Image offset density distribution model and recognition of hand knuckle
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Abstract
The accurate description of hand posture plays an important role in the manmachine interaction involved in coordinated assembly. Knuckle image extraction and recognition are of great significance to refine and enrich handpose information. These are based on nonparametric density kernel estimation observation sets corresponding to unilateral and bilateral excursion of the hand knuckle gray image. In this paper, sets of pixel positions belonging to the upper and middledensity intervals are used as two types of image targets. Random clustering and random field multiclassification target modeling are used to learn and estimate the two target distributions of the image. The discriminant field classification learning method is used to fuse the two kinds of target models. A comprehensive representation of the image offset features is obtained. Finally, the knuckle image sample set is used to train the model, and the adaptive threshold is used to identify the hand knuckle image. The results show that the proposed method is feasible.
Keywords
Knuckle recognition Image offset density Gaussian process Infinite Dirichlet process1 Introduction
In intelligent manufacturing systems, the development of detection technology with high intelligence and strong environmental adaptability is of great significance to improve production efficiency and enhance the flexibility of manufacturing systems and product quality [1, 2]. Machine visionbased humancomputer interaction coordination assembly technology uses human assembly gestures obtained from image analysis as input information for robot task planning [3] to realize an efficient and flexible coordinated assembly process [4]. The overall information, including the biological structure of the human hand image and associated hand assembly posture [5], is the basis for inferring the gesture intention.
Gesturerecognition research has two main directions. One uses sensors, detectors, and other peripheral tools to achieve gesture recognition. Lee and You [6] identified complex static gestures using wrist bandbased contour features (WBCFs). The user must wear black wristbands to accurately segment the hand area. Moschetti et al. [7] recognized nine gestures with inertial sensors placed on the index finger and wrist. This kind of method, which uses external equipment to extract the hand position and posture to achieve more accurate gesture recognition, lacks convenience. Another research direction is unmarked gesture recognition with captured images. Bao et al. [8] classified images of gestures using deep convolutional neural networks. This method requires no segmentation or detection to distinguish irrelevant nonhand regions. Dehankar et al. [9] used accurate endpoint identification (AEPI) to recognize handgesture images against varying backgrounds and blurred images. However, the above unmarked gesturerecognition methods are not sufficiently accurate. Their robustness and stability are insufficient, and the pose cannot be completely extracted. Further research is needed to improve their ability to accurately extract hand positions.
Many new identification technologies have emerged in the field of imagefeature detection. These methods are used in different fields and vary in their focus. Some focus on featureextraction techniques. Ding et al. [10] used double local binary patterns (DLBPs) to detect frame peaks in video. Yao et al. [11] presented a featureselection method based on filters. Some have focused on model building, such as Wang and Wang [12], who modeled an action class of body space configuration with flexible quantities. A hierarchical spatial SPN method was developed to simulate the spatial relationships among subimages, and subimage correlation was modeled by additional layers of the SPN. Panda et al. [13] proposed a featuredriven selection classification algorithm (FALCON) to optimize the energy efficiency of machinelearning classifiers. The study of feature clustering is helpful for imagefeature classification. Li et al. [14] used an unsupervised principal component analysis (PCA)based feature clustering algorithm to automatically select the optimal number of clusters to solve the problem of automatic anomaly detection in monitoring applications. Jiang et al. [15] proposed a selforganizing feature clustering algorithm based on fuzzy similarity to extract text features. This method is fast and can extract features better than other methods. Rahmani and Akbarizadeh [16] proposed a spectral clustering method using unsupervised feature learning (UFL).
There is a strong correlation between the structured information of the hand image and the biological structure of the hand. The specific structural information varies with the gesture model, depending on the simplified biological structure. Under static conditions, visionbased gesturestructure modeling is mainly classified as either feature template representation based on twodimensional models or hand geometry representation based on threedimensional models, depending on the dimension of the investigated spatial domain [17, 18]. The latter is divided into a volumetric model that considers the surface structure of the hand [19] and a jointlinking model that considers the anatomy of the hand, according to the established differences in the geometric characteristics [20]. The templatebased modeling is characterized by gesturecontour information, which makes it difficult to provide detailed kinematic parameter information, and is suitable for scenes where the gesture is simple and the semantic features are clear. For complex situations in which the hand posture is variable, semantic features and time are related, and the structural parameters of the “jointlink” model of the hand are modeled. The overall kinematic representation of the hand can be obtained through structural parameter detection.
The biometric identification of the hand includes skincolor location, fingertip root detection [21], knuckle recognition, finger positioning, and kinematic correlation between features. The knuckle position feature has an important influence on the accuracy of the opponentpose inference. Knuckle image detection methods are mainly classified as geometric analysis or texture recognition [22, 23, 24]. Current research of knuckle images focuses on the use of knuckles for identification, sometimes combined with fingerprints. The way and purpose of its research is similar to fingerprint detection [25]. Usha and Ezhilarasan [26] used featureextraction methods based on angle geometry analysis (AGFEM) and contourlet transform (CTFEM) to authenticate the finger back surface (FBKS) [27], and pointed out that the distal phalangeal region of FBKS, the finger joint area near the tip of the finger, has great potential for recognition. Recognition performance is improved through extraction and integration of knuckle geometry and texture features simultaneously with fractional fusion. Lin et al. [28] provided a practical solution for biometric systems based on the back of the finger through the FKP recognition algorithm. Gao et al. [29] used an adaptive binary fusion rule to adaptively fuse the matching distances before and after reconstruction, reducing falserejection rate. Kumar and Xu [30] used an automatic fingerrecognition study of the lowest finger joint pattern formed between the metacarpal and the proximal phalange.
