Touch object recognition method based on gradient adaptive sampling and 3D neural network

Abstract

The application provides a haptic object recognition method based on gradient adaptive sampling and a 3D neural network, and is used for solving the technical problems of information redundancy / loss caused by the use of a uniform sampling strategy by an existing haptic object recognition model and the technical problem of insufficient generalization ability to process haptic data under different grasping speeds. The steps of the application are as follows: the original haptic frame is sent into a gradient adaptive sampling strategy for adaptive selection of the haptic frame, and a haptic frame set with rapid gradient change is obtained; the haptic frame set is down-sampled under multiple time scales; an MR3D-18 network is used to extract features of the down-sampled haptic frame to obtain features under different time scales; the features under different time scales are fused, and the category of the object is recognized according to the fused features to obtain a predicted classification result. The application is based on a gradient adaptive sampling strategy and a multi-time scale 3D convolutional neural network, and can effectively improve the recognition accuracy of the haptic object recognition task.

Description

Technical Field

[0001] This invention relates to the field of deep learning technology, and in particular to a tactile object recognition method based on gradient adaptive sampling and 3D neural networks. Background Technology

[0002] Vision and touch are two primary ways robots perceive the world. Visual perception only provides robots with the appearance of objects; the physical characteristics of objects, such as hardness, roughness, and texture, must be obtained through tactile perception. my country's robotics industry has developed rapidly, and tactile object recognition is one of the key technologies for robot perception. It is also one of the core issues in applications such as automated production, intelligent driving, virtual reality, intelligent prosthetics, telemedicine, and waste sorting, and has significant application value. Robot tactile perception technology plays a vital role in promoting the development of machine intelligence and solving practical problems.

[0003] Tactile object recognition can be broadly divided into two parts: acquiring tactile data and identifying the object category based on the tactile data. First, tactile sensors on a robotic arm are used to acquire tactile data (usually pressure data) of the object. Then, the CPU on the robot is used to identify the object category based on the tactile data, which is the subject of this invention. Currently, the mainstream methods for tactile object recognition include feature extraction-based methods, pattern recognition-based methods, and deep learning-based methods. Among these, deep learning-based tactile object recognition methods have higher recognition accuracy and robustness, and therefore are gradually becoming a research hotspot.

[0004] Currently, most deep learning-based tactile object recognition methods do not utilize temporal information. These methods use single-frame tactile data as input, resulting in lower computational costs and better real-time performance. However, in daily life and industrial production, most objects typically have similar appearances, which reduces the recognition accuracy of models using single frames. Another type of tactile object recognition method utilizes temporal information, employing multi-frame temporal tactile data to model objects. Because it covers more surface tactile information, this type of method offers higher recognition accuracy and robustness. Summary of the Invention

[0005] To address the issues of information redundancy / loss caused by the uniform sampling strategy in existing tactile object recognition models, and the insufficient generalization ability to handle tactile data at different grasping speeds, this invention proposes a tactile object recognition method based on gradient adaptive sampling and a 3D neural network. The gradient adaptive sampling strategy can acquire as much richer tactile information as possible, while the multi-timescale 3D convolutional neural network can improve the recognition effect on tactile data generated at different grasping speeds, thereby effectively improving the recognition accuracy of tactile object recognition tasks.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows: a tactile object recognition method based on gradient adaptive sampling and 3D neural networks, comprising the following steps:

[0007] Step 1: Use a gradient adaptive sampling strategy to adaptively select the original tactile frames and obtain a set of tactile frames with rapid gradient changes; this makes most of the sampled tactile frames contain richer tactile information, thereby solving the data redundancy or data loss problems of traditional sampling strategies.

[0008] Step 2: Perform multi-timescale downsampling on the tactile frame set obtained in Step 1;

[0009] Step 3: Use the MR3D-18 network to extract features from the downsampled tactile frame set to obtain features at different time scales; fuse the features from different time scales, and identify the object category based on the fused features to obtain the predicted classification result. The multi-time-scale 3D convolutional neural network model can improve the generalization ability of existing tactile object recognition models to tactile data generated at different grasping speeds, and effectively improve the recognition accuracy of the grasped object.

