Scale-space Analysis Research Articles

Improving model performance of shortest‐path‐based centrality measures in network models through scale space

SummaryThe quality of the solution in resolving a complex network depends on either the speed or accuracy of the results. While some health studies prioritize high performance, fast algorithms are favored in scenarios requiring rapid decision‐making. A comprehensive understanding of the problem necessitates a detailed analysis of the network and its individual components. Betweenness Centrality (BC) and Closeness Centrality (CC) are commonly employed measures in network studies. This study introduces a new strategy to compute BC and CC that assesses their sensitivity in the scale space while measuring the shortest path. The scale space is generated by incorporating a scale parameter that is shown to achieve up to 60% performance improvements for various datasets. The study provides in‐depth insights into the importance of the scale space analysis. Finally, a flexible measurement tool is provided that is suitable for various types of problems. To demonstrate the flexibility and applicability, we experimented with two methods for 10 different graphs using the proposed approach.

Asymmetric morphological filter for roughness evaluation of multifunctional surfaces

The scope of multifunctional surfaces in mechanical engineering and instrumentation is constantly expanding. Examples are products with multilayer coatings, products made of composite materials or using additive manufacturing technologies. A feature of multifunctional surfaces is two levels of texture with different parameter values. Various types of filters are used to decomposition and then analyze texture components. Traditionally, for such problems, a robust Gaussian regression filter and a morphological filter are used. The advantage of the morphological filter lies in the lower computational complexity and the ease of removing the shape component from the profile. This research presents generalized analysis of various types of an asymmetric morphological filter based on simulation. The asymmetric filter differs from the standard morphological filter by using different nesting indexes for combinations of morphological opening and closing operations. We have designed a compositional model of profile, which is superposition of two Gaussian distributions with different parameters and waviness. Relative filtering error of the arithmetic mean heights Ra was chosen as evaluation parameter. Based on the Monte Carlo experiments technique, the relative errors of the filters are determined. The main result of the research is algorithm for choosing nesting indexes depending on the type of primary profile. Thus, we give scientifically justified choice of the filter type and its task-specific parameters for applied use. The choice of filter type and two different nesting indexes in accordance with the developed algorithm provide relative error with a coverage interval less 3 % for 95 % coverage probability. The asymmetric morphological filter is effective for scale space analysis of surfaces with significant shape errors and waviness. The results obtained can be used to analyze the tribological properties of multifunctional surfaces of products.

Band decomposition of asynchronous electroencephalogram signal for upper limb movement classification.

Decoding asynchronous electroencephalogram (A-EEG) signals is a crucial challenge in the emerging field of EEG based brain-computer interface. In the case of A-EEG signals, the time markers of motor activity are absent. The paper proposes a method to decompose the A-EEG signals using gabor elementary function designed with Gabor frames. The scale-space analysis extracts Gabor dominant frequencies from A-EEG signals. Statistical and temporal moment dependent features are used to create the feature vector for each estimated gabor band. The statistical significance of the features is tested with the Kruskal-Wallis test. The deep neural network is implemented with bi-directional long short-term memory block to classify the upper limb movement. The EEG data of healthy volunteers have been collected using the Enobio-20 electrode system and ArmeoSpring rehabilitation device. The proposed methodology has achieved an average classification accuracy of 96.83%, precision 0.96, recall 0.96, and F1-score of 0.93 on the acquired data set. The designed framework for decoding upper limb movement outperforms the existing state-of-the-art methods. In the future, the proposed framework could increase classification performance by incorporating multiple types of biological inputs for investigating various brain functions.

