A fast target detection method based on depth separable convolution

Abstract

The application discloses a kind of fast target detection methods based on depth separable convolution, comprising the following steps, construct fast target detection network based on depth separable convolution;The proposed detection network is trained using back propagation on training set until the detection network converges;The trained detection network is used to detect test image;Output final result.The beneficial effects of the present application are as follows: by using depth separable convolution with large convolution kernel, the processing speed of the model can be improved, and the feature extraction capability of the convolution network can be effectively improved;To solve the problem of losing more local detail information by maximum pooling, the features at different scales can fully cover a large enough image range, and the positioning of multi-scale targets is significantly improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of automatic driving, and in particular to a fast target detection method based on deep separable convolution. BACKGROUND

[0002] In recent years, with the vigorous development of deep learning technology, computer vision has made great breakthroughs, and many advanced visual perception algorithms have been proposed. Among them, target detection as a basic task has attracted the attention of many researchers. Existing detection algorithms can be roughly divided into two categories: two-stage method and single-stage method. Among them, the detection network of the single-stage method only propagates forward once, generates a large number of detection frames through dense sampling of image regions, and outputs prediction frames and classification results for each possible target position. It has low computational complexity, fast processing speed, great advantages and potential in actual application, especially in real-time scenarios, and therefore is widely studied.

[0003] Because maxpool is usually used in the shallow layer of the classification network to reduce the sampling features, and fewer convolution layers are used, more local detail information is easily lost, which is extremely unfavorable for small target detection; at the same time, when dealing with multi-scale target detection tasks, multiple layers of features are needed to detect targets of corresponding scales, and the receptive field of the image classification-based network at these layers is usually not suitable for the detection of targets of the corresponding scale, that is, the receptive field of the feature cannot effectively perceive the information of the target to be detected, so it is also easy to cause missed detection. SUMMARY

[0004] This section aims to summarize some aspects of the embodiments of the present application and briefly introduce some preferred embodiments. Some simplifications or omissions may be made in this section and the abstract and title of the specification to avoid obscuring the purpose of this section, abstract and title, and such simplifications or omissions cannot be used to limit the scope of the present application.

[0005] In view of the above existing problems, the present application is proposed.

[0006] Therefore, the technical problem solved by the present application is: to improve the speed of the convolution network while maintaining efficient feature extraction capability.

[0007] To solve the above technical problems, the present application provides the following technical scheme: a fast target detection method based on deep separable convolution, comprising the following steps: constructing a fast target detection network based on deep separable convolution; training the proposed detection network using backpropagation on the training set until the detection network converges; using the trained detection network to detect test images; and outputting the final result.

[0008] As a preferred scheme of the fast target detection method based on deep separable convolution, the fast target detection network comprises a basic network part, a feature pyramid and a multi-target detection.

[0009] As a preferred scheme of the fast target detection method based on deep separable convolution, the basic network part comprises a basic network convolution list, the basic network convolution list comprises a general convolution layer of conv1, a deep separable convolution of DwConv, and Block[5*5, 60, s1]*3 represents repeating three basic convolution modules in series, a 5*5 convolution is used in a large number of shallow convolution layers, and a 3*3 deep separable convolution is used in a last deep convolution layer.

[0010] As a preferred scheme of the fast target detection method based on deep separable convolution, the method further comprises the following steps: a deep separable convolution with a step of 2 is used instead of maximum pooling downsampling; a 5*5 deep convolution is used to increase the receptive field range of the convolution layer, and two basic convolution modules are used for stage 2 to extract sufficient image detail features; four output features of stage 3 to stage 6 are used for target detection.

[0011] As a preferred scheme of the fast target detection method based on deep separable convolution, the theoretical receptive field size of the fast target detection network at four convolution feature layers is 139, 491, 715 and 1035 respectively, which is approximately 4 times the size of the current detected target scale, and sufficient image information can be extracted to complete target positioning and classification.

[0012] As a preferred scheme of the fast target detection method based on deep separable convolution, the multi-target detection part also uses a deep separable convolution to output the position coordinates and category probability of the target, four layers of features are used for target prediction, and the basic scale sizes of anchor points are 32, 64, 128 and 256 respectively, and the aspect ratio sizes of the anchor boxes are 1:1, 1:2 and 2:1.

[0013] As a preferred scheme of the fast target detection method based on deep separable convolution, the training of the detection network comprises the following steps: the basic network part is pre-trained in a classification task; a softmax classification layer is added behind stage 6 to continue fine-tuning training on a specific data set by using the pre-trained basic network part; and the number of iterations is more than that of a general detection network during fine-tuning training, and the number of iterations is about eight thousand times of the number of detection categories.

