Sum Of Squared Distances Research Articles

Quantifying coordinative patterns in steady‐state running: The impact of footwear and foot strike on joint coupling variability

AbstractIn this study, we aimed to compare and contrast the intralimb coordinative patterns of habitual forefoot strikers (FFS) and rearfoot strikers (RFS) during steady‐state running across three different shoe types: minimalist, neutral and cushioned shoes. To describe these coordinative patterns, we implemented the concept of the ‘preferred movement path’ which represents the movement path that runners naturally select in response to their physical capacity and external environment. We quantified cycle‐to‐cycle consistency (ACC) and within‐trial variance in coordination patterns (SoV) using joint angle data from the ankle and knee for ankle‐knee coupling and from the knee and hip for knee‐hip coupling. Additionally, we calculated the measure of shape difference in joint coupling as the sum of squared distances (SSD) between/within conditions and groups. The percentage of runners who displayed shape differences below certain SSD thresholds was also evaluated. Our findings revealed no significant group or shoe type effect on any of the variability measures (ACC: p = 0.460 for ankle‐knee and p = 0.832 for knee‐hip; SoV: p = 0.345 for ankle‐knee and p = 0.755 for knee‐hip). However, there was a significant (p < 0.001) shape difference observed between the most extreme shoe conditions. Despite this, when runners switched shoes, 70%–90% of them maintained their original coordinative pattern across both joint couplings, indicating a strong adherence to their preferred movement path. This suggests that while shoe type can influence the shape of the coordinative pattern, the inherent movement tendencies of the runners remain largely consistent.

An Improved Evolutionary Multi-Objective Clustering Algorithm Based on Autoencoder

Evolutionary multi-objective clustering (EMOC) algorithms have gained popularity recently, as they can obtain a set of clustering solutions in a single run by optimizing multiple objectives. Particularly, in one type of EMOC algorithm, the number of clusters k is taken as one of the multiple objectives to obtain a set of clustering solutions with different k. However, the numbers of clusters k and other objectives are not always in conflict, so it is impossible to obtain the clustering solutions with all different k in a single run. Therefore, evolutionary multi-objective k-clustering (EMO-KC) has recently been proposed to ensure this conflict. However, EMO-KC could not obtain good clustering accuracy on high-dimensional datasets. Moreover, EMO-KC’s validity is not ensured as one of its objectives (SSDexp, which is transformed from the sum of squared distances (SSD)) could not be effectively optimized and it could not avoid invalid solutions in its initialization. In this paper, an improved evolutionary multi-objective clustering algorithm based on autoencoder (AE-IEMOKC) is proposed to improve the accuracy and ensure the validity of EMO-KC. The proposed AE-IEMOKC is established by combining an autoencoder with an improved version of EMO-KC (IEMO-KC) for better accuracy, where IEMO-KC is improved based on EMO-KC by proposing a scaling factor to help effectively optimize the objective of SSDexp and introducing a valid initialization to avoid the invalid solutions. Experimental results on several datasets demonstrate the accuracy and validity of AE-IEMOKC. The results of this paper may provide some useful information for other EMOC algorithms to improve accuracy and convergence.

Easy pair selection method for Kinship Verification using fixed age group images

Kinship Verification (KV) by using facial images is a relevant and challenging research problem in the field of computer vision. Facial features are extracted from the input pair of images and subsequently analyzed to find out existence of kin relation between them. Weights of the training model are suitably learned and adapted for the same. In most of the existing schemes, non kin pairs are randomly generated from the existing kin pair database for the learning process of the model. Since non-kin pairs are formed randomly from the true kin pair database itself, hence there is a significant probability that some non kin pairs have more similarity in feature space which is ideally undesirable and leads to improper learning of the model and results into errors. To reduce such errors, we have proposed a new scheme called easy-pair selection method for KV. Kin and non kin pairs are categorized into easy and hard pairs based on sum of square distance with respect to the feature space of the pairs. Suitable kin-margin (KM) value is chosen to classify the pair as easy or hard. Further, selected easy pairs are used to compute the optimized training weights (W) from the training dataset. The obtained weights will ensure to minimize the distance of kin pairs and maximize the distance of non-kin pairs in feature space. A fixed age group image database (FAG) have also been proposed through this article which contains the corresponding facial images of the parents and their children from the same age group to minimize the issue of age in-variance as well. Extensive experiments have been performed to validate the accuracy of the proposed scheme and is found to outperform the existing relevant schemes for KV.

