RETRACTED ARTICLE: Complex image recognition algorithm based on immune random forest model

Abstract

With the continuous advancement of science and technology, the social network based on the Internet has gradually penetrated into people’s daily lives. The image data shared on social media using platforms such as mobile phones has exploded, and hundreds of millions of dollars are generated every day with picture information. In the past, the traditional ways of expressing textual information that people are familiar with have begun to be gradually replaced by image information that is not subject to regional culture such as language and script. In modern warfare, with the continuous development and equipment of highly sophisticated weapons and equipment, the amount of information that the entire combat system needs to process will also increase. In particular, the air defense system needs to quickly and accurately identify the aircraft targets that are coming. It mainly uses computer to extract the feature information of the acquired image and converts the content in the image into a feature expression that can be processed by the computer. After the appropriate classification algorithm, the image is the target object is classified by category. In this paper, we propose a complex image recognition algorithm based on immune random forest model. The experimental results show that the proposed algorithm has high recognition efficiency and higher robustness.

1 Introduction

With the rapid development of science and technology, big data and artificial intelligence have promoted the increasing renewal of Internet technology, and at the same time brought about the rapid growth of information. How to extract valuable information from massive databases has become the key to the development of modern technology problem. Classification technology is a very important research topic in the field of data mining. The decision tree algorithm is a typical single classifier in the classification algorithm. It is widely used in the fields of classification and prediction because of its easy-to-understand theory, simple structure and good classification effect. As the classification problems that need to be dealt with in real life become more and more complex, the performance requirements of classification algorithms in various fields are gradually improved. As the most basic single classifier, decision trees still have many limitations in dealing with continuous data and avoiding algorithm over-fitting. In such an environment, a multi-classifier algorithm based on a decision tree is used to generate a random forest (Patel et al. 2016; Hassan et al. 2015; Oshiro et al. 2012).

Manual analysis has not been able to meet the demand for processing massive remote sensing data, because the period of manual analysis is longer and subjective. In order to realize automatic processing of remote sensing information, the development of artificial intelligence algorithms has greatly helped remote sensing image processing. Many algorithms in the field of artificial intelligence are imitating the characteristics of humans or creatures. They have great similarities with manual analysis. They are all learning data, discovering laws, then combining knowledge reasoning, and finally classifying new data. Information production is a comprehensive analysis process from the table to the inside. The artificial immune system mimics the biological immune mechanism and is successfully applied to optimization problems. Random forest is an important integrated learning algorithm, which is widely used in remote sensing images because of its advantages for small samples and strong stability (Peng et al. 2013; Rodriguez-Galiano et al. 2012a, b; Ghimire et al. 2010).

Because the random forest algorithm has good anti-noise ability and outlier tolerance, and the random forest algorithm does not need the prior knowledge of the classification sample, it simplifies the related work of data preprocessing (Ghimire et al. 2010). Although the random forest algorithm performs well in many aspects, there are still some imperfections. For example, the random forest algorithm randomly filters from the data set during feature selection, and the parameters of the random forest algorithm are artificially set (Naidoo et al. 2012). These operations will be invisible, increasing the error of the classification results. From the practical application point of view, it is necessary to further enhance the ability of random forest algorithm to extract high-quality features and optimize parameter selection, thereby further reducing the generalization error of random forest model and improving the classification accuracy of random forest algorithm. At present, how to extract useful feature information or rules from high-dimensional data and how to construct an optimal feature selection algorithm to improve the prediction and classification effect of classification and regression algorithms have become a popular research direction for scholars at home and abroad.

Deep learning utilizes multiple nonlinear layers in a deep neural network to extract different features in the target image and express the original image using abstract semantic concepts. The use of deep learning to extract and classify the target in the image can realize the automation of image feature extraction and classification recognition (Pierce et al. 2012). It eliminates the traditional method of labeling image features in the traditional image recognition process, which greatly improves the recognition speed and recognition accuracy. The application of deep learning to image recognition, especially in aircraft target recognition, enables the air defense system to quickly determine the target category of the acquired aircraft image and automatically take countermeasures, which greatly saves the reaction time of the system and reduces the overall combat (Zou et al. 2010). The amount of information the system needs to process. Therefore, in-depth study of deep learning techniques and its application to image recognition greatly improve the recognition rate and accuracy of image target objects (Jaderberg et al. 2014).

Aiming at the insufficiency of the efficiency of integrated learning, this paper focuses on the analysis of random forest classifiers and proposes a random forest algorithm based on spectral clustering (Lecun et al. 2014). The main idea of the algorithm is as follows: Through the good clustering performance of the spectral clustering technique, the original samples are preliminarily divided, and multiple samples with similar positions are clustered into clusters, and a random sample in the cluster is used to represent all the clusters. The training samples participate in the final classification training, thereby greatly reducing the number of training samples. Since the samples in the cluster are close to each other and have strong similarity, the randomly selected samples in the cluster can effectively represent the original samples in the cluster to participate in the training. The algorithm in this paper can achieve higher classification accuracy with higher running efficiency.