[0010] Preferably, the method for adaptively selecting haptic frames using the gradient adaptive sampling strategy is as follows:

[0011] S1: Perform matrix subtraction on adjacent original tactile frames in the input tactile data to obtain the absolute gradient matrix of two adjacent tactile frames at time t; and perform matrix subtraction on the starting tactile frame itself to obtain the absolute gradient matrix of the tactile frame at the initial time.

[0012] S2: Normalize the absolute gradient matrix in the time dimension and calculate the cumulative distribution of the normalized gradient;

[0013] S3: Divide the sampling time of the tactile frame into N intervals according to the cumulative gradient distribution, and randomly select one frame from each of these N intervals as a tactile frame. The N tactile frames form a tactile frame set.

[0014] Preferably, step S1 is implemented as follows:

[0015]

[0016] Where D represents the set of original haptic frames, H, W, and T represent the height, width, and number of original haptic frames, respectively, and F t F represents the original haptic frame at time t. t-1 FG represents the original haptic frame at time t-1. t FG1 represents the absolute gradient matrix of two adjacent original haptic frames at time t, and FG1 is the absolute gradient matrix of the starting frame.

[0017] The implementation method of step S2 is as follows:

[0018]

[0019] Among them, FG t (x,y) represents the absolute value matrix of the gradient FG t The values ​​of row x and column y at time t, NFG t FG represents the absolute value matrix of the gradient. t The normalized matrix, AFG t ∈[0,1] represents the gradient accumulation at time t, and AFG1=0, AFG T =1.

[0020] Preferably, the method for acquiring the haptic frame set is as follows:

[0021] Gradient accumulation AFG t It is divided into N sub-intervals, namely {[0,1N],...,[n-1N,nN],...,[N-1N,1]}, and the gradient accumulation AFG is calculated. t The function curve yields N sub-intervals on the time axis, namely {[0, si1], ..., [si n-1 ,si n ],...,[si N-1 Finally, a sampling point is randomly selected from each of the N sub-intervals of the time axis, resulting in N sampling points, forming a sampling point set TS = {ts1, ts2, ..., ts}. N}; Sample from the original tactile frame set D based on the sampling point set TS, and the sampled tactile frame set is labeled as Where T represents the number of original haptic frames, si n Point nN represents the gradient accumulation on the vertical axis based on gradient accumulation AFG. t The mapping points of the function curve on the time axis, ts1, ts2, ..., ts N This represents the N selected sampling points.

[0022] Preferably, the method for implementing the multi-timescale downsampling is as follows:

[0023]

[0024] Where, r m =(0.5) m-1 Let DS(·,·) represent the downsampling rate at the m-th time scale, and let DF represent the downsampling operation (implemented through average pooling). m Represents the haptic frame set F TS The set of haptic frames sampled at the m-th time scale, N m Represents the tactile frame set DF m The number of haptic frames included.

[0025] Preferably, the MR3D-18 network is obtained by modifying the ResNet3D-18 network provided in the literature [Hara, K., Kataoka, H., & Satoh, Y. (2018). Canspatiotemporal 3d cnns retrace the history of 2d cnns and imagenet? . In Proceedings of the IEEE conference on Computer Vision and Pattern Recognition (pp. 6546-6555).]. The MR3D-18 network removes a pooling layer from the ResNet3D-18 network; the MR3D-18 network adds a Dropout layer after the Res2 layer of the ResNet3D-18 network.

[0026] Preferably, when the size of the input haptic frame is 32×32, the architecture comparison between the ResNet3D-18 network and the MR3D-18 network is as follows:

[0027]

[0028]

[0029] Preferably, the method for implementing step three is as follows:

[0030] The set of tactile frames sampled at M time scales The features are fed into the MR3D-18 network for feature extraction, and the extracted multi-timescale features are {SF1,...,SF...} m ,...,SF M};

[0031] Multi-timescale features {SF1,...,SF m ,...,SF MThe features are fused by summation, and then passed sequentially through an FC layer and a softmax classifier to obtain the predicted classification result:

[0032] S=Softmax(FC(FUSION(SF1,...,SF m ,...,SF M )))

[0033] Wherein, FUSION(·) represents the feature fusion operation, which is a summation operation in this invention; FC(·) represents the fully connected convolution operation; and Softmax(·) represents the softmax classification operation. Represents the haptic frame set F TS The predicted classification results are given, where C represents the number of target categories, and the category corresponding to the highest-scoring element in S is considered as the predicted target category.

