Description Method for image segmentation matching Technical Field The invention relates to a computer implemented method for image segmentation matching in the fields of computer visions and deep learning for autonomous driving. The invention further relates to a processing circuitry configured to run a computer program for image segmentation matching, and a computer readable medium on which a computer program for image segmentation matching is stored. Background As a critical and fundamental technique in vision-based artificial systems, image matching is widely used in many applications, such as object detection, image recognition, image retrieval, vehicle re-identification, place recognition, accurate localization and Simultaneous Localization And Mapping (SLAM). The target of matching task is to solve similarity correspondence problem for contents from image pairs. In traditional image matching methods, the handcrafted local features from the statistics of pixels or gradient information are used. The similarity of features pairs is commonly computed using different predefined metrics, like L2 distance and Cosine distance. More efficient neighborhood information for the statistics may be obtained by computing circular patterns with an adjustable radius. However, these handcraft features are not robust enough to the changes of different viewpoints, illuminations and transformations. Consequently, the matching performance for the methods based on handcraft local features is not stable. Summary of the invention There may be a desire to provide an improved method for image segmentation matching. The problem is solved by the subject-matter of the independent claims. Embodiments are provided by the dependent claims, the following description and the accompanying figures. The described embodiments similarly pertain to the computer implemented method, the processing circuitry, and the computer readable medium. Synergetic effects may arise from different combinations of the embodiments although they might not be described in detail. Further on, it shall be noted that all embodiments of the present invention concerning a method might be carried out with the order of the steps as described, nevertheless this has not to be the only and essential order of the steps of the method. The herein presented methods can be carried out with another order of the disclosed steps without departing from the respective method embodiment, unless explicitly mentioned to the contrary hereinafter. Technical terms are used by their common sense. If a specific meaning is conveyed to certain terms, definitions of terms will be given in the following in the context of which the terms are used. According to a first aspect, a computer implemented method for image segmentation matching of a first segmentation y _k of a first image with a second segmentation x _k of a second image, where the first segmentation y _k and second segmentation x _k are a pair of segmentations, is provided. The method comprises the steps learning joint features and metric of the first segmentation y _k and the second segmentation x _k using joint feature and metric learning, and regulating the joint feature and metric learning using a graph G ^yk containing a global spatial relationship between the first segmentation y _k corresponding to the second segmentation x _k and neighboring segmentations of the first segmentation y _k , and using the second segmentation x _k . The segmentations x _k and y _k are a k-th pair of two images, comprising, for example, the same object or part of an object, therefore x _k corresponds to y _k in this regard. For the regulation, the segmentation x _k of the second image is used and the segmentations of the neighbor segmentations of the corresponding y _k segmentation are used. That is, the neighbor segmentations specified by G ^yk are segmentations of the first image. These neighbor segmentations of the first image and the segmentation x _k of the second mage are input to a regulation network. The first image is also referred to as frame Fy, and the second image also referred to as frame Fx in this disclosure. The k-th pair of segmentations ( x _k , y _k ) may be a randomly sampled pair. For the regulating of the joint feature and metric learning, additionally a graph G ^xk containing a global spatial relationship between the first segmentation y _k corresponding to the second segmentation x _k and a second segmentation x _k may be used. According to an embodiment, the method is executed within a framework, which comprises a basic model for the joint feature and metric learning, a graph-based regularization part for regulating the joint feature and metric learning, and a loss layer. The basic model comprises a first image feature extraction module, a second image feature extraction module and a fully connected neural network. The method further comprises the following steps: Extracting first image features f(y _k ) of the first segmentation y _k by the first image feature extraction module and outputting the extracted first image features f(y _k ) to the fully connected neural network. Extracting second image features f(x _k ) of the second segmentation x _k by the second image feature extraction module and outputting the extracted second image features f(y _k ) to the fully connected neural network. Comparing the extracted first image features f(y _k ) and the extracted second image f(x _k ) features and outputting a predicted result to the loss layer (106), by the fully connected neural