Gauss Gradient and SURF Features for Landmine Detection from GPR Images

Recently, ground-penetrating radar (GPR) has been extended as a well-known area to investigate the subsurface objects. However, its output has a low resolution, and it needs more processing for more interpretation. This paper presents two algorithms for landmine detection from GPR images. The first algorithm depends on a multi-scale technique. A Gaussian kernel with a particular scale is convolved with the image, and after that, two gradients are estimated; horizontal and vertical gradients. Then, histogram and cumulative histogram are estimated for the overall gradient image. The bin values on the cumulative histogram are used for discrimination between images with and without landmines. Moreover, a neural classifier is used to classify images with cumulative histograms as feature vectors. The second algorithm is based on scale-space analysis with the number of speeded-up robust feature (SURF) points as the key parameter for classification. In addition, this paper presents a framework for size reduction of GPR images based on decimation for efficient storage. The further classification steps can be performed on images after interpolation. The sensitivity of classification accuracy to the interpolation process is studied in detail.

Box filtering for real-time curvature scale-space computation

Curvature scale-space (CSS) analysis is an important technique for contour-based object recognition in digital images. To compute the CSS for a given contour, it is systematically convolved (smoothed) with Gaussians with increasing standard deviation. The convolutions are computationally expensive, especially for large and high resolution contours, but can be approximated using box filtering (also known as mean and average filtering). Together with running sums, the convolutions can be accelerated by 2–3 magnitudes without significant loss of precision. Nonetheless, box filtering has not been systematically investigated in connection with CSS computation. In this work, we present a theoretical and experimental analysis of different box-filtering techniques in this context and conclude which is the most efficient implementation. Based on this, the CSS of a contour can be computed in real time with high precision.

Dark infrared night vision imaging proposed work for pedestrian detection and tracking

This framework presents three efficient proposed algorithms for pedestrian detection and tracking in Dark Infrared Night Vision (DIRNV) images. The first approach is relied on Gradient Estimation (GE) after mixing structure Equalization Exponential Contrast Limited Adaptive Histogram Equalization (ECLAHE) with Gamma Correction, and finally Cumulative Histogram (GECUGC) for discrimination. The GECUGC relies on enhancement using mixing ECLAHE Using Gamma Correction (ECUG) in addition to pre-processing followed by the GE using Laplacian Filter (LAF), and finally Cumulative Histograms (CH) for the detection or classification task. The second approach is based GE after a hybrid structure Histogram Equalization (HE) with Nonlinear Technique and finally CH (GHNTC) for discrimination. The GHNTC depends on enhancement by merging HE with Nonlinear Technique (NT) (HENT) followed by the GE using LAF and finally CH for pedestrian detection and tracking using DIRNV imaging. After the CH estimation, the difference between cumulative histograms with and without objects is estimated and used for pedestrian detection and tracking using DIRNV imaging. The third algorithm is based scale space analysis with the number of the Speeded Up Robust Features (SURF) points as the key parameters for classification. This technique is presented to detect the features of DIRNV pedestrian images and tracking. The performance metrics are the difference area between the cumulative histograms of DIRNV images with and without pedestrian, computation time, points of features and speed up factor. Simulation results prove that the success of three suggested techniques in pedestrian detection and tracking using DIRNV imaging. By comparing the three presented algorithms, it is clear that the second suggested technique gives superior for pedestrian detection and tracking from point view difference area between the cumulative histograms.On the other hand the first suggested technique is the best algorithms for pedestrian detection and tracking from point view the computation time. The obtained results clear that the third approach has sucesseded in gait pedestrian detection and tracking using DIRNV imaging.

Precise Analysis of Kymograph Data for Biological Atomic Force Microscopy using the Line Detection Algorithm

