain and achieved an improved accuracy over all tests, making our method a promising candidate for the emerging privacy-related facial biometric applications.

With the rapid development of Internet-of-Things (IoT), face scrambling has been proposed for privacy protection during IoT-targeted image/video distribution. Consequently, in these IoT applications, biometric verification needs to be carried out in the scrambled domain, presenting significant challenges in face recognition. Since face models become chaotic signals after scrambling/encryption, a typical solution is to utilize the traditional data-driven face recognition algorithms. While chaotic pattern recognition is still a challenging task, in this paper, we propose a new ensemble approach-many-kernel random discriminant analysis (MK-RDA)-to discover discriminative patterns from the chaotic signals. We also incorporate a salience-aware strategy into the proposed ensemble method to handle the chaotic facial patterns in the scrambled domain, where the random selections of features are made on semantic components via salience modeling. In our experiments, the proposed MK-RDA was tested rigorously on three human face data sets: the ORL face data set, the PIE face data set, and the PUBFIG wild face data set. The experimental results successfully demonstrate that the proposed scheme can effectively handle the chaotic signals and significantly improve the recognition accuracy, making our method a promising candidate for secure biometric verification in the emerging IoT applications.

This book is part of the CRC Press Digital Imaging and Computer Vision Series of books with a focus on the growing field of digital analysis of dermoscopy images. The dermatoscope has become a ubiquitous tool for dermatologists to evaluate pigmented lesions, but it can have a steep learning curve, and the current reporting/grading schemes are highly subjective, making it difficult to achieve interobserver consistency. Having more algorithmic approaches towards processing dermoscopy images could lead to more consistent interpretation and aid in training residents, fellows and practicing dermatologists. Additionally, the existence of this digital imaging data will allow more advanced computer-aided diagnosis (CAD) methods to be applied in this field, allow data to be shared among clinicians through common databases and electronic medical records, and advance research in this field by providing expanded access to imaging data for a larger variety of skin conditions. This book provides a comprehensive summary of the current state of the art in digital dermoscopic image analysis across a wide variety of topics.

Robustness is one of the most important characteristics of computer-aided diagnosis systems designed for dermoscopy images. However, it is difficult to ensure this characteristic if the systems operate with multisource images acquired under different setups. Changes in the illumination and acquisition devices alter the color of images and often reduce the performance of the systems. Thus, it is important to normalize the colors of dermoscopy images before training and testing any system. In this paper, we investigate four color constancy algorithms: Gray World, max-RGB, Shades of Gray, and General Gray World. Our results show that color constancy improves the classification of multisource images, increasing the sensitivity of a bag-of-features system from 71.0% to 79.7% and the specificity from 55.2% to 76% using only 1-D RGB histograms as features.

Development of Computer Aided Diagnosis systems that mimic the performance of dermatologists when diagnosing dermoscopy images is a challenging task. Despite the relevance of color in the diagnosis of melanomas, few of the proposed systems exploit this characteristic directly. In this paper we propose a new methodology for color identification in dermoscopy images. Our approach is to learn a statistical model for each color using Gaussian mixtures. The results show that the proposed method performs well, with an average Spearman correlation of 0.7981, with respect to a human expert.

Several methods have been proposed to detect melanomas in dermoscopy images. However, most of these methods are tuned to specific acquisition conditions. That is, their performance is affected when the acquisition setup changes or when data comes from multiple sources. This is what happens with EDRA database that contains images acquired in three different hospitals. In this paper, we discuss the use of color compensation techniques that try to reduce the influence of the acquisition setup on the color features extracted from the images. We show that color compensation provides a significant improvement on the performance of two different systems.

In this demo paper, we present an image browsing system that is suitable for online visualisation and browsing of search results from Google Images. Our approach is based on the Huffman tables available in the JPEG headers of Google Images thumbnails. Since these are adapted to the images, we employ them directly as image features. We then generate a visualisation of the search results by projection onto a 2-dimensional visualisation space based on principal component analysis derived from the Huffman entries. Images are dynamically placed into a grid structure and organised in a tree-like hierarchy for visual browsing. Since we utilise information only from the JPEG header, the requirements in terms of bandwidth are low, while no explicit feature calculation needs to be performed, thus allowing for interactive browsing of online image search results.

Almost all images are stored in compressed form, most commonly in (lossy) JPEG format. In this paper, we show that compression leads to a drop in performance of texture retrieval algorithms, and propose a method that reverses this performance drop. We achieve this by what might at first glance seem counter-intuitive, namely by compressing the images even more. In particular, we recompress images (or rather re-quantising their DCT coefficients) to their lowest common image quality setting. We demonstrate, on a large benchmark texture retrieval database and using standard texture algorithms, that this results in improved image retrieval performance close to that obtained on uncompressed images.

