Research On Curve Similarity Measurement And Its Application Based On Combined Gaussian Model

Curve similarity measurement is an important method for pattern recognition,and has been extensively used in the fields of sequence analysis,pattern classification,and image matching.A large number of similarity judgments and classification problems can be transformed into curve similarity measurement problems.Personal handwritten signatures reflect their inherent writing habits and the law of movement.Their signature trajectories are similar,and at the same time they are slightly different from imitation signature trajectories.Curve similarity can be used to verify the authenticity of the signature,thereby achieving personal identity authentication.Human-machine collaboration is of profound significance for assisting exoskeleton robotic systems.With the help of human-machine contact sensor signals,the recognition of human movement status and movement intention is linked to the smooth implementation of human-machine collaboration.Gait events such as Heel-Strike(HS)and Toe-Off(TO),and intention are taken into account in the touch sensor signals with certain differences,and at the same time,they have self-similarities.Using curve similarity measurement can achieve accurate classification of motion state and intention.Traditional curve similarity measurement methods include dynamic time warping(DTW),Hausdorff and Fréchet distance.Aiming at the problems of scale transformation,outliers(segmentations)in the curve similarity measurement,in this paper the approximate solution of the optimal curve matching under the scale transformation can be calculated by using an EC method,and the optimal matched distance can be considered as the curve similarity distance measurement.Then use the combined Gaussian model(CGM)and use multiple different Gaussian kernel functions to convert the distance measurement to similarity to adapt to the similarity measurement and classification between curves under different scale conditions and outliers(segmentation).The specific content of the paper is as follows:1.A curve similarity distance measurement model based on the scale transformation(CSDM-CST)is proposed.Under the condition of scale transformation,the optimal curve matching distance is obtained by EC,which is used as curve similarity measurement to calculate the curve similarity.2.A segmentation curve similarity measurement model(SCSM)is proposed.There are often abnormal segmentations in the curve,which have a serious impact on the overall curve matching.In this paper,the idea of divide and rule is used to divide the curves.The similarity distance of each curve segmentation can be calculated respectively.In the segmented matching process,the segmented matching adjustment algorithm can be utilized to partially overlap and discard the two matching curves to achieve elastic matching of the overall curve.The similarity between the overall curves can be calculated by CGM based on the distance measurement of each segmentation.3.A curve similarity distance measurement model based on CGM(CSDM-CGM)is proposed.In the similarity calculation of segmented curves,the distance measurement is transformed into similarity by CGM,and similarly the similarity distance measurement of template curve and test curve is also calculated by CGM.As a classifier,the template curve can represent the classification center,given the decision threshold and positive and negative sample data,the parameters of the CGM can be trained by EC as the template curve parameters,where the center of the Gaussian kernel represents the position of the template curve,The Gaussian kernel width indicates the distribution of each position of the curve.4.Utilize the SCSM for online handwritten signature authentication,and use the differences between the signature curves to identify the authenticity of the signature.Utilizing the CGM,combining the similarity distances of each segmentation and other matching curve similarity features,the curve similarity of each segmentation is calculated by weighting.The overall similarity of the signature curve is the average of the similarity of each segmentation.The overall similarity is directly compared with the decision threshold to determine the authenticity of the signature.On 6 public data sets,a single reference signature system based on SCSM is used to obtain the best performance of a known single reference signature system;in a multiple reference signature authentication system,a signature template clustering is used to calculate the signature clustering.The inner average distance of each class and the average distance between classes are used as the hierarchical decision threshold in two-level signature authentication.The overall authentication performance of a multi-signature authentication system is equivalent to other state-of-art systems.5.CSDM-CGM is used in gait event and phase detection to realize human intention recognition by using plantar pressure signal curve of exoskeleton robot.Common gait phase detection methods rely on plantar pressure thresholds.Plantar pressure changes greatly under different weights and speeds,and the threshold calculation is unstable,which makes it difficult to effectively distinguish gait phases.It is found that the same phase curve of gait is similar and different phase curves are different whether the weight and speed are the same or not.However,due to body weight,walking speed,collector interference and other reasons,the same phase curve has problems such as different scales,local abnormal point interference and so on.In this paper,CSDM-CGM is used to detect gait phase.Using gait phase labeling data,the classifier decision threshold is given,and the CGM parameters are trained by EC as template curve parameters.The real-time gait phase detection of one foot and two feet is realized by using the trained model and rule algorithm.Using the same training model,24 subjects were tested at different speeds,and the accuracy rate of single foot gait event detection was 93%;among them,10 subjects were tested at variable speed,and the accuracy rate of bipedal gait phase detection was97%.Using only one subject's gait phase labeling data,the accuracy of the training model in the rest 23 subjects' gait phase detection results is more than 90%.The experimental results show that the curve similarity measurement model based on the CGM proposed in this paper has good robustness,and can be suitable for different applications where there are curve scale transformations and outliers.