network, and calculating a total loss ltotal as a sum of the loss lce based on the predicted result and a loss l _reg based on the result of the graph-based regularization part, by the loss layer. According to an embodiment, the graph-based regularization part comprises a third image feature extraction module, a fourth image feature extraction module, a graph attention network, and a discriminator, and the method further comprises the following steps: Extracting third image features f(x _k ) of the second segmentation x _k by the third image feature extraction module and outputting the extracted third image features f(x _k ) to the discriminator. Extracting fourth image features f(y _l ) of neighboring segmentations contained in graph G ^yk of the first image segmentation y _k by the fourth image feature extraction module and outputting the extracted fourth image features f(y _l ) to the graph attention network. Executing attention functions over the fourth image features f(y _l ), in a multi-head module to obtain high dimensional features g(G ^yk ) of the neighboring segments, and outputting the high dimensional features g(G ^yk ) of the neighboring segmentations to the discriminator, by the graph attention network, and comparing the extracted third image features f(x _k ) with the high dimensional features g(G ^yk ) of the neighboring segmentations contained in graph G ^yk in layers of the discriminator and outputting the result L _empirical-ID (x, G ^y ) to the loss layer, by the discriminator. According to an embodiment, additionally the above steps are performed with respect to image features f(y _k ) of the first segmentation y _k and image features f(xl)) of neighboring segmentations contained in graph G ^xk of the second image segmentation x _k , and to compare third image features f(y _k ) of the first segmentation (y _k ) with the high dimensional features g(Gx _k ) of the neighboring segmentations in layers of the discriminator (108) and outputting the result L _empirical-ID (y, G ^x ) to the loss layer, by the discriminator. These steps are: Extracting third image features f(y _k ) of the second segmentation y _k by the third image feature extraction module and outputting the extracted third image features f(y _k ) to the discriminator. Extracting fourth image features f(x _l ) of neighboring segmentations contained in graph G ^xk of the first image segmentation x _k by the fourth image feature extraction module and outputting the extracted fourth image features f(x _l ) to the graph attention network. Executing attention functions over the fourth image features f(xl), in a multi-head module to obtain high dimensional features g(G ^xk ) of the neighboring segments, and outputting the high dimensional features g(G ^xk ) of the neighboring segmentations to the discriminator, by the graph attention network, and comparing the extracted third image features f(y _k ) with the high dimensional features g(G ^xk ) of the neighboring segmentations contained in graph G ^xk in layers of the discriminator and outputting the result L _empirical-ID (y, G ^x ) to the loss layer, by the discriminator. According to an embodiment, the discriminator comprises a bilinear layer with a trainable matrix M. According to an embodiment, the bilinear layer form is given as d(a, b) = σ(a ^τ M b), where σ(·) denotes the sigmoid function, where, a ^τ is a weight vector, and a and b are placeholders for f(x _k ) or f(y _k ), wherein the discriminator computes a loss L _{pair-empirical-ID} according to a discrimination function, which is defined as L _{pair-empirical-ID} = L _empirical-ID (x, G ^y ) + L _empirical-ID (y, G ^x ) = wherein 1{-} is an indicator and denotes a match or mismatch with respect to a kth segmentation pair (x _k , y _k ). According to an embodiment, the loss l _reg is calculated as loss l _reg = - L _{pair-empirical-ID} , by the loss layer. According to an embodiment, a loss function for calculating the loss lce is a cross entropie over pairs of segmentation samples using a ground-truth label and the predicted result from the basic model, and the result obtained from graph-based regularization part, wherein the total loss is the weighted sum of the losses lce and l _reg . According to an embodiment, the loss function l _ce is defined by , wherein k is a k-th pair of segmentation samples, α _k a ground-truth label (, i.e., “1” for matched or “0” for unmatched label), and is a predicted result from the basic model based on a sigmoid function. According to an embodiment, the first image contains a street scene from a first perspective under first environmental conditions and the second image contains a street scene from a second perspective under second environmental conditions. According to an embodiment, the first and the second image segmentations comprise spatial information. The spatial information could get from sensors like radar, LiDAR, stereo camera and depth camera or even from other estimation methods like the monocular depth estimation networks. According to an embodiment, the first, the second, the third, and the fourth image feature extraction modules are one shared network, which serves as feature descriptor function f and extracts the first, second, third and fourth image features as high dimensional features from the respective image segmentations. According to an embodiment, the shared network is a residual neural network, ResNet. According to a further aspect, a computer readable medium is provided on which a computer program for image segmentation matching