In summary, the vast number of scholars at home and abroad has made significant improvements to the random forest algorithm, but the random forest algorithm itself still has imperfections. Therefore, how to give full play to the excellent performance of the random forest algorithm, improve the limitations of the random forest algorithm, and make it have in-depth research and application value in many fields such as data mining, is still the hot spot of future research.

The random forest is an integrated learning algorithm based on CART decision tree proposed by Breiman of the American Academy of Sciences. Random forest is a nonparametric pattern recognition classification method that can be applied to most data classifications without prior knowledge or assumption of data distribution. This is also the key to better than traditional statistical learning methods. Maximum likelihood often assumes that the data is in a normal distribution, or that the professional knows the distribution of the data beforehand. There are no complicated parameter adjustments in random forests. In the past ten years, there have been a wide range of applications in remote sensing image classification, such as land classification and ecological region classification of remote sensing images, and analysis of tree species. Pierce first extracts different features of canopy and uses random forests to warn forest fires, reducing the difficulty of fire protection. Random forests are also used to detect bare carbon resources and analysis of urban areas. Random forests are also used for the classification of hyperspectral remote sensing images. The random selection of random forest algorithm features makes it more suitable for processing high-dimensional data, which is more efficient and less sensitive to small sample data. The sample variable dimension is larger than the sample. In the case of the number, there is also a good classification effect (Bala et al. 2019).

Hence, to effectively present the proposed methodology, this paper is organized as follows. In Sect. 2, the immune random forest model is presented. In Sect. 3, the complex image recognition technology is presented. In Sect. 4, the experiment is conduct, and finally in Sect. 5, the conclusion is done.

2 Immune random forest algorithm

2.1 Decision tree classification

Random Forest (RF) is a typical multi-classifier algorithm. The base classifier that constitutes the random forest algorithm is the decision tree. The essence of the decision tree is actually a tree composed of multiple judgment nodes. The basic principle of the random forest algorithm is to use the resampling technique to form a new training set by randomly extracting samples and then use the autonomous data set to model the decision tree and form a random forest, and the classification result is used for voting decision. This chapter starts from the basic forest classifier decision tree of random forest and briefly introduces the performance and shortcomings of the decision tree algorithm and then introduces the basic principles, construction process and performance indicators of random forest, so as to understand the formation of random forest algorithm more deeply process (Bhowmik and Ray 2019).

Since the advent of random forest technology, it has been widely used in many areas of intelligence. The outstanding advantages of random forest are as follows: (1) it can effectively avoid over-fitting; (2) it has good anti-noise ability; (3) it has good nonlinear data fitting ability; (4) the algorithm has good comprehensibility; (5) the importance of the feature attributes can be accurately judged (Merigó et al. 2019).

The decision tree is composed of a root node, an intermediate node and a leaf node. Each non-leaf node selects the optimal attribute in the attribute set as the split attribute of the node according to the attribute selection criterion, and then recursively according to different values of the split attribute. The branch of the next layer of the node is established until the node meets a certain stop split criterion, and this node is the leaf node of the decision tree. Each internal node has several branches down, which means that each internal node stores several splitting criteria, and the leaf nodes store only the category information predicted by the decision tree (Zhu et al. 2019).

A general description of the decision tree construction is given below:

• 1. First construct the root node of the decision tree from the empty tree and the original training set (each node has a one-to-one correspondence with the sample set).

• 2. If the class attribute of the sample set of the node is of the same class or meets some stop splitting criterion, the node is defined as a leaf node, and category information is added to the leaf node.

• 3. Select the attribute with the highest value as the split attribute of the node, and store the split attribute and the split criterion in the node (Chen et al. 2018).

• 4. Recursive split subnodes, repeat steps 2–3 until there are no nodes that can be split.

After generating the decision tree, the main task is to use the decision tree to classify the unclassified data samples. The decision tree is represented by t, and the prediction of the sample data x by the decision tree t is a path-finding process from the root node to the leaf node. Taking the binary decision tree as an example, the prediction function can be expressed as follows:

$$ h(x|N(\psi ,t_{1} ,t_{r} )) = \left\{ \begin{aligned} h(x|t_{1} ) \hfill \\ h(x|t_{r} ) \hfill \\ \end{aligned} \right. $$

(1)

$$ h(x|L(\pi ) = \pi $$

(2)

where $\psi (x)$ is the splitting function (split criterion) of the decision tree node, which determines whether the sample data selects the right or left sub-decision tree at the node. Starting from the root node, up to the leaf node, and giving the data x the category $\pi$, and $\pi$ is the category information of the leaf node (Song et al. 2019).