[0034] Preferably, the predicted classification results are supervised by manually labeled classification results to complete the training of the entire multi-timescale 3D convolutional neural network; the loss function used during training is the traditional binary cross-entropy function.

[0035] Compared with existing technologies, the beneficial effects of this invention are as follows: The gradient adaptive sampling strategy adaptively determines the sampling interval based on the gradient value of the tactile frame, thereby acquiring as much richer tactile information as possible under the condition of the same number of input frames, thus solving the problem of information redundancy or loss caused by traditional sampling strategies; The multi-timescale 3D convolutional neural network solves the problem that the generalization ability of existing tactile object recognition models is insufficient to handle tactile data generated under different grasping speeds by extracting and fusing deep features at multiple timescales; Based on the gradient adaptive sampling strategy and the multi-timescale 3D convolutional neural network, this invention can effectively improve the recognition accuracy of tactile object recognition tasks. Attached Figure Description

[0036] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0037] Figure 1 This is a schematic diagram of the model of the present invention.

[0038] Figure 2 This is a diagram illustrating the gradient adaptive sampling strategy of the present invention, wherein (a) is a diagram illustrating the gradient of the tactile frame, and (b) is a diagram illustrating the cumulative gradient distribution of the tactile frame. Detailed Implementation

[0039] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0040] like Figure 1 As shown, a tactile object recognition method based on gradient adaptive sampling and 3D neural networks comprises the following steps:

[0041] Step 1: Use a gradient adaptive sampling strategy to adaptively select the original haptic frames to obtain a set of haptic frames with rapid gradient changes;

[0042] like Figure 2 As shown in (a), firstly, matrix subtraction is performed on adjacent original tactile frames in the input tactile data to obtain the absolute gradient matrix of two adjacent tactile frames at time t; for the initial tactile frame, matrix subtraction is performed on itself to obtain the absolute gradient matrix of the initial tactile frame. The specific implementation method is as follows:

[0043]

[0044] Where D represents the set of original haptic frames, H, W, and T represent the height, width, and number of original haptic frames, respectively, and F t F represents the original haptic frame at time t. t-1 FG represents the original haptic frame at time t-1. t FG1 represents the absolute gradient matrix of two adjacent original tactile frames at time t, where FG1 is the initial absolute gradient matrix. Matrix subtraction between adjacent original tactile frames can extract change information from the tactile signal, which can be used to quantify the degree of change between the two adjacent tactile frames.

[0045] For the gradient absolute value matrix FG t Normalization is performed along the time dimension, and then the cumulative gradient distribution is calculated. The specific implementation is as follows:

[0046]

[0047] Among them, FG t (x,y) represents the absolute value matrix of the gradient FG t The value of row x and column y at time t, NFG t FG represents the absolute value matrix of the gradient. t The normalized matrix, AFG t ∈[0,1] represents the gradient accumulation at time t, i.e.: AFG1=0, AFG T =1. For example... Figure 2 As shown in (b), the horizontal and vertical axes represent time t and gradient accumulation AFG, respectively. t The curve represents the gradient accumulation AFG. t The function curve relative to time t.

[0048] The sampling time of the haptic frame is divided into N intervals according to the cumulative gradient distribution. One frame is randomly selected from each of these N intervals as the input to the subsequent multi-timescale 3D convolutional neural network. The specific implementation process is as follows: Gradient Accumulation (AFG) t It is divided into N sub-intervals, namely {[0,1 / N],...,[n-1 / N,n / N],...,[N-1 / N,1]}, and the gradient accumulation AFG is calculated. t The function curve can be used to obtain N sub-intervals on the time axis, namely {[0, si1], ..., [si n-1 ,si n ],...,[si N-1 ,T]},si n Point nN represents the gradient accumulation on the vertical axis based on gradient accumulation AFG. t The function curve is mapped onto the time axis. Finally, a sampling point is randomly selected from each of the N sub-intervals of the time axis to obtain N sampling points, i.e., the sampling point set TS = {ts1, ts2, ..., ts...}. N}, ts1, ts2, ..., ts N This represents the N selected sampling points, such as Figure 2 (b) shows the black dots. At this point, the tactile frames input to the multi-timescale 3D neural network can be sampled from the original set of tactile frames D based on the sampling point set TS. The sampled tactile frame set is labeled as follows. like Figure 2 As shown, according to this gradient adaptive sampling strategy, most of the sampled tactile frames are in sub-intervals with rapid gradient changes, that is, sub-intervals containing richer tactile information.

