Approximation of the Euclidean Distance by Chamfer Distances

Medial Axis, also known as Centres of Maximal Disks, is a representation of a shape, which is useful for image description and analysis. Chamfer or Weighted Distances, are discrete distances which allow to approximate the Euclidean Distance with integers. Computing medial axis with chamfer distances has been discussed in the literature for some simple cases, mainly in 2D. In this paper we give a method to compute the medial axis for any chamfer distance in 2D and 3D, by local tests using a lookup table. Our algorithm computes very efficiently the lookup tables and, very important, the neighbourhood to be tested.

New sequential exact Euclidean distance transform algorithms based on convex analysis

A distance transformation (DT) takes a binary image as input and generates a distance map image in which the value of each pixel is its distance to a given set of object pixels in the binary image. In this research, DT's for multi class data (MCDTs) are developed which generate both a distance map and a class map containing for each pixel the class of the closest object. Results indicate that the MCDT based on the Fast Exact Euclidean Distance (FEED) method is a factor 2 tot 4 faster than MCDTs based on exact or semi-exact euclidean distance (ED) transformations, and is only a factor 2 to 4 slower than the MCDT based on the crude city-block approximation of the ED. In the second part of this research, the MCDTs were adapted such that they could be used for the fast generation of distance and class maps for video sequences. The frames of the sequences contain a number of fixed objects and a moving object, where each object has a separate label. Results show that the FEED based version is a factor 2 to 3.5 faster than the fastest of all the other video-MCDTs which is based on the chamfer 3,4 distance measure. FEED is even a factor 3.5 to 10 faster than another fast exact ED transformation. With video, multi class FEED it will be possible to measure distances from a moving object to various identified stationary objects with nearly the frame rate of a webcam. This will be very useful when the risk exists that objects move outside surveillance limits.

The relationship between the installment and machining errors and the follower displacement error for a translating roller follower plate cam was studied. The formulae of the follower displacement error were derived. These expressions can be used to calculate the follower displacement error. The follower displacement error of a translating roller follower cam system is closely related to the cam geometric error and offset distance error. By taking the values and signs of the cam geometric error and offset distance error properly, we can minimize the roller follower displacement error and design the high precision translating roller follower plate cam

Wavelet is one method that can be used as a step to recognition an individual . Wavelet is used to perform an image feature extraction . In the process of image texture analysis , showed the value of the coefficients of a wavelet . The magnitude of the coefficients obtained using wavelet feature extraction is influenced by several factors . Besides affected by the type of wavelet used , is also influenced by the magnitude of the wavelet decomposition level of itself. In the wavelet is known as the wavelet energy retention , which means the number of retained energy after undergoing a process of decomposition and cutting coefficients . During the decomposition process , the calculation for texture analysis is often a constraint . In order for the current calculation lighter texture analysis , necessary to the process of cutting coefficients based on the retention factor of the wavelet coefficients . Based on these issues , created a program to analyze the influence of variations in the level of wavelet decomposition and coefficient of variation coefficient of cutting a cut on the image . The object of this final project is 30 iris image that has been converted into polar form presented . Having experienced the process of cutting coefficients , to prevent the image of the reverse transformation has a big difference to the original image , in this study was calculated Mean Square Error ( MSE), Peak Signal to Noise Ratio ( PSNR), and Euclidean distance to determine the level of similarity of image input and output images . The Highest values of Retention ​, MSE and the Euclidean distance is obtained at the level of decomposition of 1 and the lowest at the level of decomposition 6 . While the truncated coefficient and PSNR values ​​obtained at the highest level of decomposition of 6 and the lowest level of decomposition of 6 . The variation coefficient of pieces , value retention and highest PSNR obtained at koefsien piece 5 and the lowest coefficient of 50 pieces . While the coefficient value is truncated , MSE and the highest Euclidean distance is obtained at koefsien pieces 50 and the lowest coefficient of 5 pieces . Keywords: iris, texture analysis, Haar wavelet transform, MSE, PSNR, E uclidean distance