of a first segmentation of a first image with a second segmentation of a second image is stored. The computer program comprises a basic model module configured to learn joint features and metric of a first segmentation of a first image and a second segmentation of a second image, and a graph-based regularization part configured to regulate the joint feature and metric learning using a graph G ^yk containing a global spatial relationship between the first segmentation y _k corresponding to the second segmentation x _k and neighboring segmentations of the first segmentation y _k ; and using the second segmentation x _k . According to a further aspect, a processing circuitry configured to run a computer program for image segmentation matching of a first segmentation of a first image with a second segmentation of a second image is provided. The computer program comprises a basic model module configured to learn joint features and metric of a first segmentation of a first image and a second segmentation of a second image, and a graph-based regularization part configured to regulate the joint feature and metric learning using a graph G ^yk containing a global spatial relationship between the first segmentation y _k corresponding to the second segmentation x _k and neighboring segmentations of the first segmentation y _k ; and using the second segmentation x _k . The computer program may be part of a further computer program, but it can also be an entire program by itself. For example, the computer program may be used to update an already existing computer program to get to the present invention. The processing circuit may comprise circuits without programmable logics or may be or comprise a processor, a signal processor, a micro controller, a field programmable gate array (FPGA), an ASIC, a Complex Programmable Logic Devices (CPLD), and/or any other programmable logic devices known to person skilled in the art. The computer readable medium may be seen as a storage medium, such as for example, a USB stick, a CD, a DVD, a data storage device, a hard disk, or any other medium on which a computer program as described above can be stored. These and other features, aspects and advantages of the present invention will become better understood with reference to the accompanying figures and the following description. Short Description of the Figures Fig.1 shows a block diagram of an image segmentation matching framework, Fig.2 shows a block diagram of an example of a Graph Attention Network (GAT) block, Fig.3 shows a block diagram of an example of the structure of the image feature extraction module, Fig.4 shows a block diagram of an example of the fully connected neural network, Fig.5 shows a block diagram of an example of the discriminator, Fig.6 shows a flow diagram of the method, Fig.7 shows a flow diagram of further steps of the method, in particular relating to the basic model, Fig.8 shows a flow diagram of further steps of the method, in particular relating to the regulating of the joint feature and metric learning. Detailed Description of Embodiments Corresponding parts are provided with the same reference symbols in all figures. The notation x is used to denote a random sample from the image segmentations and F ^x is used to denote the frame from which x is extracted. The corresponding probability space for x is denoted by where is the sample space of all available segmentations from denotes the collection of all subsets of which is also a σ-algebra, being the probability mass function. The notation G ^x is used to denote the neighborhood graph with respect to x. G ^x is constructed with vertices being the K image segmentations (objects) around x and edges being established within all pairs of the K vertices. In other words, G ^x is a complete graph. E(G ^xk ) (an all-ones matrix) is used to denote the adjacent matrices of G ^xk , which represent the connection relationships between vertices in the corresponding neighborhood graphs. The probability space for random graphs is , where G is the set of all graphs with vertex set S. Given two arbitrary frames F ^x and F ^y , let (x _k , y _k ) be the k-th pair of segmentations random sampled independently from Let G ^xk and G ^yk denote the neighborhood graphs around x _k and y _k respectively. Fig.1 shows block diagram of an image segmentation matching framework 100. The framework 100 consists of two parts 102, 104, which are the basic model 102 for the joint feature and metric learning and the graph-based regularization part 104 for regulating the joint feature and metric learning. These parts are connected to a loss layer 106 that receives the outputs of the said two parts 102, 104 and calculates the loss. In the image segmentation matching framework 100, three types of modules are used, namely a shared image feature extraction module 111, 112, 113, 114 for image feature extraction, for example realized as Resnet, a graph attention network (GAT) 120 for neighborhood graph feature description and a fully connected neural network 116 for feature comparison. The shared image feature extraction module 110 is shown in Fig.1 as separate modules 111, 112, 113, 114, corresponding to its functions in the basic model 102 and the graph-based regularization part 104. The input to the image segmentation matching framework 100 are image segmentations y _k 131 of a first image, image segmentations x _k 132 of a second image, and neighboring image segmentations 133 of the first image, which are specified by neighborhood graphs 134. The image