An important concept of decision trees is the measure of attribute value, which is the basis for distinguishing different decision trees. The core link of decision tree generation is that when each decision tree node is constructed, it should be selected as the split attribute of the node, which determines the direction and structure of the decision tree. If a measure of attribute value is selected, each decision tree can recursively select the highest value attribute from top to bottom. According to different metrics, it can be divided into different decision trees. For example, the classic ID3 algorithm proposed by Quinlan in 1986 is based on the information entropy theory, and the maximum information entropy gain is used as the attribute value measurement criterion. The C4.5 algorithm is developed after inheriting the ID3 algorithm. It is based on the information entropy gain rate. The advantage of this criterion relative to the information entropy gain of ID3 is that the ID3 is modified to choose more attribute values when selecting attributes. Attributes. Another decision tree is the CART Tree (Classification and Regression Trees), which is based on the Gini coefficient (Zhang et al. 2019).

The C4.5 algorithm optimizes the ID3 algorithm, and the C4.5 algorithm uses the gain ratio to improve the inadequacies of ID3. First, the C4.5 algorithm defines a “split information metric” whose definition can be expressed as:

$$ {\text{split}} = - \sum\limits_{j = 1}^{v} {\frac{{|D_{j} |}}{|D|}\log_{2} } \frac{{|D_{j} |}}{|D|} $$

(3)

The meaning of each symbol in the C4.5 formula is the same as the ID3 algorithm, so the information gain rate is defined as:

$$ {\text{gain\_ratio}}(A) = \frac{{{\text{gain}}(A)}}{{{\text{split}}(A)}} $$

(4)

C4.5 uses the information gain rate to select features, which avoids the problem that the ID3 algorithm uses information gain biased to select more feature values. Although C4.5 has optimized some of the limitations of the ID3 algorithm, there is still room for improvement. For example, C4.5 generates a multi-fork tree, but the binary tree model in the computer is more efficient. In addition, the C4.5 algorithm can only be used for classification and cannot be used for regression; the internal computation principle of the C4.5 algorithm is time consuming and the accuracy needs to be improved. The CART classification tree algorithm is a further optimization of the C4.5 algorithm. The Gini coefficient is used for feature selection. The Gini coefficient represents the impureness of the model. That is to say, the smaller the Gini coefficient, the lower the purity, and the better the feature. This is the opposite of the information gain (ratio) (Li et al. 2019).

According to the research on decision tree, the following problems can be summarized:

• 1. Continuous variables need to be divided into discrete variables. Decision trees cannot handle continuous variables and need to be discretized to convert continuous variables into discrete variables.

• 2. The classification rules are complex. Decision trees are greedy algorithms. Each time you select only one attribute to build a tree, you will generate a very large number of classification rules (Singh et al. 2019).

• 3. Over-fitting, if the model complexity is too high, and the training data is less, the problem of over-fitting may occur.

2.2 Spectral clustering algorithm

The spectral clustering algorithm is based on the spectral theory. Compared with the traditional clustering algorithm, it has the advantage of being able to cluster on the sample space of arbitrary shape and converge to the global optimal solution. Spectral clustering algorithms were originally used in computer vision, VLSI design, etc., and have only recently begun to be used in machine learning, and have quickly become a research hotspot in the field of machine learning in the world. The spectral clustering algorithm is based on the spectral theory in graph theory. Its essence is to transform the clustering problem into the optimal partitioning problem of graphs. It is a point-to-point clustering algorithm and has a good application to data clustering. prospect.

The spectral clustering algorithm treats each object in the dataset as the vertex V of the graph, and the similarity between the vertices as the weight of the corresponding vertex join edge E, thus obtaining a similarity-based undirected weighted graph G (V, E); then the clustering problem can be transformed into the partitioning problem of the graph. The optimal partitioning criterion based on graph theory is to maximize the internal similarity of subgraphs and minimize the similarity between subgraphs. That is, the sum of the weights of the edges that need to be cut when dividing the subgraph is as small as possible. Usually, the sum of the weights of the edges to be cut off is defined as the segmentation loss. The goal of spectral clustering is to minimize the above-mentioned segmentation loss, so as to obtain an optimal graph decomposition scheme, and then obtain the corresponding clustering results. In order to obtain a more balanced and reasonable clustering result, various deformations can be performed on the above-mentioned dicing loss function, so that a series of spectral clustering algorithms can be derived, such as ratio spectrum clustering algorithm, regular spectrum clustering algorithm and minimum maximum segmentation algorithm (Nielsen et al. 2019).