A fast and exact Euclidean distance transformation using decomposed grayscale morphological operators is presented. Applied on a binary image, a distance transformation assigns each object pixel a value that corresponds to the shortest distance between the object pixel and the background pixels. It is shown that the large structuring element required for the Euclidean distance transformation can be easily decomposed into 3/spl times/3 windows. This is possible because the square of the Euclidean distance matrix changes uniformly both in the vertical and horizontal directions. A simple extension for a 3D Euclidean distance transformation is discussed. A fast distance transform for serial computers is also presented. Acting like thinning algorithms, the version for serial computers focuses operations only on the potential changing pixels and propagates from the boundary of objects, significantly reducing execution time. Nonsquare pixels can also be used in this algorithm. An example application, shape filtering using arbitrary sized circular dilation and erosion, is discussed. Rotation-invariant basic morphological operations can be done using this example application. >

Iris recognition has become a trend in the biometric discipline to identify an individual and is widely used compared to other biometrics and the traditional recognition system. Various factors, such as the obstruction of eyelids, eyelashes, shadows, specular reflection by eyeglasses, and other noises, can cause the occlusion of iris images. This study aims to propose a hybrid U-Net with ResNet segmentation method (HUREIS) in occlusion iris images for iris recognition. The HUREIS was compared with VGG-16 to determine its benchmark based on segmentation ac curacy and computational time. This study employed a MICHE I dataset that only considers occlusion images for eyelids and eyelashes for mobile devices. The findings showed that HUREIS performed the best dice score at 93.7% and Jaccard score at 88.3%, respectively. The performance of HUREIS is 5.4% better than VGG-16, with approximately 84% minimum computational time. The segmentation accuracy was compared with the state of-the-art methods based on the MICHE-I dataset and the U Net segmentation method to validate the effectiveness of the proposed iris segmentation method. Furthermore, this study evaluated the feature vector of HUREIS and VGG-16 to obtain the performance of iris classification using a support vector machine and decision tree C4.5 based on Euclidean distance and Cosine similarity. The Euclidean distance and cosine similarity were compared to determine the best image similarity score close to one. The results show that SVM for HUREIS achieved the optimal classification accuracy at 100% using Euclidean distance. Compared to decision tree C4.5, VGG-16 achieved 94.41% of accuracy using Euclidean distance.

Accurate estimation of photovoltaic (PV) system performance is crucial for determining its feasibility as a power generation technology and financial asset. PV-based energy solutions offer a viable alternative to traditional energy resources due to their superior Levelized Cost of Energy (LCOE). A significant challenge in assessing the LCOE of PV systems lies in understanding the Performance Loss Rate (PLR) for large fleets of PV systems. Estimating the PLR of PV systems becomes increasingly important in the rapidly growing PV industry. Precise PLR estimation benefits PV users by providing real-time monitoring of PV module performance, while explainable PLR estimation assists PV manufacturers in studying and enhancing the performance of their products. However, traditional PLR estimation methods based on statistical models have notable drawbacks. Firstly, they require user knowledge and decision-making. Secondly, they fail to leverage spatial coherence for fleet-level analysis. Additionally, these methods inherently assume the linearity of degradation, which is not representative of real world degradation. To overcome these challenges, we propose a novel graph deep learning-based decomposition method called the Spatio-Temporal Graph Neural Network for fleet-level PLR estimation (PV-stGNN-PLR). PV-stGNN-PLR decomposes the power timeseries data into aging and fluctuation components, utilizing the aging component to estimate PLR. PV-stGNN-PLR exploits spatial and temporal coherence to derive PLR estimation for all systems in a fleet and imposes flatness and smoothness regularization in loss function to ensure the successful disentanglement between aging and fluctuation. We have evaluated PV-stGNN-PLR on three simulated PV datasets consisting of 100 inverters from 5 sites. Experimental results show that PV-stGNN-PLR obtains a reduction of 33.9% and 35.1% on average in Mean Absolute Percent Error (MAPE) and Euclidean Distance (ED) in PLR degradation pattern estimation compared to the state-of-the-art PLR estimation methods.