Atomic Force Microscopy (AFM) has become a popular technique for studying the dynamics of single-molecule systems including membrane protein complexes in near native conditions. Though the past decades have seen significant enhancements in scanning speed, AFM remains a serial imaging process in which a single tip is physically rastered in x and y over a region of interest. A long-standing question is, “How can one improve the temporal resolution without sacrificing precision?” A kymograph is a graphical representation of spatial position over time, t, where the slow axis of the raster scan has been disabled, converting Z(x,y) → Z(x,t). Another overall challenge is a lack of objective analysis methods for biological AFM. A recent advance in this avenue is the Hessian blob algorithm [Marsh et al. Sci Rep 8, 978 (2018)], which employs scale space analysis along with local image curvature to define particles with high precision. While this method is independent of user parameters, it was developed for punctate “blobs” such as individual membrane protein protrusions, and cannot be applied to non-localized linear features such as kymographs. By utilizing the image skeleton rather than minimizing the determinant of the Hessian Matrix, we demonstrate a line detection algorithm to handle linear features while still avoiding the potential bias of a user defined threshold. The utility of the algorithm is shown by studying conformational dynamics of the general secretory (Sec) system of Escherichia coli. In particular, we analyzed the Sec translocase, which comprises SecA, the ATPase of the Sec system, bound to the translocon, SecYEG. This work demonstrates a statistical analysis of translocase kymographs in the presence and absence of ligands that modulate Sec system activity.

PlenoptiCam v1.0: A Light-Field Imaging Framework.

Light-field cameras play a vital role for rich 3D information retrieval in narrow range depth sensing applications. The key obstacle in composing light-fields from exposures taken by a plenoptic camera is to computationally calibrate, align and rearrange four-dimensional image data. Several attempts have been proposed to enhance the overall image quality by tailoring pipelines dedicated to particular plenoptic cameras and improving the consistency across viewpoints at the expense of high computational loads. The framework presented herein advances prior outcomes thanks to its novel micro image scale-space analysis for generic camera calibration independent of the lens specifications and its parallax-invariant, cost-effective viewpoint color equalization from optimal transport theory. Artifacts from the sensor and micro lens grid are compensated in an innovative way to enable superior quality in sub-aperture image extraction, computational refocusing and Scheimpflug rendering with sub-sampling capabilities. Benchmark comparisons using established image metrics suggest that our proposed pipeline outperforms state-of-the-art tool chains in the majority of cases. Results from a Wasserstein distance further show that our color transfer outdoes the existing transport methods. Our algorithms are released under an open-source license, offer cross-platform compatibility with few dependencies and different user interfaces. This makes the reproduction of results and experimentation with plenoptic camera technology convenient for peer researchers, developers, photographers, data scientists and others working in this field.

Implementation face based cancelable multi-biometric system

This paper suggests novel two proposed cancellable biometric realization techniques recognition and template protection. In this paper, the Homomorphic Key (HK) encoding algorithm is utilized for cancelable face system. In the first suggested scheme, the HK algorithm is applied on the face images. The resultant map is encrypted, in order to the second HK utilized in the HK is produced from the image. This approach can be used to develop a frequency domain procedure for making this system for biometric template protection. The second algorithm presents a new approach to detect the features of face images depending the Speeded Up Robust Features (SURF) and Optimum Global Thresholding (OTSU) method. This algorithm is relied on scale space analysis with the number of SURF feature points as the key parameters for classification. Simulation results using evaluation metrics False Positive Rate (FPR), False Negative Rate (FNR), Equal Error Rate (EER), Receiver Operating Characteristic (ROC) and Area under ROC (AROC) prove that the first proposed cancelable biometric technique with the second key are best with comparing the other keys. The obtained results clear that the second suggested technique has sucesseded in detection the features of the skin, eyes, nose, hair, ears images and the face positions.

Heterogeneous Image Matching via a Novel Feature Describing Model

Computer vision has been developed greatly in the past several years, and many useful and interesting technologies have been presented and widely applied. Image matching is an important technology based on similarity measurement. In this paper, we propose a novel feature describing model based on scale space and local principle component analysis for heterogeneous image matching. The traditional uniform eight-direction statistics is updated by a task-related k-direction statistics based on prior information of the keypoints. In addition, the k directions are determined by an approximately solution of a Min-Max problem. The principle component analysis is introduced to compute the main directions of local patches based on the gradient field. In addition, the describing vector is formed by then implementing PCA on each sub-patch of a 4 × 4 mesh. Experimental results show the accuracy and efficiency of proposed method.