[0049] Step 2: Utilize a multi-timescale 3D convolutional neural network to process the tactile frame set F obtained in Step 1. TS Perform downsampling at multiple time scales.

[0050] For tactile frame set F TS Multi-timescale downsampling is performed as follows:

[0051]

[0052] Where, r m =(0.5) m-1This represents the downsampling rate at the m-th time scale. The setting of the downsampling rate for each time scale generally needs to be considered in conjunction with the specific application scenario and dataset. This is the optimal sampling rate in the MIT-STAG dataset. DS(·,·) represents the downsampling operation (implemented through average pooling), and DF... m Represents the haptic frame set F TS The set of haptic frames sampled at the m-th time scale, N m Represents the tactile frame set DF m The number of haptic frames included. The number of time scales generally needs to be considered in conjunction with the specific application scenario and dataset. The choice of the number of time scales in this invention (3 here) yields the best results on the MIT-STAG dataset.

[0053] Multi-timescale 3D convolutional neural networks can improve the generalization performance of tactile object recognition models on tactile data with different grasping speeds. In a multi-timescale 3D convolutional neural network, firstly, the network downsamples the input tactile data at different time scales to obtain downsampled data at different time scales, as shown in formula (3). Then, the network extracts features from the downsampled data at different time scales to obtain features at different time scales. These fused features are then used to identify the grasped object. Therefore, multi-timescale 3D convolutional neural networks can adapt to tactile data generated at different grasping speeds in this way.

[0054] Step 3: Use the MR3D-18 network to extract features from the downsampled tactile frame set to obtain features at different time scales; fuse the features at different time scales, and identify the category of the object based on the fused features to obtain the predicted classification result.

[0055] This invention uses the MR3D-18 network to extract features from haptic frames. The MR3D-18 network is a modified version of the lightweight ResNet3D-18 model provided in the literature [Hara, K., Kataoka, H., & Satoh, Y. (2018). Can spatiotemporal 3D CNNs retrace the history of 2D CNNs and ImageNet? . In Proceedings of the IEEE conference on Computer Vision and Pattern Recognition (pp. 6546-6555).]. The modifications of MR3D-18 compared to ResNet3D-18 include the following two aspects:

[0056] 1. The MR3D-18 network removes a pooling layer from the ResNet3D-18 network. Haptic frames are typically no larger than 32x32 pixels; therefore, if the pooling operations at the bottom layers reduce the feature size too much, the convolutional operations at the top layers will require a significant amount of zero-padding. Removing a pooling layer reduces the error caused by excessive zero-padding.

[0057] 2. The MR3D-18 network adds a Dropout layer after the Res2 layer of the ResNet3D-18 network. In convolutional neural networks, Dropout is a regularization method that helps reduce overfitting. During neural network training, Dropout randomly discards some neurons, setting their outputs to 0, thus forcing the network to learn more robust and general features without relying on any single neuron. The Dropout rate refers to the proportion of neurons randomly dropped in each training iteration; for example, when the Dropout rate = 0.3, 30% of neurons are dropped in each training iteration. In tactile data, objects of the same category may look different, and the grasping position of the same object may differ at each grasping moment, leading to high diversity in tactile data of the same category. Therefore, unless there are a large number of manually labeled samples, training 3D convolutional neural networks is prone to overfitting. Therefore, adding a Dropout layer is necessary to improve the generalization ability of the MR3D-18 network.

[0058] When the input haptic frame size is 32×32, the specific details of the ResNet3D-18 network and the MR3D-18 network are shown in Table 1.