HYBCIM: Hypercube Based Cluster Initialization Method for k-means

Clustering is a data processing technique that is extensively used to find novel patterns in data in the field of data mining and also in classification techniques. The k-means algorithm is extensively used for clustering due to its ease and reliability. A major effect on the accuracy and performance of the k-means algorithm is by the initial choice of the cluster centroids. Minimizing Sum of Squares of the distance from the centroid of the cluster for cluster points within the cluster (SSW) and maximizing Sum of Square distance between the centroids of different clusters (SSB) are two generally used quality parameters of the clustering technique. To improve the accuracy, performance and quality parameters of the k-means algorithm, a new Hypercube Based Cluster Initialization Method, called HYBCIM, is proposed in this work. In the proposed method, collection of k equi-sized partitions of all dimensions is modeled as a hypercube. The motivation behind the proposed method is that the clusters may spread horizontally, vertically, diagonally or in arc shaped. The proposed method empirically evaluated on four popular data sets. The results show that the proposed method is superior to basic k-means. HYBCIM is applicable for clustering both discrete and continuous data. Though, HYBCIM is proposed for k-means but it can also be applied with other clustering algorithms which are based on initial cluster centroids.

Shape-appearance constrained segmentation and separation of vein and artery in pulsatile tinnitus patients based on MR angiography and flow MRI

This study reports on the development and evaluation of a novel segmentation method for extracting the internal jugular vein and the adjacent carotid artery from magnetic resonance (MR) images of patients with pulsatile tinnitus. A narrow band level set method with combined shape and appearance constraints was developed and applied to high-resolution MR images from 17 pulsatile tinnitus patients (age 52 ± 23 years, 10 females). The proposed method was validated by comparing with the manual segmentation as well as by identifying the jugular vein and carotid artery based on 4D flow MRI in which the two types of vessels have opposing flow. Our study showed that the vein and artery are in contact with each other on 30.2% of all the slices. Dice value, Peak signal-to-noise ratio (PSNR), Hausdorff distance and mean sum of square distance (MSSD) between automatic and manual segmentation were 89.13 ± 2.84%, 27.36 ± 2.39%, 17.2 ± 6.9 mm, 7.4 ± 5.5 mm, demonstrating good segmentation accuracy. The average Dice similarity coefficient and the coefficient of variation compared with 4D flow MRI was 91.42 ± 1.63% and 89.28 ± 4.54% for the internal jugular vein and the carotid artery. The present pipeline for automatic internal jugular vein quantification holds promise for efficient image interpretation in large-scale cohort studies.

Multi-clustering via evolutionary multi-objective optimization

The choice of the number of clusters (k) remains challenging for clustering methods. Instead of determining k, the implicit parallelism feature of evolutionary multi-objective optimization (EMO) provides an effective and efficient paradigm to find the optimal clustering in a posteriori manner. That is, first EMO algorithms are employed to search for a set of non-dominated solutions, representing different clustering results with different k. Then, a certain validity index is used to select the optimal clustering result. This study systematically investigates the use of EMO for multi-clustering (i.e., searching for multiple clustering simultaneously). An effective bi-objective model is built wherein the number of clusters and the sum of squared distances (SSD) between data points and their cluster centroids are considered as objectives. To ensure the two objectives are conflicting with each other, a novel transformation strategy is applied to the SSD. Then, the model is solved by an EMO algorithm. The derived paradigm, EMO-k-clustering, is examined on three datasets of different properties where NSGA-II serves as the EMO algorithm. Experimental results show that the proposed bi-objective model is effective. EMO-k-clustering is able to efficiently obtain all the clustering results for different k values in its single run.

Exact pseudopolynomial algorithm for one sequence partitioning problem

We consider a strongly NP-hard problem of partitioning a finite sequence of vectors in a Euclidean space into two clusters of given size with the criterion of minimizing the total sum of square distances from cluster elements to their centers. The center of the first cluster is subject to optimization, defined by the mean value of all vectors in this cluster. The center of the second cluster is fixed at the origin. The partition is subject to the following condition: the difference between indices of two subsequent vectors included in the first cluster is bounded from above and below by given constants. We propose an exact pseudopolynomial algorithm for the case of a problem where the dimension of the space is fixed, and components of input vectors are integer-valued.

Binocular vision calibration and 3D re-construction with an orthogonal learning neural network

A new approach for binocular vision system calibration and 3D re-construction is proposed. While the system is calibrated, the sum of square distances between the vector coordinates recombined with...

Multi-scale and shape constrained localized region-based active contour segmentation of uterine fibroid ultrasound images in HIFU therapy.