K-means is undoubtedly the most widely used partitional clustering algorithm. Unfortunately, due to its gradient descent nature, this algorithm is highly sensitive to the initial placement of the cluster centers. Numerous initialization methods have been proposed to address this problem. Many of these methods, however, have superlinear complexity in the number of data points, making them impractical for large data sets. On the other hand, linear methods are often random and/or order-sensitive, which renders their results unrepeatable. Recently, Su and Dy proposed two highly successful hierarchical initialization methods named Var-Part and PCA-Part that are not only linear, but also deterministic (nonrandom) and order-invariant. In this paper, we propose a discriminant analysis based approach that addresses a common deficiency of these two methods. Experiments on a large and diverse collection of data sets from the UCI machine learning repository demonstrate that Var-Part and PCA-Part are highly competitive with one of the best random initialization methods to date, i.e. k-means++, and that the proposed approach significantly improves the performance of both hierarchical methods.

Color quantization is an important operation with many applications in graphics and image processing. Most quantization methods are essentially based on data clustering algorithms. Recent studies have demonstrated the effectiveness of hard c-means (k-means) clustering algorithm in this domain. Other studies reported similar findings pertaining to the fuzzy c-means algorithm. Interestingly, none of these studies directly compared the two types of c-means algorithms. In this study, we implement fast and exact variants of the hard and fuzzy c-means algorithms with several initialization schemes and then compare the resulting quantizers on a diverse set of images. The results demonstrate that fuzzy c-means is significantly slower than hard c-means, and that with respect to output quality the former algorithm is neither objectively nor subjectively superior to the latter.

Reduced ordering based nonlinear vector filters have proved successful in removing long-tailed noise from color images while preserving edges and fine image details. These filters commonly utilize variants of the Minkowski distance to order the color vectors with the aim of distinguishing between noisy and noise-free vectors. In this paper, we review various alternative distance measures and evaluate their performance on a large and diverse set of images. The results demonstrate that there are in fact strong alternatives to the popular Minkowski metrics.

Wireless Capsule Endoscopy (WCE) is a relatively new technology (FDA approved in 2002) allowing doctors to view most of the small intestine. One of the most important goals of WCE is the early detection of colorectal polyps. In this paper an unsupervised method for the detection of polyps in WCE videos is presented. Our method involves watershed segmentation with a novel initial marker selection method based on Gabor texture features and K-means clustering. Geometric information from the resulting segments is extracted to identify polyp candidates. Initial experiments indicate that the proposed method can detect polyps with 100% sensitivity and over 81% specificity.

Dynamic backgrounds and sudden illumination changes are two of the major problems associated with background subtraction techniques. In this paper, we present a novel approach to background subtraction that addresses both of these challenges. In particular, we present an improved codebook background modelling and subtraction technique. We utilise image segmentation on the background image and model the background with a codebook for each pixel along with a pseudo background layer. We perceive background motion as an occlusion of one background layer by a nearby background layer. In other words, sliding of one background layer over a neighbouring layer causes background motion and will hence result in false segmentation. We present our approach of codeword spreading across layer boundaries to handle background motion. Furthermore, we present a two-step update of the background codebook to handle both sudden and gradual illumination changes.

Dermoscopy is one of the major imaging modalities used in the diagnosis of melanoma and other pigmented skin lesions. Due to the difficulty and subjectivity of human interpretation, automated analysis of dermoscopy images has become an important research area. Border detection is often the first step in this analysis. In many cases, the lesion can be roughly separated from the background skin using a thresholding method applied to the blue channel. However, no single thresholding method appears to be robust enough to successfully handle a wide variety of dermoscopic images. In this paper, we present an automated method for detecting lesion borders in dermoscopy images using a fusion of several thresholding methods. Experiments on a difficult set of 90 images demonstrate that the proposed method achieves both fast and accurate results when compared to six state-of-the-art methods.

Color space transformations are frequently used in image processing, graphics, and visualization applications. In many cases, these transformations are complex nonlinear functions, which prohibits their use in time-critical applications. In this paper, we present a new approach called Minimax Approximations for Color-space Transformations (MACT). We demonstrate MACT on two commonly used color space transformations. Extensive experiments on a large and diverse image set and comparisons with well-known multidimensional lookup table interpolation methods show that MACT achieves an excellent balance among four criteria: ease of implementation, memory usage, accuracy, and computational speed.