segmentations can be extracted from the full images using well known semantic or instances segmentations methods like DeepLab, Deep Parsing Network and Mask R-CNN. Here, it is assumed that the segmentation can be well obtained. The segmentations of the vertices yl of the neighborhood graphs G ^yk including information about the edges relating to the second image are input to the neighborhood graphs handling network 124. The information about the edges relating to the second image is handled by module 122, which outputs matrix E(G ^xk ). E(G ^xk ) is an all-ones matrix that is used to denote the adjacent matrices of G ^xk representing the connection relationships between vertices in the corresponding neighborhood graphs. Spatial information may be obtained from sensors like radar, LiDAR, stereo camera and depth camera or even from other estimation methods like the monocular depth estimation networks. Here, there are no stringent requirements regarding the accuracy of the spatial information. The graph model is constructed with edges connected between K-nearest neighbors in terms of spatial locations. In the scenarios of street scenes, a depth estimation method with 50 cm, 1 m, 2 m or even more meters accuracy may be sufficient. In the same way, segmentations y _k 131 of the first image, segmentations of the vertices x _l 133 of the neighborhood graphs G ^xk including information about the edges relating to the second image are input to the third image feature extraction module 113 and the neighborhood handling network 124, respectively. For the sake of clarity, this path is not shown in Fig.1, however it is taken into account in the descriptions and equations in the following. The first image and the second image may contain similar contents. For example, they contain the same objects, captured from a different perspective and different ambient conditions such as daytime, seasonal conditions or light conditions. The typical application is a street scene in autonomous driving. The first image feature extraction module 111 extracts the first image features f(y _k ) of the first segmentation y _k and outputs the extracted first image features f(y _k ) to the fully connected neural network 116. The second image feature extraction module 112 extracts the second image features f(x _k ) of the second segmentation x _k and outputs the extracted second image features f(x _k ) also to the fully connected neural network 116. The fully connected neural network 116 compares the extracted first image features f(y _k ) with the extracted second image features f(x _k ) and outputs a predicted result , for example an estimated classification, to the loss layer 106. The loss layer 106 then calculates a total loss ltotal as a sum of the loss lce based on the predicted result from the fully connected neural network 116 and a loss l _reg based on the result of the graph-based regularization part 104. The graph-based regularization part 104 comprises a third image feature extraction module 113 and a neighborhood graphs handling network that extracts features of the neighboring segmentations or vertices {yl}, which are elements of the neighborhood graphs G ^yk using the information about the edges of the graphs G ^yk . Descriptively said, neighborhood graphs handling network 124 including the graph attention (GAT) network 120 emphasizes the relevant neighboring segmentations of segmentation y _k , compares the resulting features with the extracted features of segmentation x _k in the discriminator layer of discriminator 108 and provides the result to the loss layer 106 for regulation. In particular, the graph-based regularization part 104 comprises a fourth image feature extraction module 114, a graph attention network 120, and a discriminator 108. The third image feature extraction module 113 extracts third image features of the second segmentation x _k and outputs the extracted third image features f(x _k ) to the discriminator 108. The fourth image feature extraction module 114 extracts fourth image features f(y _l ) of neighboring segmentations contained in graph G ^yk of the first image segmentation y _k and outputs the extracted fourth image features f(y _l ) to the graph attention network 120. The graph attention network 120 executes attention functions over the fourth image features and provides the output to the multi-head module 128, which are concatenated and averaged by the concatenation module 129 to obtain high dimensional features f(̃yc) of the neighboring segments. The high dimensional features f(̃yc) = g(G ^yk ) of the neighboring segmentations are finally output to the discriminator 108 by the graph attention network 120. The discriminator 108 compares the extracted third image features f(x _k ) with the high dimensional features g(G ^yk ) of the neighboring segmentations contained in graph G ^yk in layers of the discriminator 108 and outputs the result L _empirical-ID (x, G ^y ) to the loss layer 106. The loss layer subtracts L _empirical-ID (x, G ^y ) from the loss lce obtained from the basic model 102 as to regulate the joint feature and metric learning of the basic model 102. Fig.3 shows a block diagram of an example of the structure of the image feature extraction module 110 in more detail. The module 110 is shared by the first, second, third, and fourth image feature extraction module 111, 112, 113, and 114, respectively, which therefore have the same structure. The reference sign 110 is therefore representative for any of the modules 111, 112, 113, and 114. The image