PurposeTo overcome the severe intensity inhomogeneity and blurry boundaries in HIFU (High Intensity Focused Ultrasound) ultrasound images, an accurate and efficient multi-scale and shape constrained localized region-based active contour model (MSLCV), was developed to accurately and efficiently segment the target region in HIFU ultrasound images of uterine fibroids.MethodsWe incorporated a new shape constraint into the localized region-based active contour, which constrained the active contour to obtain the desired, accurate segmentation, avoiding boundary leakage and excessive contraction. Localized region-based active contour modeling is suitable for ultrasound images, but it still cannot acquire satisfactory segmentation for HIFU ultrasound images of uterine fibroids. We improved the localized region-based active contour model by incorporating a shape constraint into region-based level set framework to increase segmentation accuracy. Some improvement measures were proposed to overcome the sensitivity of initialization, and a multi-scale segmentation method was proposed to improve segmentation efficiency. We also designed an adaptive localizing radius size selection function to acquire better segmentation results.ResultsExperimental results demonstrated that the MSLCV model was significantly more accurate and efficient than conventional methods. The MSLCV model has been quantitatively validated via experiments, obtaining an average of 0.94 for the DSC (Dice similarity coefficient) and 25.16 for the MSSD (mean sum of square distance). Moreover, by using the multi-scale segmentation method, the MSLCV model’s average segmentation time was decreased to approximately 1/8 that of the localized region-based active contour model (the LCV model).ConclusionsAn accurate and efficient multi-scale and shape constrained localized region-based active contour model was designed for the semi-automatic segmentation of uterine fibroid ultrasound (UFUS) images in HIFU therapy. Compared with other methods, it provided more accurate and more efficient segmentation results that are very close to those obtained from manual segmentation by a specialist.

Eigenvector analysis of gravity gradient tensor to locate geologic bodies

We have developed a new method to locate geologic bodies using the gravity gradient tensor. The eigenvectors of the symmetric gravity gradient tensor can be used to estimate the position of the source body as well as its strike direction. For a given measurement point, the eigenvector corresponding to the maximum eigenvalue points approximately toward the center of mass of the causative body. For a collection of measurement points, a robust least-squares procedure is used to estimate the source point as the point that has the smallest sum of square distances to the lines defined by the eigenvectors and the measurement positions. It’s assumed that the maximum of the first vertical derivative of the vertical component of gravity vector [Formula: see text] is approximately located above the center of mass. Observation points enclosed in a square window centered at the maximum of [Formula: see text] are used to estimate the source location. By increasing the size of the window, the number of eigenvectors used in the robust least squares and subsequently the number of solutions increase. As a criterion for selecting the best solution from a set of previously computed solutions, we chose that solution having the minimum relative error (less than a given threshold) of its depth estimate. The strike direction of the source can be estimated from the direction of the eigenvectors corresponding to the smallest eigenvalue for quasi 2D structures. To study the effect of additive random noise and interfering sources, the method was tested on synthetic data sets, and it appears that our method is robust to random noise in the different measurement channels. The method was also tested on gravity gradient tensor data from the Vredefort impact structure, South Africa. The results show a very good agreement with the available geologic information.

Application of Sanger Operator with Lateral Connection in Fitting Micro-Drill’s Main Lips

A new approach for straightness fitting of micro-drill’s main lips is proposed. While its chips are measured, micro-drill’s projective images are collected with high precision automatic test system of PCB Micro-drill, and sub-pixel edge features are extracted. The sum of square distances' from the coordinates of sample points to fitted line is taken as objective function. Then a Sanger neural network with lateral connection is designed, where a self-adaptive minor component extracting method is adopted. When the system comes to equilibrium, the eigenvector of minimum eigen value is the fitted line coefficient, from which chips of micro-drill main lips are obtained. The proposed approach is the novel application of Sanger neural network in straightness fitting.

An iterative approach for fitting multiple connected ellipse structure to silhouette

In many image processing applications, the structures conveyed in the image contour can often be described by a set of connected ellipses. Previous fitting methods to align the connected ellipse structure with a contour, in general, lack a continuous solution space. In addition, the solution obtained often satisfies only a partial number of ellipses, leaving others with poor fits. In this paper, we address these two problems by presenting an iterative framework for fitting a 2D silhouette contour to a pre-specified connected ellipses structure with a very coarse initial guess. Under the proposed framework, we first improve the initial guess by modeling the silhouette region as a set of disconnected ellipses using mixture of Gaussian densities or the heuristic approaches. Then, an iterative method is applied in a similar fashion to the Iterative Closest Point (ICP) ( Alshawa, 2007; Li and Griffiths, 2000; Besl and Mckay, 1992) algorithm. Each iteration contains two parts: first part is to assign all the contour points to the individual unconnected ellipses, which we refer to as the segmentation step and the second part is the non-linear least square approach that minimizes both the sum of square distances between the contour points and ellipse’s edge as well as minimizing the ellipse’s vertex pair (s) distances, which we refer to as the minimization step. We illustrate the effectiveness of our methods through experimental results on several images as well as applying the algorithm to a mini database of human upper-body images.