Since the samples in the cluster are close to each other and have strong similarity, the randomly selected samples in the cluster can effectively represent the original samples in the cluster to participate in the training. The random forest algorithm based on spectral clustering proposed in this paper can achieve higher classification accuracy with higher running efficiency. Due to the reduced number of training samples, the random forest algorithm proposed in this paper is more efficient than the traditional random forest algorithm in terms of operational efficiency.

The integrated learning idea combines many algorithms that are applicable to different scopes and have different functions, and concentrates various excellent performances to solve a complex task. That is to say, the algorithm with “collective intelligence” can satisfy both complex task requirements and performance better than a single algorithm. Therefore, the integrated classification model often has a good classification effect and is highly generalized (Sun 2019).

For the classification problem, the integrated classifier can be composed of many base classifiers, and the space size is assumed to be H. Assuming each base classifier is h, let each input space X pass through learning and output a class label corresponding in space H. The mapping function of Y. The general representation of the integrated classifier is as follows:

$$ f \in C:\left\{ {f: \to \sum\limits_{h \in H} {a_{h} h(x)|a_{h} \ge 0} } \right\} $$

(5)

The Boosting algorithm is basically similar to the Bagging algorithm. It assigns the same weight initialization to each training sample, such as averaging, and then iterates multiple times for each sample training set. Each time, a learning model is generated. The weights of the training samples of the weaker learning algorithms are assigned to larger values. The purpose is to promote multiple weak learning models into strong learning models, and finally generate m prediction functions, and each m will have a weight, and the prediction effect is good. The weight of the function will be larger (Ping et al. 2019).

2.3 Mathematical model analysis of random forest

The basic unit of random forest is the decision tree, and its essence is actually the integrated learning method. In the classification problem, for an input data set, n decision trees will produce n classification results. The random forest algorithm integrates all the classified voting results, and the most polled results are the final classification results. It is not difficult to see from the name of the random forest that the random forest mainly contains two keywords, one is “random” and the other is “forest”. “Forest” is well understood by literal meaning. A tree called a tree, then a combination of hundreds of trees can be called a forest (Agarwal and Srivastava 2019). The RF algorithm is performed by multiple decision tree classifiers in parallel and simultaneously processing corresponding sample subsets. First, the RF algorithm filters the features through the node splitting of the decision tree and subdivides the samples layer by layer until the training subset of each training sample is correctly classified, and the speed is slow. Then, the RF algorithm directly classifies the samples based on the trained features. At this time, the speed is faster, and the overall process is somewhat a “foolish” strategy. It can be seen from the construction process of the RF algorithm that the randomness of the RF algorithm is mainly reflected in the randomness of the sample and the randomness of the selection of the node splitting properties. With these two random guarantees, the RF algorithm will not over-fitting. It can be seen that in order to make the forest composed of multiple decision trees effectively avoid the limitations of over-fitting and local optimization, it is necessary to reflect the randomness of the algorithm at all times.

Over-fitting means that a classification model containing several unknown parameters can be used to obtain the parameters of the training sample well by the optimization algorithm, but when other verification data sets are independently extracted from the same data set as the training samples, it will be found at this time. The classification model does not fit well with the randomly extracted validation data. The random forest introduces a margin function that allows quantitative analysis of random forests. It is assumed that the training set is obtained by randomly and randomly sampling the X, Y vectors of the unknown distribution, and is represented by {(x, y)}. The marginal function of the sample (x, y) is expressed as follows:

$$ mg(x,y) = av_{K} I(f_{K} (x) = y) - \mathop {\hbox{max} }\limits_{j \ne y} av_{K} I(f_{K} (x) = j) $$

(6)

where I is an indicative function, taking the random forest classifier as an example. The category information of the random forest is obtained by voting. The most voting is the final category, and the marginal value indicates the vote between the true category and the other categories. The difference also reflects a measure of the confidence of the random forest.

Out-of-bag data (OOB) in random forests is an important concept and a criterion for random forest generalization ability evaluation. As mentioned above, the training samples of each base classifier of the random forest are obtained according to the Bagging resampling method, and the random resampling refers to the random sampling that is put back on the original training set, and each time it is not sample data which is called extra-bag data (OOB).

Since the training data of each decision tree is randomly and independently extracted, the out-of-bag data and the in-band data (decision tree training data) are all distributed, so the decision tree trained by the data in the bag is out of the bag. It is reasonable to verify the generalization error (Zhang et al. 2018).

Random forest is an integrated algorithm of decision trees, which has stronger generalization ability than single decision tree. Some of the advantages of random forests for remote sensing image information processing are given below:

• 1. The increase in random forest size does not overfit.

• 2. It also has good generalization ability under small sample data.

• 3. Has good anti-noise ability and is very tolerant for a certain amount of data loss.

• 4. Tolerate loss of values for some features in the data set.