feature extraction module 110 may be a Resnet, which comprises, after an input layer, a convolutional layer 301, a max pooling layer 302, several blocks 310 containing convolutional layers 301, and an average pooling layer 304. The structure may differ from the one shown. The Resnet 110 provides residual learning in which the subtraction of features is learnt from the input of that layer by using shortcut connections, that is, directly connecting input of (n)th layer to some (n+x)th layer, which is shown as curved arrow in Fig.3. The residual learning improves the performance of model training, especially when the model is a deep network with more than 20 layers, and also revolves the problem of degrading accuracy in deep networks. The outputs from the Resnet are provided to the fully connected neural network 116, which may be a hidden-layers neural forward network. Fig.4 shows a block diagram of an example of the fully connected neural network 116 within the basic model 102 that receives the output of the Resnets 111 and 112. The fully connected neural network 116 may consist of several fully connected layers 401, each followed by a ReLU or LeakyReLU layer performing corresponding activation functions 402 and a final sigmoid layer 403 performing a sigmoid activation function. The fully connected neural network serves the decision-making. The input of the sigmoid function in the last layer is the squared difference between the two high-dimensional features of a pair of samples output from the Resnets 111 and 112. The output of the sigmoid function is the predicted result where k denotes the k-th pair of segmentation samples. Fig.5 shows a block diagram of an example of the discriminator 108. The discriminator 108 contains a discriminator layer 501 in form of a bilinear layer 501, and a sigmoid layer 502. For the regularization, the high dimensional feature f(x _k ) of the vertex x _k is compared with the feature g(G ^yk ) of the neighborhood graph G ^yk in the bilinear layer 501 with a trainable matrix M ∈ Rn×m: d(a, b) = σ(a ^т M b), (3) where σ(·) denotes the sigmoid function, a is a placeholder for f(x _k ) or f(y _k ) and b is a placeholder for g(Gyk) or g(Gyk). The following function discrimination function is defined: L _{pair-empirical-ID} = = L _empirical-ID (x,Gyk) + L _empirical-ID (y,Gxk) in which is the indicator, as well as denote the matching or mismatching relationship with respect to the k-th segmentation pair (x _k , y _k ), respectively. Since L _empirical-ID (x, G ^y ) is similar to L _empirical-ID (y, Gx) in a symmetrical way, in the theoretical analysis below, L _empirical-ID (x, G ^y ) are simply denoted by L _empirical-ID . Referring again to Fig.1, the output of the fully connected neural network 116 and the output L _{pair-empirical-ID} of the discriminator 108 are provided to the loss layer 106. The loss function part computed by the loss layer for the fully connected neural network is the cross entropy given by where k denotes the k-th pair of segmentation samples, α _k denotes the ground-truth label, that is “1” (one) for matched or “0” (zero) for unmatched label, and is the predicted result based on the sigmoid function Actually, L _{pair-empirical-ID} is designed based on an information distance between the distributions conditioned by matched and unmatched pairs, which is explained in details in Proposition 1 below. In thefinal loss function, the loss function part computed by the loss layer for the fully discriminator 108 is set to to maximize the information distance. The final loss function is defined as where λ > 0, is the predefined weight parameter. For example, λ = 0.5 may be chosen. Fig.2 shows a block diagram of an example of a Graph Attention Network (GAT) block 121. The GAT block 121 comprises a multi-head attention module, where the graph attention network is extended to multiple heads, which runs through an attention mechanism several times in parallel, to increase the expressiveness of the graph attention network, which is indicated in Fig.1 by the indices 1...d...K. The extracted high dimensional features f(y _c ) corresponding to g(G ^yk ), which are in this case extracted from segmentations of neighbors of the segmentation y as defined by the output E(G ^yk ) of module 122, are input to the attention function. The attention functions are softmax functions, where a non-linearity (here LeakyReLU) is applied before the softmax. E.g., for the first head, the head function can be expressed as headl = Attention(W(r)ƒ(y _c ), W(r)ƒ(y _d )) = softmax( a ^τ ( W(r)ƒ(y _c ), W(r)ƒ(y _d ))) with a ^T being a transposed weight vector a, W(r) a weight matrix, and d runs from 1 to K. The result are attention coefficients ƞ _cd that are multiplied with W(r)ƒ(y _d ), concatenated and averaged.

Fig. 6 shows a flow diagram of a computer implemented method 600 for image segmentation matching of a first segmentation y _k of a first image with a second segmentation x _k of a second image, where the first segmentation y _k and second segmentation x _k are a pair of segmentations, comprising the steps: learning 602 joint features and metric of the first segmentation y _k and the second segmentation x _k using joint feature and metric learning; and regulating 604 the joint feature and metric learning using a graph G ^yk containing a global spatial relationship between the first segmentation y _k corresponding to the second segmentation x _k and neighboring segmentations of the first segmentation y _k ; and using the second segmentation x _k .