[0014] As a preferred scheme of the fast target detection method based on deep separable convolution, the detection picture comprises the following steps: the trained detection network is applied in an actual scene; the image collected by the camera is preprocessed; the image is scaled to 320*320 and then normalized; the image is normalized to zero mean and variance of 1; and the preprocessed image is input into the detection network for forward propagation inference to obtain detection results at each scale.

[0015] As a preferred scheme of the fast target detection method based on deep separable convolution, the preprocessing comprises binarization processing of the image according to the following formula:

[0016]

[0017] wherein, D p The image is enhanced by cross double filtering.

[0018] As a preferred scheme of the fast target detection method based on deep separable convolution, the cross double filtering comprises,

[0019]

[0020] ω(p)=∑ q∈Ω s(||p-q||)r(|I(q)-I(p)|)c(q)

[0021] wherein, D` is an input image, p is an input pixel value, D is an output image, q is an output pixel value, Ω is a set of pixels around p, ω(p) is a normalization parameter, s is a spatial filter kernel, r is a range filter kernel, I is an estimation object, and c is an edge value.

[0022] The beneficial effects of the present application: by using deep separable convolution with a large convolution kernel, the processing speed of the model can be improved, and the feature extraction capability of the convolution network can be effectively improved; in view of the problem that the maximum pooling loses more local detail information, the deep separable convolution with a step of 2 is used for down-sampling, which is fast and can retain sufficient detail information, which is beneficial to improve the performance of small scale target detection; at the same time, in view of the problem of multi-scale target detection, the characteristics of the target detection task are fully considered, and the network model with more balanced receptive field distribution makes the features of different scales fully cover a large enough image range, which has obvious improvement effect on the positioning of multi-scale targets. BRIEF DESCRIPTION OF DRAWINGS

[0023] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings needed in the embodiment description will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor. Among them:

[0024] Figure 1 The first embodiment of the present application is a schematic diagram of a fast target detection network based on deep separable convolution.

[0025] Figure 2 The schematic diagram of the basic convolution module described in the first embodiment of the present application is shown in the figure.

[0026] Figure 3 The detection result schematic diagram of the basic convolution module described in the first embodiment of the present application is shown in the figure. DETAILED DESCRIPTION

[0027] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the specific embodiments of the present application will be described in detail below with reference to the drawings of the specification. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor should be within the scope of protection of the present application.

[0028] In the following description, many specific details are set forth in order to provide a thorough understanding of the present application, but the present application can also be implemented in other ways different from those described herein, and those skilled in the art can make similar generalizations without departing from the connotation of the present application, therefore the present application is not limited to the specific embodiments disclosed below.

[0029] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0030] This invention is described in detail with reference to the schematic diagrams. When detailing the embodiments of this invention, for ease of explanation, the cross-sectional views illustrating the device structure may be partially enlarged, not adhering to the usual scale. Furthermore, the schematic diagrams are merely examples and should not be construed as limiting the scope of protection of this invention. In actual fabrication, the three-dimensional spatial dimensions of length, width, and depth should be included.

[0031] Furthermore, in the description of this invention, it should be noted that the terms "upper," "lower," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. These terms are used solely for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. In addition, the terms "first," "second," or "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0032] Unless otherwise explicitly specified and limited, the terms "installation," "connection," and "joining" in this invention should be interpreted broadly. For example, they can refer to fixed connections, detachable connections, or integral connections; similarly, they can refer to mechanical connections, electrical connections, or direct connections, or indirect connections through an intermediate medium, or internal connections between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0033] Example 1

[0034] Reference Figures 1-2 As illustrated, this embodiment proposes a fast object detection method based on depthwise separable convolution, using a fast object detection model for embedded target detection. This embodiment constructs a lightweight detection network based on depthwise separable convolution, significantly improving the inference speed. Furthermore, it uses depthwise separable convolution with a stride of 2 instead of common max pooling, effectively reducing the loss of local detail information and improving the detection performance of small-scale targets. By fusing deep and shallow features, the information content of shallow features is further increased, enhancing the detection performance of small targets. Additionally, the receptive field distribution of each feature map in this model is more balanced, better meeting the requirements of multi-scale object detection tasks and contributing to improved multi-scale object detection performance. The technical solution of this embodiment includes the following steps:

[0035] S1: Construct a fast target detection network based on depth separable convolution.

[0036] S2: Train the proposed detection network using backpropagation on the training set until the detection network converges.

[0037] S3: Use the trained detection network to detect test images and output the final result.