• 5. Decision trees can be parallelized, and random forest algorithms are relatively efficient (Alshafai et al. 2019).

When the feature dimension is relatively small, such as a TM image, the feature space selected by each decision tree is very limited. In this way, the decision tree node has a higher probability of selecting the same attribute, which increases the similarity of the decision tree and has a greater correlation, which will affect the classification accuracy of the forest. If the information of the combined features can be mined, the degree of correlation between the decision trees can be reduced, and the random forest can show greater advantages in feature selection. Increasing the size of random forests can increase generalization ability and stability, but it also increases the storage capacity of random forests, and the classification prediction speed is significantly reduced, especially for high-resolution remote sensing image classification. Selecting a more effective combination in the integration to reduce the size of the forest without compromising the generalization ability of the forest, selective integration learning algorithms have important research significance (Qi et al. 2019).

As a machine learning method, if the training sample does not represent the distribution of the total set well, the classifier thus trained will also be affected. The training samples in remote sensing images are manually selected and subjective, while semi-supervised learning ideas can use the information of unlabeled categories to reduce the impact of subjectivity of training samples.

2.4 Image feature distribution transfer analysis

Migration learning is mainly used to reduce the distribution difference between the clear image domain and the blurred image domain, so in this section we will analyze how the blur leads to the transfer of the feature distribution between the two domains. We assume that the user can collect a lot of clear images with labels (source domain) and some unlabeled blurred images (target domains), which have the same object class and are in the same feature space, and both have Fixed but unknown feature distribution (Muneeswari and Manikandan 2019).

Blurring changes the visual characteristics of clear images, so that their texture and edge information are greatly affected, but many of the known descriptors are extracted based on texture and edges, so the blurring of these feature spaces will cause two domains to be generated. The feature distribution is shown in Fig. 1. Since the general classification task assumes that the training set and the test set satisfy the same distribution, if we still use the existing clear image to train the classifier without considering the influence of the distribution transfer, then the recognition rate of the test set in these feature spaces will be Significant decline (Jiao et al. 2019) (Fig. 2).

Fig. 1

Schematic diagram of the effect of fuzzy on feature distribution transfer

Fig. 2

Fuzzy image recognition framework based on subspace alignment

We consider two cases, one is that the fuzzy domain is a single fuzzy type, and the other is that the fuzzy domain has multiple ambiguities. In the first case, the target domain is blurred by the same fuzzy type, including Gaussian blurs with standard deviations of 3 and 5, motion blurs with horizontal offsets of 8 and 10, and dispersions with radii of 2 and 3. Defocused. At this point, the ROD values between the two domains are shown in the following table (Table 1).

Table 1 ROD measure value of different feature spaces in single fuzzy case

We can see that the increase in the degree of blurring does increase the ROD measure between the two domains. When there is no blur, the difference between the two domains in the different feature spaces is the smallest. When the target domain is obtained by a variety of fuzzy types, in our experiment, each image in the target domain is randomly obtained from the above six fuzzy kernel ambiguities. The experimental results are shown in Table 2.

Table 2 ROD measure value of different feature spaces in multiple fuzzy cases

We can see that the difference between the two domains increases when the blurred image domain is in multiple fuzzy types compared to the case without blur. In summary, the blur does cause the clear image domain and the blurred image domain to bring about the feature distribution shift.

Since the samples of the clear image domain and the blurred image domain need to be mapped into the respective new subspaces, the selection of the subspace dimension d has an important role, and is also the only parameter that can be adjusted by the method.

In order to illustrate the influence of subspace dimension d selection on feature recognition, this paper conducts experiments on face datasets, in which 4 clear face images in each class are used as training sets, and the remaining images are subjected to Gaussian blurring. Test set. The experiment used the LPQ visual descriptor, and the selected Gaussian fuzzy kernel scale was 7, with a standard deviation of 3. We select the dimensions of different subspaces and get the recognition performance of the visual descriptors when we get different subspace dimensions, as shown in the following figure (Fig. 3).

Fig. 3

The effect of subspace dimension on descriptor recognition rate

As can be seen from the figure, the subspace dimension has little change in recognition performance in the range of 50–150, but its recognition rate drops significantly in other dimensions. Therefore, choosing the appropriate subspace dimension has a great influence on the recognition rate after migration learning.

2.5 Image processing step details

Image processing refers to the processing of the image to be recognized by the computer, which satisfies the subsequent needs of the recognition process, and is mainly divided into two steps of image preprocessing and image segmentation. Image preprocessing mainly includes image restoration and image transformation. Its main purpose is to remove interference and noise in the image, enhance useful information in the image, and improve the detectability of the target object. At the same time, due to the real-time requirements of image processing, Re-encoding and compressing images reduces the complexity and computational efficiency of subsequent algorithms. Image segmentation is the process of dividing the image to be identified into several sub-regions, the features of each region have obvious differences, and the internal features of each region have certain similarities. Existing image segmentation methods mainly include methods based on edge segmentation, threshold segmentation, and region segmentation.