Image segmentation based on a skincolor model can initially solve the problem of imagepositioning in the hand. The important image features that characterize the biological structure of the hand, such as finger posture and knuckle position, still must be further identified. The human finger section is the important positioning point for the human hand posture. Gesture recognition requires accurate knuckle position information for threedimensional reconstruction to restore the hand biostructure. In the half and fullgrip postures of the hand, corresponding to the joint structure at the joint position of the hand, the grayscale distribution of the knuckle image presents an irregular convexhull structure near the local position of the finger. A nondeterministic irregular convex hull can be used as a kind of random hidden structure of knuckle images. In a previous article [31], the author took a finger joint image as an example. The examples are directed to a random image with the above gray structure ambiguity, feature ambiguity, and difficulty in extraction. The hidden feature observation of the image is obtained by the density estimation of the gray distribution. This observation is used to establish the framework of learning and estimating algorithms for imageryimplicit feature patterns. The extraction and analysis methods of the offset features on random images are given.
In this paper, the humancomputer interaction is coordinated and assembled in an indoor environment where the light intensity is relatively stable and the camera angle is relatively fixed. The research in this paper is based on the image offset density distribution. First, the image upper level density feature is modeled and analyzed with an infinite Dirichlet process model. Then, the image middledensity feature is modeled and analyzed with a Gaussian process classifying model. Finally, the twolevel density features are fused by a binary Gaussian process classification. Experiments are carried out to verify the feasibility of the process.
2 Infinite Dirichlet process knuckle image highlevel data hybrid model
where \( \widehat{\mu} \) is the approximation form of the offset measure, \( \mathbb{D} \) is the fusion structure between different offset set models under different offset parameters, \( {{\tilde{\mu}}_{{\mathbb{G}}_1\mid \mathrm{\mathbb{P}}}}^{\hbox{'}} \) is the highlevel offset set probability measure, and \( {{\tilde{\mu}}_{{\mathbb{G}}_2\left\mathrm{\mathbb{P}}\right.}}^{\hbox{'}} \) is the middle offset set probability measure.
where p(⋅) is the nonnegative twodimensional density function corresponding to the target distribution.
For the learning problem of unilateral offset density in image stochastic models, this section uses an infinite Dirichlet process hybrid model. Based on the graylevel position data extracted from the nonparametric density kernel estimation results, the probability measure \( {{\tilde{\mu}}_{{\mathbb{G}}_1\mid \mathrm{\mathbb{P}}}}^{\hbox{'}} \) of the offset set belonging to the fixed threshold c in the image domain is learned. The number of clusters is described as a random state, and the Gibbs sampling method is used to iteratively study the density structure of the hierarchical probability form under the assumption of the Markov neighborhood. Through learning and modeling the offset set distribution, the unilateral estimation of the gray particle random model is realized.
2.1 Horizontal density clustering and Markov assumptions for discrete observations
Among them, the marker amount constitutes a hidden variable at the observation grid Z. To learn the distribution model of the observations by using observations, the relationship between observations, label classes, and offset measures on grid Z must be established. On V and Z\V, respectively, the position in the observed set V has a definite marker class 1 on the image. However, the labeling category Z\V on the unobserved position set is uncertain. Under the assumption of the continuity of the distribution model, the position where the marker category is indefinite should be understood as not observed, and the 0 marker cannot directly determine the corresponding observation result. The label category indicates whether the observation position belongs to the offset set under the level c. However, when estimating the overall offset measure using the observation data, it is necessary to further specify the mark relationship between the elements of the sets V and Z\V to integrate the mark relationships on the entire grid point Z. In connection with the dataextraction process in the previous article [30], the dependency relationship between grid observations can be established on Z using the mixture graph structure as a basis for subsequent inference learning using observation data. The relationship between marker categories and grid positions is established through a directed graph structure. At the same time, pairwise Markov random fields are used to establish a dependency relationship between the discrete grid points on the imaging domain, i.e., the distribution of p(⋅) on Z.
That is to say, observations that depend on the overall distribution are separated from the whole in the form of local associations.
According to the above analysis, on the one hand, the offset measure on the random hyperparameter field f reflects the characteristics of the observation mark classification and the density distribution agglomeration under the local relation. On the other hand, considering that when the offset set level parameter is higher, the Euler indicative number of the offset set is larger, and it shows that the local coverage of the offset set at the high level in the planar domain is more complete and shows more of a clustering trend. Therefore, the learning problem for p(⋅) can be transformed to a random clustering learning problem. This section uses the infinite Dirichlet process mixture model of the clustering model to construct the probability density p(⋅) in Eq. 2. The Gibbs sampling method is used to iteratively study the density structure of the hierarchical probability form under the assumption of the Markov neighborhood.
2.2 Nonparametric distributions and infinite Dirichlet processes
where θ is a hyperparameter, which is not limited to a limited form of distribution to improve the learning effectiveness and imagerecognition rate.
The random process DP(α, H) is defined by the central parameter α and the base measure H.
where N is the number of samples and k_{s} may have a degeneration value of K.
By sampling the above distribution, an effective clustering parameter update can be obtained, and the update learning of parameters in each mixed Gaussian component can be realized.
2.3 Infinite Dirichlet process mixed model based on collapsed Gibbs sampling
According to the N observations \( x={\left\{{x}_i\right\}}_{i=1}^N \) of the Dirichlet process mixed model, the hidden variable label z_{i}, the total number of clusters, and the corresponding parameter \( {\left\{{\theta}_k\right\}}_{k=1}^K \) are inferred. The exact posterior distribution p(π, θ x) contains the distributions corresponding to all possible category labeling spaces, and it uses a collapsed Gibbs sampling algorithm to implement iterative learning of an infinite clustering mixture model. First, all observed variables are sampled with their corresponding hidden variables z_{i}, then the posterior edge π of the polynomial corresponding to the current label class distribution and all clustering hyperparameters \( {\left\{{\theta}_k\right\}}_{k=1}^K \) is calculated.