[0038] The method proposed in this embodiment includes the following improvements:

[0039] (1) Speed up the processing speed of the algorithm:

[0040] This embodiment makes full use of the advantage of small computational load of the depth separable convolution network, designs a very lightweight detection model, and can realize real-time processing of target detection tasks on an embedded platform. The model has a high degree of parallelization and can achieve fast target detection inference on a GPU. The running time of this embodiment on a single 1080TI GPU can reach 160fps, meeting the real-time processing requirements.

[0041] (2) Improve the detection performance of small-scale targets:

[0042] The detection model designed in this embodiment removes the common max pooling layer, uses depth separable convolution with a stride of 2 to realize feature down-sampling, and appropriately increases the shallow convolution layer, which can effectively extract sufficient detailed information. Compared with similar lightweight detection networks, it has higher small-scale target detection performance. At the same time, this embodiment uses a feature pyramid structure to further optimize the information expression ability of shallow features. By up-sampling the deep features and then fusing them into the shallow features, the semantic information of the shallow features can be increased, the perception ability of the surrounding environment can be increased, and the positioning ability of small targets can be improved.

[0043] (3) Feature maps have balanced receptive field distribution:

[0044] The detection network model designed in this embodiment uses 4 layers of features for detection. This embodiment reasonably designs the distribution of convolution layers so that each feature map can have a balanced receptive field distribution, which can effectively detect targets at the corresponding scale. Since depth separable convolution has a high degree of parallelization in actual operation, the speed difference between 5*5 and 3*3 depth separable convolution is not large, so this embodiment uses 5*5 depth separable convolution for feature extraction. This can effectively increase the receptive field size while avoiding the introduction of too many convolution layers, effectively improving the operation speed of the detection network. The model ensures that its effective receptive field size is twice the size of the target size at this scale, which can effectively cover the area of the target to be detected and also extract the environmental information around the target, which is beneficial to improving the accuracy of target positioning.

[0045] The embodiment proposes a fast target detection network based on deep separable convolution, and a structure of the network is as shown in Figure 1 The embodiment uses four layers of features with different scales to detect targets with different scales. In order to improve the detection performance on small targets, the four layers of features are further fused, as shown in Figure 1 The feature pyramid structure part can effectively improve the semantic information of the shallow features and the perception of the overall image information by adding deep features to the shallow features, and is beneficial to the positioning of small targets.

[0046] The basic network part designed in the embodiment is shown in Table 1. The conv1 is a general convolutional layer, and the number of groups is 1, which can effectively extract sufficient image features. The DwConv is a deep separable convolution, which includes a deep convolution and a 1*1 convolution, s2 represents a convolution step of 2, and s1 represents a convolution step of 1. The Block[5*5, 60, s1]*3 represents that three basic convolution modules (the structure of the basic convolution module is shown in Figure 2 The size of the convolution kernel of the deep convolution is 5*5, the number of channels is 60, and the convolution step is 1. Since the time consumption difference between the 5*5 deep separable convolution and the 3*3 deep separable convolution is not large in actual operation, in the future, in order to improve the effective receptive field size of the detection features, the embodiment applies a large number of 5*5 convolutions in the shallow convolutional layer, and only uses a 3*3 deep separable convolution in the last deep convolutional layer. In this way, the number of convolutional layers can be reduced, but sufficient image information can be extracted, which is beneficial to fast and efficient detection.

[0047] Table 1: Convolution list of basic network

[0048]

[0049]

[0050] In the traditional image classification network, the maximum value pooling is generally used in the stage2 part to perform feature down-sampling, but this will greatly lose the detailed information of the image, which is extremely unfavorable for the positioning of small targets. Therefore, considering the characteristics of the target detection task, the embodiment uses a deep separable convolution with a step of 2 to replace the maximum value pooling for down-sampling, which can maintain the rapidity of the network model and does not lose the detailed information.

[0051] Considering that different convolutional layers are used to detect targets of different scales, in order to obtain ideal detection performance, the convolutional features need to have appropriate receptive field sizes so as to have sufficient feature extraction capability. In this embodiment, 5*5 deep convolution is used to increase the receptive field range of the convolutional layer, and two basic convolution modules are used for stage 2 to extract sufficient image detail features, which is not available in general image classification networks because image classification pays more attention to global information, while detection, especially small target detection, pays more attention to local details.