Vibration‐based damage detection relies on changes in structural dynamic features. However, environmental and operational variations (EOVs) can cause changes in dynamic features that mask those caused by damage. In addition, the EOV effects on dynamic features are often nonlinear, which limits the application of many linear damage detection methods. A novel nonlinear output‐only method is proposed to address this. This method leverages variational mode decomposition (VMD) as a preprocessing step to remove seasonal patterns and noise from the modal frequencies. The first modes of the decomposition results (IMF1 signals) are then used to calculate the Euclidean distance based on the residual obtained by the principal component analysis (PCA) method. To eliminate the nonlinear EOV effects and provide normalized damage features for reliable continuous dynamic monitoring, a Gaussian process regression (GPR) model is trained to learn the underlying calculation rule of the PCA Euclidean distance. Due to the linear nature of PCA, the nonlinear EOV effects are still retained in both the PCA Euclidean distance and the GPR–predicted value. Through a subtraction process, their common nonlinear environmental effects can be removed, and the resulting prediction error can serve as a normalized feature sensitive to structural damage. The proposed method is validated through a simulated 7‐DOF example and real data from the Z24 bridge, with several comparisons highlighting its effectiveness.

The distance-based regression model has many applications in analysis of multivariate response regression in various fields, such as ecology, genomics, genetics, human microbiomics, and neuroimaging. It yields a pseudo F test statistic that assesses the relation between the distance (dissimilarity) of the subjects and the predictors of interest. Despite its popularity in recent decades, the statistical properties of the pseudo F test statistic have not been revealed to our knowledge. This study derives the asymptotic properties of the pseudo F test statistic using spectral decomposition under the matrix normal assumption, when the utilized dissimilarity measure is the Euclidean or Mahalanobis distance. The pseudo F test statistic with the Euclidean distance has the same distribution as the quotient of two Chi-squared-type mixtures. The denominator and numerator of the quotient are approximated using a random variable of the form \(\xi\chi_d^2+\eta\) and the approximate error bound is given. The pseudo F test statistic with the Mahalanobis distance follows an F distribution. In simulation studies, the approximated distribution well matched the “exact” distribution obtained by the permutation procedure. The obtained distribution was further validated on H1N1 influenza data, aging human brain data, and embryonic imprint data.

Boykov and Kolmogorov showed that it is possible to find globally minimal contours and surfaces via graph cuts by embedding an appropriate metric approximation into the graph edge weights and derived the requisite formulas for Euclidean and Riemannian metrics [3]. In [9] we have proposed an improved Euclidean metric approximation that is invariant under (horizontal and vertical) mirroring, applicable to grids with anisotropic resolution and with a smaller approximation error. In this paper, we extend our method to general Riemannian metrics that are essential for graph cut based image segmentation or stereo matching. It is achieved by the introduction of a transformation reducing the Riemannian case to the Euclidean one and adjusting the formulas from [9] to be able to cope with non-orthogonal grids. We demonstrate that the proposed method yields smaller approximation errors than the previous approaches both in theory and practice.

This paper looks into relations between repre-sentational methods and conceived architectural space on Le Corbusier's axonometric drawings.Conclusions are followings. 1) Axonometric drawings are made on and after La-Chaux-Fonds period, but military projection is conciously used nearly after 1925.2) Origins of using axonometric drawings are O. Choisy's “Histoire d'Architecture”and Exposition of De Stijl. 3) Time of starting to use military projection consciously corresponds to time of establishing modules on plan and using ‘polychromie’ as a design method. 4) By using ‘polychromie’, geometrical distances and sensuous distances are introduced into architectural design.We can understand that military projection is used not only to show exact geometrical distances between walls, but also to show sensuous distances by coloring walls.