① The next resample of sample marker \( {z}_i^{(t)} \) is started with the Dirichlet hyperparameters \( {\alpha}_0^{\left(t1\right)} \) and \( {z}_i^{\left(t1\right)}\left(i=1,\dots, N\right) \).

② The random array {1, 2, … , N} of the observation sequence τ(⋅) is sampled.

③ According to the last iteration, the initialization parameters are set to z = z^{(t − 1)} and \( {\alpha}_0={\alpha}_0^{\left(t1\right)} \).
 ④ For random arrangement i ∈ τ(1), … , τ(n):
 (a)
The observation data x_{i} are removed from the marker class z_{i}, and the sufficient statistics \( {S}_{z_i} \) and \( {n}_{z_i} \) of the observation class z_{i} are updated.
 (b)
If x_{i} is the only observation in the current category, the category label and all corresponding clustering parameters are cleared. Update statistics \( {S}_{z_i} \) and \( {n}_{z_i} \), total K = K − 1 of marker class.
 (c)
Relabel all nonempty activation categories 1, …, K.
 (d)
Calculate the prediction likelihood for all Klike clusters that are activated based on the statistics \( {\left\{{S}_k\right\}}_{k=1}^K \) and \( {\left\{{n}_k\right\}}_{k=1}^K \):
 (a)
 (e)
Sample new class of z_{i} from the (K + 1)dimensional polynomial distribution:
 (f)
If z_{i} = K + 1, a new clustering marker is obtained and denoted as K + 1. The new clustering parameter corresponding to (K + 1) is sampled by H(ϕ_{i} x_{i}).
 (g)
Update sufficient statistics \( {\left\{{S}_k\right\}}_{k=1}^K \) and \( {\left\{{n}_k\right\}}_{k=1}^K \) for all category markers.

⑤ It is judged whether all categories are resampled. If not, return to the flag u1, and return to ① for the next resampling.