Generic spatial-color metric for scale-space processing of catadioptric images

Images produced by omnidirectional catadioptric systems provide a larger field of view than conventional cameras. However, these images contain significant radial distortions making classical processing unadapted. In addition, color information is almost neglected in omnidirectional imaging. In this paper, we propose a unifying framework, for central catadioptric color image processing, using Riemannian embedding that deals simultaneously with the geometric deformation due to the use of curved mirrors, and the multi-dimensional characteristic of the image. Based on the introduced Riemannian metric, we derive an adapted Gaussian kernel which is essential in widely used image processing. The resulting new formulation is then applied to various image processing: Image smoothing, Difference of Gaussians filtering and scale-space analysis, edge extraction and corner feature detection using Gaussian derivatives. The experiments illustrate the potential of the proposed approach, and show the higher quality of the adapted processing.

At What Scales and Why Does Forest Structure Vary in Naturally Dynamic Boreal Forests? An Analysis of Forest Landscapes on Two Continents

Identifying the scales of variation in forest structures and the underlying processes are fundamental for understanding forest dynamics. Here, we studied these scale-dependencies in forest structure in naturally dynamic boreal forests on two continents. We identified the spatial scales at which forest structures varied, and analyzed how the scales of variation and the underlying drivers differed among the regions and at particular scales. We studied three 2 km × 2 km landscapes in northeastern Finland and two in eastern Canada. We estimated canopy cover in contiguous 0.1-ha cells from aerial photographs and used scale-derivative analysis to identify characteristic scales of variation in the canopy cover data. We analyzed the patterns of variation at these scales using Bayesian scale space analysis. We identified structural variation at three spatial scales in each landscape. Among landscapes, the largest scale of variation showed the greatest variability (20.1–321.4 ha), related to topography, soil variability, and long-term disturbance history. Superimposed on this large-scale variation, forest structure varied at similar scales (1.3–2.8 ha) in all landscapes. This variation correlated with recent disturbances, soil variability, and topographic position. We also detected intense variation at the smallest scale analyzed (0.1 ha, grain of our data), partly driven by recent disturbances. The distinct scales of variation indicated hierarchical structure in the landscapes studied. Except for the large-scale variation, these scales were remarkably similar among the landscapes. This suggests that boreal forests may display characteristic scales of variation that occur somewhat independent of the tree species characteristics or the disturbance regime.

Wavelet multiresolution analysis of particle-laden turbulence

The preferential concentration of inertial particles in isotropic turbulence is studied using wavelets, enabling the joint scale-space analysis of the flow field of the carrier phase, the concentration field of the dispersed phase, and interphase conditioned statistics.

Hierarchical representation and estimation of prosody using continuous wavelet transform

Prominences and boundaries are the essential constituents of prosodic structure in speech. They provide for means to chunk the speech stream into linguistically relevant units by providing them with relative saliences and demarcating them within utterance structures. Prominences and boundaries have both been widely used in both basic research on prosody as well as in text-to-speech synthesis. However, there are no representation schemes that would provide for both estimating and modelling them in a unified fashion. Here we present an unsupervised unified account for estimating and representing prosodic prominences and boundaries using a scale-space analysis based on continuous wavelet transform. The methods are evaluated and compared to earlier work using the Boston University Radio News corpus. The results show that the proposed method is comparable with the best published supervised annotation methods.

Characterization of strongly non-linear and singular functions by scale space analysis

A central notion of physics is the rate of change. While mathematically the concept of derivative represents an idealization of the linear growth, power law types of non-linearities even in noiseless physical signals cause derivative divergence. As a way to characterize change of strongly nonlinear signals, this work introduces the concepts of scale space embedding and scale-space velocity operators. Parallels with the scale relativity theory and fractional calculus are discussed. The approach is exemplified by an application to De Rham’s function. It is demonstrated how scale space embedding presents a simple way of characterizing the growth of functions defined by means of iterative function systems.