MIMO technology not only offers diversity and capacity gains, but also provides higher spectral efficiency and significant link reliability over SISO systems. Many methods are developed to exploit the diversity offered by multi-antenna systems such as Alamouti code and spatial multiplexing that do not require transmitter-side channel status information (Tx-CSI). Other power allocation optimization techniques, also known as precoding, require a full or partial Tx-CSI. These techniques aim to transform the signal before transmission according to different criteria, among which the minimal Euclidean distance seems to be very effective and continues to interest the researchers. Given perfect channel state information at both sides of the communication, we propose in this paper a novel design of wireless transmission schemes that joint the minimal Euclidean distance precoder and error correction coding based on the non-binary low-density parity-check code (NB-LDPC), to finally determine a power allocation optimization solution that adapts a linear precoding block to an NB-LDPC encoded MIMO transmission. In this paper we use a quadrature amplitude modulation (QAM), over a Rayleigh fading channel with a maximum likelihood detection. Simulations results in term of bit error rate confirmed that NB-LDPC codes are particularly well suited to be jointly used with precoding schemes based on the maximization of the minimum Euclidean distance criterion.

BackgroundThe principal component analysis (PCA) is known as a multivariate statistical model for reducing dimensions into a representation of principal components. Thus, the PCA is commonly adopted for establishing psychometric properties, i.e., the construct validity. Autoencoder is a neural network model, which has also been shown to perform well in dimensionality reduction. Although there are several ways the PCA and autoencoders could be compared for their differences, most of the recent literature focused on differences in image reconstruction, which are often sufficient for training data. In the current study, we looked at details of each autoencoder classifier and how they may provide neural network superiority that can better generalize non-normally distributed small datasets.MethodologyA Monte Carlo simulation was conducted, varying the levels of non-normality, sample sizes, and levels of communality. The performances of autoencoders and a PCA were compared using the mean square error, mean absolute value, and Euclidian distance. The feasibility of autoencoders with small sample sizes was examined.ConclusionsWith extreme flexibility in decoding representation using linear and non-linear mapping, this study demonstrated that the autoencoder can robustly reduce dimensions, and hence was effective in building the construct validity with a sample size as small as 100. The autoencoders could obtain a smaller mean square error and small Euclidian distance between original dataset and predictions for a small non-normal dataset. Hence, when behavioral scientists attempt to explore the construct validity of a newly designed questionnaire, an autoencoder could also be considered an alternative to a PCA.

Augmented reality (AR) has demonstrated significant potential in neurosurgical cranial, spine, and teaching applications. External ventricular drain (EVD) placement remains a common procedure, but with error rates in targeting between 10% and 40%. To evaluate Novarad VisAR guidance system for the placement of EVDs in phantom and cadaveric models. Two synthetic ventricular phantom models and a third cadaver model underwent computerized tomography imaging and registration with the VisAR system (Novarad). Root mean square (RMS), angular error (γ), and Euclidian distance were measured by multiple methods for various standard EVD placements. Computerized tomography measurements on a phantom model (0.5-mm targets showed a mean Euclidean distance error of 1.20 ± 0.98 mm and γ of 1.25° ± 1.02°. Eight participants placed EVDs in lateral and occipital burr holes using VisAR in a second phantom anatomic ventricular model (mean RMS: 3.9 ± 1.8 mm, γ: 3.95° ± 1.78°). There were no statistically significant differences in accuracy for postgraduate year level, prior AR experience, prior EVD experience, or experience with video games ( P > .05). In comparing EVDs placed with anatomic landmarks vs VisAR navigation in a cadaver, VisAR demonstrated significantly better RMS and γ, 7.47 ± 0.94 mm and 7.12° ± 0.97°, respectively ( P ≤ .05). The novel VisAR AR system resulted in accurate placement of EVDs with a rapid learning curve, which may improve clinical treatment and patient safety. Future applications of VisAR can be expanded to other cranial procedures.