⑥ Sample all clustering parameters for all tagged classes:

⑦ Sample using the auxiliary variable method:
3 Method—knuckle image midlevel data model
In view of the complexity of the random offset set itself, the difference between the offset characteristics corresponding to different offset parameter intervals is relatively large. And the further the offset parameter is from the standard value of 1, the more complex the corresponding feature. Therefore, in the learning process of random image bilateral offset measurement, especially for the case of small offset parameters, it is necessary to deeply analyze the random distribution characteristics of the actual offset observations in the training image database and to select an appropriate model for learning. In this section, we obtain the \( {{\tilde{\mu}}_{{\mathbb{G}}_2\mid \mathrm{\mathbb{P}}}}^{\hbox{'}} \) equivalent density estimate \( p\left(\cdot \right)\propto {{\tilde{\mu}}_{{\mathbb{G}}_2\mid \mathrm{\mathbb{P}}}}^{\hbox{'}}\left(\cdot \right) \) by learning the multilabel distribution random field model for the middensity location.
3.1 Midlevel data distribution training based on Gaussian process classification
where the location i tag \( {y}_i^c \) has {0, 1} value, and the f vector form is \( f=f\left({f}_1^1,\dots, {f}_n^1,{f}_1^2,\dots, {f}_n^2,{f}_1^3,\dots, {f}_n^3\right) \). It has a prior form \( f\mid X\sim \mathcal{N}\left(0,K\right) \), where K is the corresponding covariance function and n is the amount of training data. Assuming the category information is not related, K has the form of a diagonal matrix, K = diag {k_{1}, k_{2}, … , k_{c}}, where k_{c} represents the trust relationship between each type of tag data. Therefore, the learning of the middlelevel migration measure is transformed to the learning of the random quantity f.
3.2 Posterior calculations on Gaussian fields with multiple binary classifications
The maximum posterior estimate of the implicit function f is defined as \( \widehat{f}=\arg {\max}_fp\left(fX,y\right) \), \( A=\mathrm{\nabla \nabla}\log p\left(f=\widehat{f}X,y\right). \)
where Π is a Gibbs distribution π corresponding to a cn × n scale column block matrix.
where E = (K + D^{−1})^{−1} = D^{1/2}(I + D^{1/2}KD^{1/2})^{−1}D^{1/2}.

① Input observation measurement marker y, covariance matrix K, and probability marker function initialization f ≔ 0.

② Calculate the label distribution law of the current observation variable:

③ For each class of implicit labels c = 1,2, …, C, calculate:

④ Calculate transition parameters:

⑤ Calculate the objective function and determine if it converges. If it does not converge, return to ②.

⑥ Compute edge likelihood prediction and hidden signature distribution edge prediction:
3.3 Structure of positive definite kernel function of random information in the middle level
and the design parameter array is p = [1, 0.5 , 0.25; 0.5 , 1 , 0.5; 0.25 , 0.5 , 1].
In the above equation, the subdiagonal array k_{1} corresponds to the position of the image observation data at the density estimation level of 75 to 85% in the midlevel dataset of the image. After testing, it was found that although the aggregation level of this category dataset is weaker than the aforementioned highlevel data model, it still has a certain clustering trend. Therefore, the associated credits between this category of data can be designed as an exponential clustering pattern, and the closest clustering component of the observation data can be found. The final correlation result of the clustering trend between x and x^{'} is determined using an isotropic exponential function. The design of the parameter array p_{ij} further confirms the labeling of the best highlevel clustering component to which the two observations belong, i.e., when the data in the two images belong to the same clustering component in a highlevel model, they have a higher degree of trust.
3.4 Model prediction process

① Input posterior edge prediction \( \widehat{f} \), covariance matrix K, detection x.

② Calculate the current observation variable label distribution law Π:

③ For each class of implicit labels c = 1,2, …, C, calculate

④ For each type of implicit label c^{'} = 1,2, …, C, calculate

⑤ Initialize Monte Carlo posterior sampling: π_{∗} ≔ 0.

⑥ Posterior distribution of sampling test position markers:

⑦ Calculate the regularized estimate vector:

⑧ Calculate tag category prediction vector:
4 Knuckle image recognition based on learning results of two layers of observation data
In the previous section, based on the high and midlevel data in gray image density estimation, offset measurement estimation under different offset level parameters was implemented. At the same time, the learning results of the twolayer data model were used as two kinds of offset information features on the grayscale image. Since the above two types of migration features are the specific forms of the overall random set migration characteristics of the image in the interval, it is obviously necessary to integrate the above two features as the characteristics of the overall image features. According to the process of dataextraction and modelgeneration, it can be seen that there is a strong correlation between the two features, and there is even consistency in the overlapping range of the horizontal parameters. From the modeling process on the Poisson Gaussian field of random images, the two kinds of offset information also have strong compatibility.
From the perspective of information fusion and feature learning, two types of feature models that have been learned can be used as detectors of two kinds of offset features on the image, and the detection results are two likelihood values of a specific image under the above model. The likelihood value corresponding to the positive sample image is higher, and the negative sample image is the opposite. Therefore, the fusion of offset features is the learning process of jointly distributing the two likelihood values on the offset eigenvalue plane. Furthermore, since the size of the training library in the aforementioned model learning process is not large, the amount of information provided by the training results is not sufficient, and the learning result is not perfect. Also, the offset feature itself has a strong random feature. Based on the above analysis, the likelihood value fusion process in the feature plane is not suitable for learning with a generative model. Therefore, in this section, the likelihood values of the two models labeled with positive and negative samples are used as input. The Gaussian process classification in the discriminative learning method is used to fuse the likelihood values of the two types of images in the feature plane. The estimation of the joint overall distribution of the two types of features is obtained, and the joint image is directly identified based on the estimation results.
4.1 Binary classification and image offset information fusion based on Gaussian process
Depending on whether it belongs to the hand joint image, the test image is given the y mark {−1, 1} at the corresponding observed data point in the twolayer model likelihood space. In this way, the aforementioned fusion process can be presented as Binary Gaussian process learning. The learning result is the probability distribution of the marker y = 1 on the discriminant field for the joint target and nonjoint targets. Different from middlelevel information modeling, in the learning process of the classification information for the marker information y in this section, the sample domain is a training dataset generated from the two types of model likelihood values corresponding to the test image set. The learning domain is a normalized feature plane.
Since the value of label y is 0 in the range, the specific form of conditional field f ∣ X can be given by using the Gaussian process a priori \( f\mid X\sim \mathcal{N}\left(0,K\right) \), where K is the binary covariance function on field f. It can be seen that the main content of classification learning is the posterior update of f and the prediction of p(f_{∗} f, X, y, x_{∗}) at the test position x_{∗}.
where \( \widehat{f}=\arg {\max}_fp\left(fX,y\right) \) and \( A=\mathrm{\nabla \nabla}\log p\left(f=\widehat{f}X,y\right) \).
Equations 51 and 53 yield the posterior format \( q\left(fX,y\right)=N\left(\widehat{f},{\left({K}^{1}+W\right)}^{1}\right) \) of \( \widehat{f} \).
Equation 56 obviously produces a diagonal band matrix. The inverse matrix can be quickly calculated by means of Cholesky decomposition. The inversion format in Eq. 57 is more stable than the directly solved inverse matrix of A.

① Input posterior edge prediction \( \widehat{f} \), covariance function k, and detection X.

② \( W:= \mathrm{\nabla \nabla}\log p\left(y\widehat{f}\right) \).

③ L ≔ Cholesky(I + W^{1/2}KW^{1/2}).

④ \( {f}_{\ast}:= k{\left({x}_{\ast}\right)}^T\nabla \log p\left(y\widehat{f}\right) \).

⑤ v ≔ L\(W^{1/2}k(x_{∗})).

⑥ \( \mathbb{V}\left[{f}_{\ast}\right]:= k\left({x}_{\ast },{x}_{\ast}\right){v}^Tv \).