The method based on edge segmentation is to segment the image by detecting a region where the gray value of the pixel in the image is abrupt, or where the texture structure suddenly changes. The edge is usually located between two different areas. Since the gray values of different areas are different in one image, there will be obvious gray discontinuity at the joint of the two areas. Since the gray values of the pixels at the edges are not continuously distributed, differential or second-order differential can be used for detection. For the first-order differentiation of the gray value of each pixel distributed in the edge region, the pixel corresponding to the place where the extreme value appears is the edge point of the image, and the gray value of each pixel distributed in the edge region. To find the second-order differential, the pixel point where the differential value is zero is also the edge point of the image. Therefore, edge detection of an image can be performed by a differential operator method.

The Roberts differential detection operator is a method for finding the edge of an image by using local difference. The basic principle is that any pair of differences in the mutual vertical direction can be regarded as the approximation of the gradient. In practice, the diagonal direction is often used. The difference between the two-pixel values approximately replaces the gradient value. The specific calculation formula is as follows:

$$ g(x,y) = \left\{ {[f(x + 1,y + 1) - f(x,y)]^{2} + [f(x + 1,y) - f(x,y + 1)^{2} ]} \right\}^{{\frac{1}{2}}} $$

(7)

where (x, y) is a point in the image, f(x, y) is the input image, and g(x, y) is the output image. Since the calculation of the square and square roots requires a large amount of calculation, an absolute value is usually used instead.

By setting a threshold TH, if the value of g(x, y) is greater than TH, the corresponding pixel point (x, y) is considered to be a step edge point. Since the Roberts differential detection operator uses an even number of templates, the gradient magnitude value at (x, y) is actually the value at the intersection shown in the following figure, which is offset from the real position by half. pixel. Therefore, the method produces a wider response near the edges of the image, and the positioning accuracy of the edges is not high (Fig. 4).

Fig. 4

Schematic diagram of the Roberts operator algorithm

The main principle of the threshold segmentation method is image segmentation based on the difference in grayscale features between respective target regions in the image. Since there is a significant difference in gradation characteristics between the target area to be extracted in the image and other background areas, a threshold value may be set and compared with the gray value of each pixel in the image to determine the pixel point. Image threshold segmentation is a traditional image segmentation method. It has the characteristics of simple implementation, small amount of computation and stable performance of image segmentation. Therefore, it has become a widely used technology in the field of image segmentation.

The region segmentation method can be divided into two methods: regional growth method and split combination method. The principle of the region growing method is to combine pixel points with the same or similar properties to form a region. First, find an initial pixel point as a seed in each segmentation region, and compare the feature points of the seed pixel point with the surrounding adjacent pixel point set. Pixels having the same or similar feature attributes are merged with the set of seed pixel points, and the merged new set of pixel points is treated as a seed to repeat the above process until a pixel point of similar feature attributes is not found. Therefore, the focus of the regional growth method is to select appropriate seed points, set appropriate set rules, and determine termination conditions. The principle of splitting and merging method is to first determine the threshold value of image area feature consistency detection, then divide any area in the image, and perform feature consistency detection between the area and adjacent areas, respectively, firstly perform intra-area feature consistency detection. If the features in the region are inconsistent, the region is split into four equal sub-regions. When the splitting is impossible to continue sub-dividing, it is found whether the adjacent regions meet the feature consistency detection, and if the adjacent regions satisfy the feature in the case of consistency detection, the adjacent area is merged into one large area until all the areas no longer satisfy the merge condition. The region growing method saves the process of splitting than the split-merging method, and the split-merging method can perform feature determination and region merging in a larger area.

3 The proposed complex image recognition framework

3.1 Research on measurement learning technology

There are many ways to reduce the degree, mainly including unsupervised and supervised methods. Principal component analysis is one of the most commonly used unsupervised linear dimensionality reduction methods that does not require label information for known samples. It maps the original high-dimensional data into the low-dimensional space through a linear projection mechanism, so that the variance of the data after projection is maximized, so that the data can retain as much information as possible of the original data points in less dimension. LDA (Linear Discriminant Analysis) is a classic supervised method for reducing dimensions. The method considers the label information of the sample and projects the original high-dimensional vector into an optimal low-dimensional space, so that the sample is classed in the low-dimensional subspace. The distance between the two is the largest and the distance within the class is the smallest, which achieves both good classification information and the effect of compressing the feature dimension. However, the dimensionality of the method after dimension reduction is related to the number of categories of data and has nothing to do with the original dimension of the sample. This feature limits the applicability of the method.