[0059] Table 1 Comparison of ResNet3D-18 and MR3D-18 network architectures.

[0060]

[0061] The tactile frame set after downsampling at three time scales The data is fed into the MR3D-18 network for feature extraction, and the extracted multi-timescale features are labeled as {SF1, SF2, SF3}. The features extracted by the MR3D-18 network are high-level abstract representations of the data, capturing information in the spatial, temporal, and frequency domains. These features can be used to identify objects. Figure 1The minimum, medium, and maximum timescale branches all use the MR3D-18 feature extraction network, differing only in the timescale downsampling rate of the input data. The minimum timescale branch, with a timescale downsampling rate of 1 (equivalent to no timescale downsampling), extracts features at the smallest timescale. The medium timescale branch, with a timescale downsampling rate of 0.5 (doubling the timescale), and the maximum timescale branch work similarly. The purpose of multiple timescale branches is to capture information at different timescales when processing tactile sequence data, thereby improving the model's generalization ability and performance.

[0062] like Figure 1 As shown, the multi-timescale features {SF1, SF2, SF3} are fused by summation. The fused features are then passed sequentially through an FC layer and a softmax classifier to obtain the predicted classification result. This process can be described as follows:

[0063] S=Softmax(FC(FUSION(SF1,SF2,SF3))) (4)

[0064] Wherein, FUSION(·) represents the feature fusion operation, which is a summation operation in this invention; FC(·) represents the fully connected convolution operation; and Softmax(·) represents the softmax classification operation. Represents the haptic frame set F TS The predicted classification results are given, where C represents the number of target categories, and the category corresponding to the highest-scoring element in S is considered as the predicted target category.

[0065] Step 4: Supervise the classification results predicted in Step 3 using manually labeled classification results to complete the training of the entire multi-timescale 3D convolutional neural network; the loss function used for training is the traditional binary cross-entropy function.

[0066] The effectiveness of the proposed method was verified on the large tactile dataset MIT-STAG (Sundaram, S., Kellnhofer, P., Li, Y., Zhu, JY, Torralba, A., & Matusik, W. (2019). Learning the signatures of the human grasp using a scalable tactile glove. Nature, 569(7758), 698-702.). Stochastic gradient descent (SGD) (Robbins, H., & Monro, S. (1951). A stochastic approximation method. The annals of mathematical statistics, 400-407.) was used as the optimization algorithm, with weight decay and momentum set to 0.0001 and 0.9 respectively, batch size set to 32, number of epochs set to 50, initial learning rate set to 0.001, and learning rate changed to 10% of the previous stage after every 10 epochs. These parameter settings can improve model performance and training speed. The experiment was implemented in the PyTorch framework and ran on a single NVIDIA GeForce RTX 2080Ti@11GB GPU.

[0067] The experimental results are shown in Table 2, with the highest score indicated in bold. As can be seen from Table 2, the average recognition accuracy of the method proposed in this invention exceeds that of currently popular tactile object recognition methods such as Sundaram et al., Wang et al., Zhang et al., and Sharma et al. by 16.43%, 16.81%, 8.72%, and 6.99%, respectively. This indicates that the tactile object recognition method of this invention has excellent recognition accuracy. Sundaram et al., Wang et al., Zhang et al. and Sharma et al. are respectively in the literature (Sundaram, S., Kellnhofer, P., Li, Y., Zhu, JY, Torralba, A., & Matusik, W. (2019). Learning the signatures of the human grasp using ascalable tactile glove.Nature,569(7758),698-702.), (Wang, Symposium(SAS)(pp.1-6).IEEE.), (Zhang,X.,Li,S.,Yang,J.,Bai,Q.,Wang,Y.,Shen,M.,...&Song,Q.(2021).Target Classification Method of TactilePerception Data with Deep The method proposed in Learning.Entropy, 23(11), 1537.) and (Sharma, M. (2022). Tactile-ViewGCN: Learning Shape Descriptor from Tactile Data using GraphConvolutional Network. arXiv preprint arXiv:2203.06183.).

[0068] Table 2 compares the average recognition accuracy (%) with popular methods on the MIT-STAG dataset.