⑦ \( {\overline{\pi}}_{\ast}:= \int \sigma (z)\mathcal{N}\left(z{\overline{f}}_{\ast },\mathbb{V}\left[{f}_{\ast}\right]\right) dz \).
The predicted edge distribution with tag category 1 is \( {\overline{\pi}}_{\ast } \).
4.2 Knuckle target recognition algorithm based on offset feature distribution
Based on the learned image layered offset fusion GP model, the model likelihood of the fusion image of the test image is used as the image feature. In the range of the test image domain, according to this feature combined with the maximum betweenclass variance method, selfadaptive threshold recognition is performed for the far finger and middle finger in the image. The concrete manifestation is that subimage extraction is performed after the template data are calculated from the test image data. The nonparametric density kernel estimation calculations and the evolution of the level set of interest regions are performed on the obtained subimages to obtain high and midlevel data for density kernel estimation. Highlevel data are used to calculate the highlevel data model likelihood through the highlevel data model (DPMM). After the middlelevel data are transformed by the data discrete group, the midlevel data model is used to calculate the midlevel data model likelihood. We then combine the two to calculate the twolevel data fusion GP model likelihood.
The likelihood value of the fusion GP model is calculated at each template position of the test image, and this likelihood value is used as the information matrix corresponding to the image feature. Due to the limitations of the integrity of the model, detection points with higher likelihood values may appear at nonjoint target locations. The largest clusterlike variance method is used to eliminate the position with the highest GPlikelihood in the case of threshold adaptation. Then, nonlinear evolution is performed on the feature information matrix with the high likelihood value removed, the features are enhanced, and the joint target is detected again using the adaptive threshold detection method. Because the detection position of the high threshold at nonjoint positions is mostly unstable, it is difficult to recover it by the neighborhood information after rejection by the threshold. At the same time, a high threshold value at the joint location is more stable, so it can be recovered by the evolution of the neighborhood information.
5 Analysis of results and discussions
5.1 DPMM model learning process
From the results, the convergence speed of DPMM is faster and the smoothness of the likelihood curve is greater. On the one hand, because the number of clusters is flexible, the model has further improved the identification of the structure within the training dataset. The process of testing the number of linked random clusters can further clarify the sampling results. In the initial phase of the iterative process, the number of clusters suddenly increases by several times the convergence value. As shown in Figs. 4 and 5, different from the parameter optimization in the traditional finite mixture model, this stage corresponds to the sampling algorithm performing a random search in a wide range of clustering models, so that the model can quickly determine a more stable clustering mode. On the other hand, the Dirichlet distribution uses an a priori structure, so that the update process of the DPMM internal parameters can be more effectively controlled under higherlevel conditional distributions, manifesting that the convergence curve has higher smoothness in the stable region.
5.2 Offset measurement data learning results
From the prediction results in Fig. 7, it can be seen that the threecategory tag learning results of layer data in the finger image can more clearly show the design goals of the model. The marker results of the learning prediction also conform to the hypothesis of the distribution of layer data in the knuckle image.
According to Fig. 8b, in the normalized feature plane, the first characteristic direction of the positive sample fusion distribution follows the characteristic line (0, 0)(100, 100) direction in the feature plane. The second feature direction is nearly perpendicular to the feature line; the first feature direction of the negative sample fusion distribution is close to the vertical direction of the feature line. The angle relationship between the feature direction and the feature line indicates that the two types of offset features that are fused constitute a certain degree of discrimination between positive and negative samples, and the fusion results show a stronger forecast of this differentiation. Comparing the left and right graphs shown in Fig. 8b, the highend model of farknuckle images has better discrimination between positive and negative samples than the middlelevel model, while the fusion prediction of middlefinger images shows the opposite result. The main reason for the difference between the above models is the obvious differences in the random structure of the distal phalanx and middle phalanx images, which are embodied in the differences in distribution patterns at different levels of displacement.
5.3 Recognition for various algorithms