It is noted that the steps described herein may be performed in parallel or in another order where meaningful.

Fig. 7 shows a flow diagram based on the method 600 performed within the framework 100 and in particular within the basic model 102 presented in this disclosure. The flow diagram in Fig. 7 shows the part of the joint feature and metric learning 602 in more detail and uses the output of step 604 as input into the loss layer. The steps of the joint feature and metric learning 602 are the following: Extracting 702 first image features f(y _k ) of the first segmentation y _k by the first image feature extraction module 111 and outputting the extracted first image features f(y _k ) to the fully connected neural network 116. Extracting 704 second image features f(x _k ) of the second segmentation x _k by the second image feature extraction module 112 and outputting the extracted second image features f(y _k ) to the fully connected neural network 116. Comparing 706 the extracted first image features f(y _k ) and the extracted second image f(x _k ) features and outputting a predicted result to the loss layer 106, by the fully connected neural network 116. A further step 708 is performed using the output of step 604: Calculating 708 a total loss ltotal as a sum of the loss lce based on the predicted result and a loss l _reg based on the result of the graph-based regularization part, by the loss layer 106. Fig.8 shows a flow diagram that based on the method 600 and that shows the step 604 in more detail. Also this part is performed within the framework 100, in particular within the graph-based regularization part 104. This method part comprises the following steps: Extracting 802 third image features f(x _k ) of the second segmentation x _k by the third image feature extraction module 113 and outputting the extracted third image features f(x _k ) to the discriminator 108. Extracting 804 fourth image features f(y _l ) of neighboring segmentations contained in graph G ^yk of the first image segmentation y _k by the fourth image feature extraction module 114 and outputting the extracted fourth image features f(y _l ) to the graph attention network 120. Executing 806 attention functions over the fourth image features f(y _l ), in a multi-head module 128 to obtain high dimensional features g(G ^yk ) of the neighboring segments, and outputting the high dimensional features g(G ^yk ) of the neighboring segmentations to the discriminator 108, by the graph attention network 120, and Comparing 808 the extracted third image features f(x _k ) with the high dimensional features g(G ^yk ) of the neighboring segmentations contained in graph G ^yk in layers of the discriminator 108 and outputting the result L _empirical-ID (x, G ^y ) to the loss layer 106, by the discriminator 108. In the following, a theoretical analysis is provided for Graph-Based Regularization. Assumption 1. Let be a random sample pair of an image segmentation and a neighborhood graph which are from the frames respectively. As well, these random sample pairs are independent and identically distributed (i.i.d.). In this case, denotes a pair of high-dimensional features output from Resnet and GAT respectively, which is corresponding to With respect to the random sample pairs are also i.i.d. Let be the probability space for , where is the sample space of denotes the collection of all subsets of , as well as The matched conditional distribution and unmatched conditional distribution with respect to are denoted by whose densities are respectively, where the condition is whether the two image segmentations x and y are matched. When the Assumption 1 is satisfied, we shall discuss some theoretical characteristics for the objective function optimization with respect to the graph-based regularization. Wefirst state the expected form of as Proposition 1 (Relationship with KL divergence). In terms of the optimization for graph-based regularization, it is essential to update the parameters of neural networks by maximizing L _ID given by (6). Suppose that the optimal discrimina tor d* is obtained and the corresponding objective function is denoted by In this case, maximizing is equivalent to maximizing an upper bound of Kullback-Leibler (KL) divergence between Proposition 2 (Optimal solution for the regularization). As for the optimization problem with respect to the regularization, it can be described as where is given by Eq. (4), f and g denote the Resnet and GAT respectively, as well as d is the discriminator. In this case, the optimal solution is reached when the unmatched conditional distribution lies in the boundary of its range. Besides, we also investigate how the optimization objective function of the regularization is influenced by the discriminator disturbance. Proposition 3 (Effect of discriminator disturbance). Consider the case there exists a disturbance on discriminator d, that is where ε is a small enough parameter. As for the optimization objective function L _ID given by Eq. (4), it is obtained denotes the objective function with Furthermore, when the optimal discriminator d* is obtained as Eq. (8) whose corresponding object function is denoted by where denotes the objective function based on the optimal discriminator with a disturbance. Moreover, we shall discuss how the mapping from vertices to neighborhood