[0069]

[0070] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A tactile object recognition method based on gradient adaptive sampling and 3D neural networks, characterized in that, The steps are as follows: Step 1: Use a gradient adaptive sampling strategy to adaptively select the original haptic frames to obtain a set of haptic frames with rapid gradient changes; Step 2: Perform multi-timescale downsampling on the tactile frame set obtained in Step 1; Step 3: Use the MR3D-18 network to extract features from the downsampled tactile frame set to obtain features at different time scales; fuse the features at different time scales, and identify the category of the object based on the fused features to obtain the predicted classification result; The gradient adaptive sampling strategy for adaptive selection of haptic frames is as follows: S1: Perform matrix subtraction on adjacent original tactile frames in the input tactile data to obtain the absolute gradient matrix of two adjacent tactile frames at time t; and perform matrix subtraction on the starting tactile frame itself to obtain the absolute gradient matrix of the tactile frame at the initial time. S2: Normalize the absolute gradient matrix in the time dimension and calculate the cumulative distribution of the normalized gradient; S3: Divide the sampling time of the tactile frame into N intervals according to the cumulative gradient distribution, and randomly select one frame from each of these N intervals as a tactile frame. The N tactile frames form a tactile frame set. The implementation method of step S1 is as follows: ； Where D represents the set of original haptic frames, and H, W, and T represent the height, width, and number of original haptic frames, respectively. This represents the original tactile frame at time t. This represents the original tactile frame at time t-1. This represents the absolute gradient matrix of two adjacent original haptic frames at time t. The gradient absolute value matrix of the starting frame; The implementation method of step S2 is as follows: ； in, Represents the absolute value matrix of the gradient The values ​​of row x and column y at time t Represents the absolute value matrix of the gradient The normalized matrix, Let represent the gradient accumulation at time t, and , .

2. The tactile object recognition method based on gradient adaptive sampling and 3D neural network according to claim 1, characterized in that, The method for obtaining the tactile frame set is as follows: gradient accumulation It is divided into N sub-intervals, that is According to gradient accumulation The function curve yields N sub-intervals on the time axis, i.e. Finally, a sampling point is randomly selected from each of the N sub-intervals of the time axis to obtain N sampling points, which form a sampling point set. Based on the sampling point set Sample from the original tactile frame set D, the sampled tactile frame set is labeled as follows. Where T represents the number of original haptic frames, Points representing the cumulative gradient on the vertical axis Based on gradient accumulation The mapping points of the function curve on the time axis, This represents the N selected sampling points.

3. The tactile object recognition method based on gradient adaptive sampling and 3D neural network according to claim 2, characterized in that, The method for implementing the multi-timescale downsampling is as follows: ； in, This represents the downsampling rate at the m-th time scale. This indicates a downsampling operation. Represents haptic frame set The set of tactile frames sampled at the m-th time scale Represents haptic frame set The number of haptic frames included.

4. The tactile object recognition method based on gradient adaptive sampling and 3D neural network according to claim 1 or 3, characterized in that, The MR3D-18 network removes a pooling layer from the ResNet3D-18 network; the MR3D-18 network adds a Dropout layer after the Res2 layer of the ResNet3D-18 network.

5. The tactile object recognition method based on gradient adaptive sampling and 3D neural network according to claim 4, characterized in that, The implementation method of step three is as follows: The set of tactile frames sampled at M time scales The features are fed into the MR3D-18 network for feature extraction, and the extracted multi-timescale features are as follows: ; Multi-timescale features The features are fused by summation, and then passed sequentially through an FC layer and a softmax classifier to obtain the predicted classification result: ； in, This indicates a feature fusion operation, which is a summation operation. This represents a fully connected convolution operation. This represents the softmax classification operation. Represents haptic frame set The predicted classification results are given, where C represents the number of target categories, and the category corresponding to the highest-scoring element in S is considered as the predicted target category.

6. The tactile object recognition method based on gradient adaptive sampling and 3D neural network according to claim 5, characterized in that, The training of the entire multi-timescale 3D convolutional neural network is completed by supervising the predicted classification results with manually labeled classification results; the loss function used during training is the traditional binary cross-entropy function.

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