Considering that the area under the curve (AUC) on the ROC is a measure of the recognition ability of the identifier, it can be clearly seen from Fig. 9 that in the farknuckle test library, the comprehensive model recognition ability of the middlelevel data model and the twotier data is not as good as that of highlevel image features. In the middlefinger test library, the recognition curves of the two highlevel data models are low, and the corresponding AUC is less than 0.5. The recognition ability of the highlevel data model in the farfinger library is obviously higher, while the middletier data model in the middlefinger library has stronger recognition ability. The above shows that the existing data model has great differences in the ability to identify different types of knuckle objects. It also potentially indicates that there is a certain difference between deep model categories in the distribution of far and middlefinger image data.
In Fig. 9b, the AUC values of the highlevel data model corresponding to the two ROCs are 0.5134 and 0.2332. It can be seen that the recognition effect of highlevel models in the middlefinger image database (2) is not obvious, and wrong classifications even appear. Further tests show that the highlevel model with high likelihood is the middlefinger area, not the finger joint area. This phenomenon occurs because the intermediate region has relatively small local information entropy due to the smooth grayscale distribution. The highlevel data volume is larger and denser than the usual joint image data, which undermines the model’s assumptions on data distribution, and therefore, it has poor recognition capability. At the same time, according to Fig. 9, it can be seen that the ROC corresponding to the twolayer data fusion model is located between the high and middlelevel models. It shows that the recognition based on the fusion model has the effect of comprehensively judging the two features. In the case that the high and middlelevel models differ greatly in their ability to identify models, they can provide effective comprehensive evaluation, which is more prominent in Fig. 9b. The minimum area under the curve for the fusion model is (a) 0.4512 on the left of the figure, and the maximum is (b) 0.7880 on the right of the figure. The results show that the fixed threshold identification method has stable and correct classification ability under the condition of existing limited data and test set in the environment where the light intensity is relatively stable and the imaging angle does not change much.
6 Conclusions
In this paper, nonparametric density kernel estimation results are used as observation sets, and the estimation of multilevel migration of knuckle images is estimated using both random clustering iterative learning and a multiclass random field model. Further, through the fusion learning of multilayer migration features, the overall characteristics of knuckle images are constructed, and the detection and recognition capabilities of the above multiple models under fixed and adaptive thresholds are compared. At the same time, a knuckle position image recognition algorithm based on an offset feature fusion model under adaptive threshold conditions is presented. Threshold recognition is carried out on the image with relatively stable light intensity. The results show that the corresponding algorithm is feasible. For the environment with large change of light intensity and the large change of camera angle, it is necessary to further study the adaptability of image threshold.
Notes
Acknowledgements
The authors thank the editor and anonymous reviewers for their helpful comments and valuable suggestions. I would like to acknowledge all our team members, especially Luqi Gong. These authors contributed equally to this work.
About the authors
Shiqiang Yang was born in Baiyin, Gansu, P.R. China, in 1973. He received the Ph.D degree in mechanical engineering from Xi’an University of Technology of China, Xi’an, China, in 2010. From 2005 to 2018, he was with Xi’an University of Technology of China, Since 2009, he has been an associate professor with the School of Mechanical and Precision Instrument Engineering, Xi’an University of Technology, Xi’an, China. From 2011 to 2018, he conducted the Master Research with the School of Mechanical and Precision Instrument Engineering, Xi’an University of Technology, Xi’an. His current research interests include Intelligent robot control, Image recognition, behavior detection and recoginition.
Luqi Gong was born in Xianyang, Shaanxi, P.R. China, in 1991. He received the Master degree from the Xi’an University of Technology of China, Xi’an, China, in 2016. He research interests include image recognition, image processing and biometric detection.
Dan Qiao was born in Handan, Hebei, P.R. China, in 1994. He received the Bachelor degree from the Xi’an University of Technology of China, Xi’an, China, in 2016. Now, he works in Xi’an University of Technology of China as Master student. He research interests include image recognition, image processing and biometric detection.
Funding
This work is supported by the National Natural Science Foundation of China (Grant No.51475365).
Availability of data and materials
Please contact author for data requests.
Authors’ contributions
All authors take part in the discussion of the work described in this paper. These authors contributed equally to this work. All authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
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References
 1.Y. Wang, T. Chen, Z. He, C. Wu, Review on the machine vision measurement and control technology for intelligent manufacturing equipment. Control Theory Appl. 32(3), 273–286 (2015)Google Scholar
 2.M. Liu, J. Ma, M. Zhang, Z. Zhao, D. Yang, Q. Wang, Online operation method for assembly system of mechanical products based on machine vision. Comput. Integr. Manuf. Syst. 21(9), 2343–2353 (2015)Google Scholar