The common measure learning method has two main functions. One is to learn a suitable measure for some machine learning algorithms such as K-means clustering and nearest neighbor classifier, so that the data can be more easily classified or clustered under the measure. The measure of similarity between samples in these algorithms severely affects the performance of these learning algorithms.

The purpose of the LMDR measure learning method is to learn a mapping matrix M ∈ R^p×D(p ≪ D) such that the mapping matrix ensures that the distance between images of the same category is smaller, and the distance between images of different classes is larger. Therefore, this can make full use of the category information of the clear domain image and generate a clear domain subspace in a supervised manner, so that the mapped data has less redundant information and has stronger classification ability.

If the image pair is of a different category, the inner product is less than the threshold, i.e. M needs to satisfy the following constraints:

$$ y_{i,j} ( < M\varPhi_{i} ,M\varPhi_{j} > - b) > 1 $$

(8)

$$ y_{i,j} { = }1 $$

(9)

To get the optimal M, we can convert the above constraint into an objective function in the form of hinge loss:

$$ \mathop {\text{arg min}}\limits_{M,b} \sum\limits_{i,j} {\hbox{max} [1 - y_{i,j} ( < M\varPhi_{i} ,M\varPhi_{j} > - b),0]} $$

(10)

The idea of the subspace dimension selection method based on cross-validation is to use the clear image training set to select the appropriate parameters, i.e. the dimensions of the two subspaces. We divide the clear domain image data into two parts, one part as the source domain and the other part to be fuzzy to establish the target domain of the simulation. The simulated target domain image is obtained by using four Gaussian fuzzy kernels, six motion blur kernels and three defocus fuzzy kernel ambiguities to balance the effects of various types of fuzzy types in the actual test set. The source domain subspace dimension p is selected according to the variance of the covariance matrix that needs to be preserved in PCA-Whiten, and the target domain subspace dimension d is selected according to the variance of the covariance matrix to be retained in the PCA. In each dimension combination, we use a double cross-validation to get an average classification accuracy.

3.2 Selection of complex image subspace dimensions based on ROD measure

Matrix low-rank decomposition refers to the decomposition of the original matrix into a sum of a low-rank matrix and a matrix with sparse properties. Low-rank decomposition techniques have been widely used at this stage. For example, in the field of video surveillance, this method can achieve target detection in complex backgrounds, and in the field of face recognition, the method can remove the effects of shadows and highlights. The most common low-rank decomposition method is Robust PCA, which differs from the classical PCA algorithm in that it does not have dimensionality reduction. Classical principal component analysis is widely used for data analysis and dimensional reduction, but it is greatly constrained by the vulnerability to heavily polluted data. The blurred image can be regarded as the convolution of the clear image and the fuzzy kernel. We hope to obtain the recognition part from the clear image and the blurred image for subsequent migration learning, so as to improve the recognition ability of the descriptor. The low-rank decomposition can perform a good decomposition process on the image with noise perturbation, so that the most recognizable part and the part common to the image are obtained from a large number of images.

The low-rank decomposition can be solved in the following way, assuming that a contaminated image feature matrix is M₀, we can decompose it into L₀ and S₀:

$$ M_{0} = L_{0} + S_{0} $$

(11)

where L₀ and S₀ are both unknown, and L₀ is a low-rank term and S₀ is a sparse term. We can think of the process of solving L₀ and S₀ as optimizing the following equation:

$$ \min_{L,S} {\text{rank}}(L) + \gamma ||S||_{0} $$

(12)

In many applications, the low-rank components derived from decomposition are mostly used for experimental purposes, and it is desirable to eliminate the effects of noise or disturbance by low-rank decomposition. In this paper, since the blur is global, the low-rank component contains many fuzzy components. However, in the recognition problem, the low-rank component does not have strong recognition ability, so this paper uses the sparse component obtained by decomposition to carry out subsequent experiments.

The sparse matrix obtained by different γ values has a great influence on the recognition rate. Therefore, we propose to set multiple values of γ in the algorithm to obtain the matrix S with different sparsity degrees and use the average value to balance the effects of different degrees of ambiguity. Finally, the part with strong recognition ability is obtained.

In order to more intuitively illustrate the effectiveness of sparse components in low-rank decomposition, we performed low-rank decomposition experiments on clear face data sets and Gaussian fuzzy face data sets, respectively, which contain 14 types of face images. By setting different gamma values, we can get different degrees of low-rank component L and sparse component S. The lower the image is from left to right (Fig. 5).

Fig. 5

Low-rank and sparse matrices obtained by different levels of low-rank decomposition of the same face image in clear and fuzzy situations

It can be seen that the low-rank component is quite different from the original image, but the sparse component can well express the identifiable information of the original image. The information retained in the sparse components of different gamma values is also different, and the clear faces of the human face and the fuzzy face have similarities. Therefore, this paper performs integrated low-rank decomposition, using the average of different sparse components to make full use of the results of different degrees of decomposition.