Adaptive Fuzzy Weighted Template Matching Using Invariant Features for a Tracking Application

One of the common research topics for surveillance systems is tracking of a target object. Motions of both observer and target make the problem difficult to handle. In this paper, proposed algorithm tracks a target object on consecutive frames taken from a camera embedded on an unmanned aerial vehicle. Adaptive-fuzzy weighted sum of square distances (SSDs) are utilized for template matching process. SSD is computed by the pseudo-Zernike moments of the reference template and possible matching template around the search point. Fuzzy weights are obtained by taking the advantage of circular projection features. An adaptive fuzzy system is realized by updating the weights of the defuzzifier. Proposed method provides center point of the best matching template which represents the target object to be tracked. Tracking is accomplished under the presence of illumination changes and parallax, and it is seen that the proposed algorithm yields satisfactorily small errors.

Clustering Methods in Microarrays

DCT Given a finite set of points in an Euclidean space the \emph{spanning tree} is a tree of minimal length having the given points as vertices. The length of the tree is the sum of the distances of all connected point pairs of the tree. The clustering tree with a given length of a given finite set of points is the spanning tree of an appropriately chosen other set of points approximating the given set of points with minimal sum of square distances among all spanning trees with the given length. DCM A matrix of real numbers is said to be column monotone orderable if there exists an ordering of columns of the matrix such that all rows of the matrix become monotone after ordering. The {\emph{monotone sum of squares of a matrix}} is the minimum of sum of squares of differences of the elements of the matrix and a column monotone orderable matrix where the minimum is taken on the set of all column monotone orderable matrices. Decomposition clusters of monotone orderings of a matrix is a clustering ofthe rows of the matrix into given number of clusters such that thesum of monotone sum of squares of the matrices formed by the rowsof the same cluster is minimal.DCP A matrix of real numbers is said to be column partitionable if there exists a partition of the columns such that the elements belonging to the same subset of the partition are equal in each row. Given a partition of the columns of a matrix the partition sum of squares of the matrix is the minimum of the sum of square of differences of the elements of the matrix and a column partitionable matrix where the minimum is taken on the set of all column partitionable matrices. Decomposition of the rows of a matrix into clusters of partitions is the minimization of the corresponding partition sum of squares given the number of clusters and the sizes of the subsets of the partitions.

Self-Consistency and MDL: A Paradigm for Evaluating Point-Correspondence Algorithms, and Its Application to Detecting Changes in Surface Elevation

The self-consistency methodology is a new paradigm for evaluating certain vision algorithms without relying extensively on ground truth. We demonstrate its effectiveness in the case of point-correspondence algorithms and use our approach to predict their accuracy. For point-correspondence algorithms, our methodology consists in applying independently the algorithm to subsets of images obtained by varying the camera geometry while keeping 3-D object geometry constant. Matches that should correspond to the same surface element in 3-D are collected to create statistics that are then used as a measure of the accuracy and reliability of the algorithm. These statistics can then be used to predict the accuracy and reliability of the algorithm applied to new images of new scenes. An effective representation for these statistics is a scatter diagram along two dimensions: A normalized distance and a matching score. The normalized distance make the statistics invariant to camera geometry, while the matching score allows us to predict the accuracy of individual matches. We introduce a new matching score based on Minimum Description Length (MDL) theory, which is shown to be a better predictor of the quality of a match than the traditional Sum of Squared Distance (SSD) score. We demonstrate the potential of our methodology in two different application areas. First, we compare different point-correspondence algorithms, matching scores, and window sizes. Second, we detect changes in terrain elevation between 3-D terrain models reconstructed from two sets of images taken at a different time. We finish by discussing the application of self-consistency to other vision problems.

On the Maximum of the Sum of Squared Distances Under a Diameter Constraint

On the Maximum of the Sum of Squared Distances Under a Diameter Constraint

On the Maximum of the Sum of Squared Distances Under a Diameter Constraint

On the Maximum of the Sum of Squared Distances Under a Diameter Constraint