In this paper, we present a family of order-statistics based vector filters for the removal of impulsive noise from color images. These filters preserve the edges and fine image details by switching between the identity (no filtering) operation and a robust order-statistics based filter operation based on the univariate median operator. Experiments on a diverse set of images and comparisons with state-of-the-art filters show that the proposed filters combine simplicity, flexibility, good filtering quality, and low computational requirements.

Accurate color information in dermoscopy images is very important for melanoma diagnosis since inappropriate white balance or brightness in the images adversely affects the diagnostic performance. In this paper, we present an automated color normalization method for dermoscopy images of skin lesions. We develop color normalization filters based on a total of 319 images which normalize color of images using the HSV color system. We determined that the color characteristics of the peripheral part of the tumors significantly influence the color normalization and confirmed that the developed normalization filter achieved satisfactory normalization performance as evaluated by a cross-validation test.

Color quantization is an important operation with many applications in graphics and image processing. Most quantization methods are essentially based on data clustering algorithms. However, despite its popularity as a general purpose clustering algorithm, k-means has not received much respect in the color quantization literature because of its high computational requirements and sensitivity to initialization. In this paper, we investigate the performance of k-means as a color quantizer. We implement fast and exact variants of k-means with different initialization schemes and then compare the resulting quantizers to some of the most popular quantizers in the literature. Experiments on a set of classic test images demonstrate that an efficient implementation of k-means with an appropriate initialization strategy can in fact serve as a very effective color quantizer.

Vector filters based on order-statistics have proved successful in removing impulsive noise from color images while preserving edges and fine image details. Among these filters, the ones that involve the cosine distance function (directional filters) have particularly high computational requirements, which limits their use in time critical applications. In this paper, we introduce two methods to speed up these filters. Experiments on a diverse set of color images show that the proposed methods provide substantial computational gains without significant loss of accuracy.

Dermoscopy is one of the major imaging modalities used in the diagnosis of melanoma and other pigmented skin lesions. Due to the difficulty and subjectivity of human interpretation, automated analysis of dermoscopy images has become an important research area. Border detection is typically the first step in this analysis yet is often limited by the quality of the images to be analyzed. In this paper, we present an effective method to enhance the contrast in dermoscopy images. Given an input RGB image, we determine the optimal weights to convert it to grayscale by maximizing a histogram bimodality measure. Experiments on a large set of images demonstrate that this adaptive optimization scheme increases the contrast between the lesion and the background skin, and leads to a more accurate separation of the two regions using Otsu's thresholding method.

Accurate extraction of lesion borders is a crucial step in analysing dermoscopic skin lesion images. In this paper we present an effective approach to extracting lesion areas by combining an iterative segmentation algorithm with a preprocessing step that enhances colour information and image contrast. Following the pre-processing, analysis of the image background is conducted by iterative measurements based on median and standard deviation of non-lesion pixels, which in turn facilitates automatic and recurring noise reduction and enhancement. The algorithm does not depend on the use of rigid threshold values as an optimal thresholding algorithm is used to determine the optimal threshold iteratively. Extensive experimental evaluation is carried out on a dataset of 90 dermoscopy images with known ground truths obtained from three expert dermatologists. The results show that our approach is capable of providing good segmentation performance and that the colour enhancement step is indeed crucial as demonstrated by comparison with results obtained from the original RGB images.

Image segmentation plays a key role in many image content analysis applications, and a lot of effort has aimed at improving the performance of established segmentation algorithms. In this paper, we present a mean shift-based combined Dirichlet process mixture (MDP)/Markov Random Field (MRF) image segmentation algorithm. Our method incorporates a mean shift process to iteratively reduce the difference between the mean of cluster centres and image pixels within the standard MDP/MRF procedure. Experimental results show that the proposed segmentation technique outperforms the classical MDP/MRF algorithm.

Vector filters based on order-statistics have proved successful in removing impulsive noise from colour images while preserving edges and fine image details. Among these filters, the ones that involve the cosine distance function (directional filters) have particularly high computational requirements, which limits their use in time-critical applications. In this paper, we introduce two methods to speed up these filters. Experiments on a diverse set of colour images show that the proposed methods provide substantial computational gains without significant loss of accuracy.

Reduced ordering-based vector filters have proved successful in removing long-tailed noise from colour images while preserving edges and fine image details. These filters commonly utilise variants of the Minkowski distance to order the colour vectors with the aim of distinguishing between noisy and noise-free vectors. In this study, the authors review various alternative distance measures and evaluate their performance on a large and diverse set of images using several effectiveness and efficiency criteria. The results demonstrate that there are in fact strong alternatives to the popular Minkowski metrics.