To illustrate the identifiable nature of sparse components of low-rank decomposition, we also apply robust PCA on different human faces. We can get L and S for different faces by taking the same gamma value (Fig. 6).

Fig. 6

Low-rank decomposition results of different fuzzy faces

4 Experiment and analysis

4.1 Experiment 1

The following experiments verify the improved feature combination random forest algorithm. The experimental hardware platform is Intel Core I7 CPU 3.0 GHz 16G memory, and the software platform is MATLAB 2014b. In the improved random forest verification experiment, the UCI public data set was first selected for verification, and then the algorithm was applied to the complex image.

In the experiment, the public dataset in UCI was selected. The eight datasets of the experiment are shown in the following table (Table 3):

Table 3 UCI data set

The first three integrated algorithms (CRFC_RF, Forest_RC, and Bagging) randomly select 15% of the sample data as a training sample for each integration build. 15% of the verification data was not used. The training samples of the same size as the selective random forest were selected, and 70% of the remaining total samples were used as test data to test the generalization error of the forest. Repeat the above process 100 times, that is, generate 100 forests, and take the average generalization error as the experimental error result. In the random forest algorithm, the CART decision tree is used as the base classifier. The decision tree grows completely without pruning, and the size of the forest is set to 100 (Table 4).

Table 4 Classification error rate of classification algorithm on dataset

The superiority of the integrated algorithm can be seen. After the Bagging algorithm uses sample resampling, the accuracy is greatly improved compared to a single decision tree, and the average generalization error is reduced by 6%. The combination of random forests (Forest-RC) and the Bagging increased the characteristics of random sampling and combined, the generalization error increased by about 2% relative to Bagging. Compared with the improved algorithm (CRFC_RF) and Forest_RC, the accuracy improvement is not very large. Except for the first data set with a small precision drop, the other data sets increase by about 0.5% on average. This also verifies the effectiveness of increasing the randomness of decision trees in reducing random forest generalization errors.

4.2 Experiment 2

The data set of this experiment also used 10 data sets such as Sonar_lisan, Ionosphere, Glass_lisan and Vehicle_lisan for simulation experiments.

The experiment is mainly divided into two parts. The first part is the performance comparison between the RF and SARFFS algorithms on the optimized particle swarm algorithm. The corresponding parameter combinations under the optimal performance of the algorithm are obtained, and their advantages and disadvantages are analyzed through comparison. In the second part, several common classification algorithms are selected to conduct comparison experiments on the dataset. By evaluating the level of the indicators, the performance difference between the optimal forest and the other classification algorithms is improved by comparing the improved particle swarm optimization algorithm. Prove the stability and versatility of the improved particle swarm optimization algorithm in parameter optimization (Fig. 7).

Fig. 7

Average training accuracy of four algorithms

According to the experimental data, both the RF and SARFFS algorithms of the IPSO optimization have lower Run Time values than the DT and SVM Time values. After IPSO optimization parameter selection, DT’s Time is more. This shows that IPSO has a greater impact on RF and DT algorithms, and RF consumption time has increased. Due to the impact on the effects of the RF and DT algorithms, the final SARFFS Time value optimized by IPSO on both data sets is less. As with PSO, we also optimize the average training accuracy of the four sets of test data on the four algorithms after IPSO optimizes the algorithm parameters, as shown in the following figure (Figs. 8, 9 and 10).

Fig. 8

Evaluation accuracy of four algorithms

Fig. 9

Loss function of the proposed algorithm

Fig. 10

Complex image recognition result

5 Conclusion

The randomness of feature selection in random forests leads to inaccurate calculation of feature attribute weights. At the same time, as the number of iterations increases, the feature selection process leads to the problem of slower execution efficiency. Therefore, a complex image based on immune random forest model is proposed as identification algorithm. The algorithm uses the spectral clustering technique to process the original sample set, which effectively reduces the scale of the training sample and improves the running efficiency of the random forest algorithm. Aiming at the problem that the artificial solution in the random forest parameter selection affects the optimal solution and affects the classification performance, the position calculation formula of the learning factor and the historical optimal shared particle in the particle swarm optimization algorithm is improved. The traditional random forest and SARFFS algorithms are optimized using the improved algorithm. The performance of the improved algorithm is verified by simulation experiments. Finally, the improved particle swarm optimization algorithm optimizes the parameter selection of random forests, so that the random forest algorithm can efficiently learn the optimal parameter combination and improve the performance of the random forest model. Compared with the state-of-the-art approaches, the proposed model is efficient. In the future, we will test the proposed model in more scenarios.