 3.Y. Wang, D. Ewert, R. Vossen, S. Jeschke, A visual servoing system for interactive humanrobot object transfer. J. Autom. Control Eng 3(4), 277–283 (2015)CrossRefGoogle Scholar
 4.J.T.C. Tan, F. Duan, R. Kato, T. Arai, Safety strategy for humanrobot collaboration: design and development in cellular manufacturing. Adv. Robot. 24, 839–860 (2010)CrossRefGoogle Scholar
 5.M.K. Bhuyan, K.F. MacDorman, M.K. Kar, D.R. Neog, Hand pose recognition from monocular images by geometrical and texture analysis. J. Vis. Lang. Comput. 28, 39–55 (2015)CrossRefGoogle Scholar
 6.D.L. Lee, W.S. You, Recognition of complex static hand gestures by using the wristbandbased contour features. IET Image Process. 12(1), 80–87 (2018)CrossRefGoogle Scholar
 7.A. Moschetti, L. Fiorini, D. Esposito, P. Dario, F. Cavallo, Toward an unsupervised approach for daily gesture recognition in assisted living applications. IEEE Sensors J. 17(24), 8395–8403 (2017)CrossRefGoogle Scholar
 8.P. Bao, A.I. Maqueda, C.R. del Blanco, N. García, Tiny hand gesture recognition without localization via a deep convolutional network. Consum. Electron. 63(3), 251–257 (2017)CrossRefGoogle Scholar
 9.A.V. Dehankar, S. Jain, V.M. Thakare, Using AEPI Method for Hand Gesture Recognition in Varying Background and Blurred Images, 2017 International conference of Electronics, Communication and Aerospace Technology (ICECA), vol 1 (2017), pp. 404–409Google Scholar
 10.Y. Ding, Q. Zhao, B. Li, X. Yuan, Facial expression recognition from image sequence based on LBP and Taylor expansion. IEEE Access 5, 19409–19419 (2017)CrossRefGoogle Scholar
 11.C. Yao, Y.F. Liu, B. Jiang, J. Han, J. Han, LLE score: A new filterbased unsupervised feature selection method based on nonlinear manifold embedding and its application to image recognition. IEEE Trans. Image Process. 26(11), 5257–5269 (2017)MathSciNetCrossRefGoogle Scholar
 12.J. Wang, G. Wang, Hierarchical spatial sum–product networks for action recognition in still images. IEEE Trans. Circuits Syst. Video Technol. 28(1), 90–100 (2018)CrossRefGoogle Scholar
 13.P. Panda, A. Ankit, P. Wijesinghe, K. Roy, FALCON: feature driven selective classification for energyefficient image recognition. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 36(12), 2017–2029 (2017)CrossRefGoogle Scholar
 14.H. Li, A. Achim, D. Bull, Unsupervised video anomaly detection using feature clustering. IET Signal Process. 6(5), 521–533 (2012)MathSciNetCrossRefGoogle Scholar
 15.J.Y. Jiang, R.J. Liou, S.J. Lee, A fuzzy selfconstructing feature clustering algorithm for text classification. IEEE Trans. Knowl. Data Eng. 23(3), 335–349 (2011)CrossRefGoogle Scholar
 16.M. Rahmani, G. Akbarizadeh, Unsupervised feature learning based on sparse coding and spectral clustering for segmentation of synthetic aperture radar images. IET Comput. Vis. 9(5), 629–638 (2015)CrossRefGoogle Scholar
 17.R.B. Dan, P.S. Mohod, Survey on Hand Gesture Recognition Approaches [J]. Int. J. Comput. Sci. Inf. Technol. 5(2), 2050–2052 (2014)Google Scholar
 18.P. Garg, N. Aggarwal, S. Sofat, Visual based hand gesture recognition. Int. J. Comput. Electr. Autom. Control Inform. Eng. 3(1), 186–191 (2009)Google Scholar
 19.Fai CC, Silvia A, Alessandro B, Alain F, Mehdi M, Francesco, P. Constraint study for a hand exoskeleton: human hand kinematics and dynamics. J Robotics. 2013:117. https://doi.org/10.1155/2013/910961.
 20.S. Kang, B. Choi, D. Jo, Faces detection method based on skin color modeling. J. Syst. Archit. 64(C), 100–109 (2016)CrossRefGoogle Scholar
 21.G. Wu, W. Kang, Robust fingertip detection in a complex environment. IEEE Trans. Multimedia 18(6), 978–987 (2016)CrossRefGoogle Scholar
 22.A. Kumar, C. Ravikanth, Personal authentication using finger knuckle surface. IEEE Trans. Inf. Forensics Secur. 4(1), 98–110 (2009)CrossRefGoogle Scholar
 23.K. Usha, M. Ezhilarasan. Hybrid Detection of Convex Curves for Biometric Authentication Using Tangents and Secants. The 3rd IEEE International Advanced Computer Conference, Ghaziabad, India, February 22–23, 2013:763–768. Adv. Comput. Conf., 2013 , 7903 (5) :763–768Google Scholar
 24.K. Usha, M. Ezhilarasan, Finger knuckle biometrics–a review. Comput. Electr. Eng. 45(C), 249–259 (2014)Google Scholar
 25.H.C. Huanga, C.T. Hsiehb, M.N. Hsiao b, C.H. Yehb, A study of automatic separation and recognition for overlapped fingerprints. Appl. Soft Comput. 71, 127–140 (2018)CrossRefGoogle Scholar
 26.K. Usha, M. Ezhilarasan, Fusion of geometric and texture features for finger knuckle surface recognition. Alex. Eng. J. 55(1), 683–697 (2016)CrossRefGoogle Scholar
 27.K. Usha, M. Ezhilarasan, Robust personal authentication using finger knuckle geometric and texture features. Ain Shams Eng. J. (2016) In pressGoogle Scholar
 28.Z. Lin, L. Zhang, D. Zhang, H. Zhu, Online fingerknuckleprint verification for personal authentication. Pattern Recogn. 43, 2560–2571 (2010)CrossRefGoogle Scholar
 29.G. Gao, L. Zhang, J. Yang, L. Zhang, D. Zhang, Reconstruction based fingerknuckleprint verification with score level adaptive binary fusion. IEEE Trans. Image Process. 22(12), 5050–5062 (2013)MathSciNetCrossRefGoogle Scholar
 30.A. Kumar, Z. Xu, Personal identification using minor knuckle patterns from palm dorsal surface. IEEE Trans. Inf. Forensics Secur. 11(10), 2338–2348 (2016)CrossRefGoogle Scholar
 31.S. Yang, L. Gong, Excursion characteristic learning and recognition for hand image knuckles based on log Gaussian Cox field. Trans. Chin. Soc. Agric. Machinery 48(1), 353–360 (2017)Google Scholar
 32.Stanley Sawyer. Wishart Distribution and InverseWishart Sampling. Washington University. 2007, Technical ReportGoogle Scholar
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