Visual saliency based on frequency domain analysis and spatial information

Saliency detection plays an important role in computer vision field. In this paper, a saliency detection model for images is proposed based on frequency domain analysis and spatial information. Saliency is detected in the proposed model via the following main steps: coefficients of the input hyper complex image are designed in Hyper Complex Fourier Transform (HFT); then, during the analysis of the spectrum scale space in frequency domain, a series of saliency maps at different scales are obtained; finally, considering spatial relationship, the spatial contrast function is taken for selecting the optimal saliency map. Experimental results show that the proposed model can achieve high performance in terms of the average AUC and F-measure evaluation metrics and outperform state-of-the-art baselines.

Single-Shot Dense 3D Reconstruction Using Self-Equalizing De Bruijn Sequence.

Single-shot dense 3D reconstruction using colored structured light is a difficult problem due to the undesired effects of ambient lighting, object albedo, non-equal channel gains, and channel cross-talk. We propose a novel single-shot dense 3D reconstruction using colored structured light. Our method combines the self-equalizing De Bruijn sequence, scale-space analysis, and bandpass complex Hilbert filters to achieve insensitivity to ambient lighting, object albedo, and non-equal channel gains. The proposed method reconstructs about 85% of points compared to time-multiplexing structured light strategies and the decoding error in the recovered projector coordinate is less than one projector pixel for about 90% of reconstructed points.

Statistical Scale Space Methods

SummaryThe goal of statistical scale space analysis is to extract scale‐dependent features from noisy data. The data could be for example an observed time series or digital image in which case features in either different temporal or spatial scales would be sought. Since the 1990s, a number of statistical approaches to scale space analysis have been developed, most of them using smoothing to capture scales in the data, but other interpretations of scale have also been proposed. We review the various statistical scale space methods proposed and mention some of their applications.

Spectral saliency via automatic adaptive amplitude spectrum analysis

Suppressing nonsalient patterns by smoothing the amplitude spectrum at an appropriate scale has been shown to effectively detect the visual saliency in the frequency domain. Different filter scales are required for different types of salient objects. We observe that the optimal scale for smoothing amplitude spectrum shares a specific relation with the size of the salient region. Based on this observation and the bottom-up saliency detection characterized by spectrum scale-space analysis for natural images, we propose to detect visual saliency, especially with salient objects of different sizes and locations via automatic adaptive amplitude spectrum analysis. We not only provide a new criterion for automatic optimal scale selection but also reserve the saliency maps corresponding to different salient objects with meaningful saliency information by adaptive weighted combination. The performance of quantitative and qualitative comparisons is evaluated by three different kinds of metrics on the four most widely used datasets and one up-to-date large-scale dataset. The experimental results validate that our method outperforms the existing state-of-the-art saliency models for predicting human eye fixations in terms of accuracy and robustness.

Vessel transform for automatic optic disk detection in retinal images

Precise localisation of an optic disk (OD) in the retinal images is one of the most important problems in the ophthalmic image processing. Although a considerable progress has been made towards a computerised solution of the problem, the numerical algorithms often fail on retinal images characterised by poor quality. Therefore, the authors propose a new method suitable for low-quality images based on exploiting the convergence of the blood vessels to the OD. The novelty of the proposed techniques includes clustering the vessels endowed with a novel correction procedure and the vessel transform (VT) which measures the distance to the main clusters. The algorithm is integrated into the scale-space (SS) analysis to detect the boundary of the OD. The integrated method is called SS algorithm with VT (SSVT). SSVT has been tested on retinal images from two databases with fair and poor images against the fuzzy convergence (FC) method and a modification of the circular transform proposed by Lu. The absolute improvement on sensitivity of SSVT against FC and Lu's are up to 12.37% and 8.18%. Bigger improvements of SSVT in terms of positive predictive value are up to 37.46% and 30.84% against FC and Lu's, respectively.