graphs makes an effect on the matching effectiveness in some special cases. Case 1. There are two sampled frames in which there exist the same vertices, implying that the image segmentations of objects and the corresponding neighborhood graphs are all common in the two frames. Let x and y denote the random vertices from the frames as well as are the neighborhood graphs with respect to x and y, respectively. Besides, are the high-dimensional features for x and are bijective mappings represented by two neural networks. Proposition 4 (Relationship with the mapping in Case 1) When Case 1 is satisfied, if the mapping from vertices to their neighborhood graphs is injective, the correct image segmentation matching will be achieved for each pair of frames. Case 2 As for a pair of frames , there exist some uncommon vertices so that their corresponding neighborhood graphs are also not the same, which is a different condition from that in Case 1. While, the rest conditions are similar to those in Case 1. Proposition 5 (Relationship with the mapping in Case 2) When Case 2 is satisfied, if there exists an injective mapping from vertices to their neighborhood graphs, we will have the correct results for the image segmentation matching. Performance Evaluation Performance of the KITTI Dataset. This dataset is available online, which provides a deal of multi-sensors data for autonomous driving. It contains street scene images and the corresponding LiDAR points. Generally speaking, the proposed framework 100, which is also referred to as REGR Net in the following, is superior to the other methods such as MatchNet, Siamese Network, TFeat Network, L2-Net, HardNet, SOSNet, or Res-Matching Network though there exist not too much difference between it and Res-Matching Network under the measurement of Recall. Moreover, it is also not difficult to observe that REGR Net performs less unstable than the other methods when the training state tends to convergence. Actually, these methods are almost converged after around 15 epochs. As a result of the experiments, the proposed method performs better than other methods under the measurements of the whole criteria. As a result, the regularization proposed in this disclosure makes a positive difference to the matching efficiency by introducing graph-based information. Performance of a real dataset The real dataset is a dataset for autonomous driving applications, which is collected by a probe vehicle with many sensors including cameras, LiDAR, radars, etc. Similar to KITTI dataset, it also contains images and LiDAR points, which are captured on the streets in Singapore as for the objects contained in an image, there are more numerous and more various landmarks such as traffic signs, traffic lights and poses in this dataset than those in KITTI dataset. When taking experiments on the real dataset, the proposed method almost holds the optimal performance compared with the other methods, which is similar to that on KITTI dataset. Moreover, since the real dataset and KITTI dataset have different image quality and they are collected in different street scenes, there exists different performance in real data from that in KITTI data. That is, for all the discussed methods, they performs better in real data. In general, the proposed method holds its superiority on the matching prediction in the case of high-quality image datasets and more amount of valuable objects. Other variations to the disclosed embodiments can be understood and effected by those skilled in the art in practicing the claimed invention, from the study of the drawings, the disclosure, and the appended claims. In the claims, the word “comprising” does not exclude other elements or steps and the indefinite article “a” or “an” does not exclude a plurality. A single processor or other unit may fulfill the functions of several items or steps recited in the claims. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage. Any reference signs in the claims should not be construed as limiting the scope of the claims. List of reference signs 100 Framework 102 Basic model 104 Graph-based regularization part 106 Loss layer 108 Discriminator 110 Shared image feature extraction module, Resnet 111 First image feature extraction module, Resnet 112 Second image feature extraction module, Resnet 113 Third image feature extraction module, Resnet 114 Fourth image feature extraction module, Resnet 116 Fully connected layer 120 GAT (graph attention) network module with GAT blocks 121 GAT block 122 Module with Information of edges 124 Neighborhood graphs handling network 128 Multi-head module 129 Concatenation module 131 Image segmentation of a first image 132 Image segmentation of a second image 133 Image segmentations of the first (or second) image 134 Neighborhood graphs 301 Convolution layer 302 Max pooling 304 Average pooling 310 Resnet convolution layer block 401 Fully connected layer 402 ReLU or LeakyReLU layer 403 Sigmoid layer 501 Bilinear layer 502 Sigmoid layer 600 Method (flow diagram) 602 First step of method part 1 604 Second step of method part 1 702 First sub-step of first step 602 704 Second sub-step of first step 602 706 Third sub-step of first step 602 708 Further step of method part 1 802 First sub-step of second step 604 804 Second sub-step of second step 604 806 Third sub-step of second step 604