[0052] In this embodiment, the four output features of stage 3 to stage 6 are used for target detection. In order to make the effective receptive field size of each feature cover the scale of the target to be detected in the current stage (the basic scales of the targets to be detected by the four features are 32, 64, 128, and 256 respectively), the number of basic convolution modules is reasonably allocated when designing stage 2 to stage 6. Since the actual effective receptive field size is often smaller than the theoretical receptive field (generally at least 2-4 times smaller), the theoretical receptive field size of the network designed in this embodiment at the four convolutional feature layers is 139, 491, 715, and 1035 respectively, which is about 4 times the size of the scale of the target to be detected, and sufficient image information can be extracted to complete the positioning and classification of the target.

[0053] The multi-target detection part involved in this embodiment also uses deep separable convolution to output the position coordinates and class probability of the target. The position coordinates include four values (x, y, w, h), and the class probability includes the categories of the target of interest plus the background. When regressing the position coordinates of the target, the commonly used anchor point matching based method is used. Since four layers of features are used to predict the target in this embodiment, the basic scale sizes of the anchor points are 32, 64, 128, and 256 respectively, and the aspect ratio sizes of these anchor boxes are 1:1, 1:2, and 2:1 respectively. This anchor point design can basically cover most of the detection task requirements.

[0054] It should be appreciated that embodiments of the present application can be realized or implemented by computer hardware, a combination of hardware and software, or through computer instructions stored in a non-transitory computer readable storage medium. The method can be implemented in a computer program using standard programming techniques, including a non-transitory computer readable storage medium configured with a computer program, wherein the storage medium thus configured causes a computer to operate in a specific and predefined manner according to the methods described in the specific embodiments and the accompanying drawings. Each program can be implemented in a high-level procedural or object-oriented programming language to communicate with a computer system. However, if necessary, the program can be implemented in assembly or machine language. In any case, the language can be a compiled or interpreted language. Furthermore, for this purpose, the program can be run on a programmed special-purpose integrated circuit.

[0055] Further, the operations of the processes described herein can be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. The processes described herein (or variations and / or combinations thereof) can be implemented under the control of one or more computer systems configured with executable instructions (e.g., computer programs, one or more computer programs, or one or more applications) to perform the processes of the application. The computer programs include machine instructions, which can be executed by one or more processors.

[0056] Further, the methods can be implemented in any type of computing platform operably connected to any suitable type of computing platform, including but not limited to a personal computer, mini-computer, mainframe, workstation, networked or distributed computing environment, separate or integrated computer platforms, or in communication with charged particle tools or other imaging devices, and the like. Aspects of the present application can be implemented in machine readable code stored on a non-transitory storage medium or device, whether removable or integrated into a computing platform, such as a hard disk, optical read and / or write storage media, RAM, ROM, and the like, such that it can be read by a programmable computer to configure and operate the computer to perform the processes described herein when the storage medium or device is read by the computer. Further, the machine readable code, or portions thereof, can be transmitted over a wired or wireless network. The present application described herein includes these and other different types of non-transitory computer readable storage media when such media include instructions or programs that implement the steps described above in conjunction with a microprocessor or other data processor. The present application also includes the computer itself when programmed in accordance with the methods and techniques described herein. The computer program is capable of applying to input data to perform the functions described herein, thereby transforming the input data to generate output data that is stored to non-volatile memory. The output information can also be applied to one or more output devices, such as a display. In a preferred embodiment of the present application, the transformed data represents a physical and tangible object, including a particular visual depiction of a physical and tangible object produced on a display.

[0057] Example 2

[0058] To verify the effect of the fast target detection method based on depth separable convolution, the present application uses the stochastic gradient descent (SGD) method to optimize the detection network. When training the network model for a specific data set, the detection network is trained in two steps:

[0059] First, the base network part needs to be pre-trained in the classification task, that is, the detection network is removed from the feature pyramid part, and then a softmax classification layer is added behind stage6. For example, it can be fully trained in the classic ImageNet image classification challenge, so that the parameters of the base network part can learn the basic visual features of the image;

[0060] Then continue to fine-tune the training on the specific data set using the pre-trained base network part. Since the detection network designed in the present application is a lightweight network and is not easy to overfit, more attention needs to be paid to the underfitting problem of the model, so the number of iterations needs to be considered more than the general detection network during fine-tuning training. It is recommended that the number of iterations be about 8000 times the number of detection categories.

[0061] During the fine-tuning training process, the accuracy of the model needs to be tested on the validation set in a timely manner, and the model with the best accuracy is saved as the training

[0062] The trained detection network needs to be preprocessed when applied in actual scenarios,

[0063] including image size scaling to 320*320, then image normalization, normalizing the image to zero mean and variance of 1, and then binarizing the image according to the following formula:

[0064]

[0065] where D p is the pixel gray value of the image after binarization, and dp is the pixel gray value of the image collected by the camera;

[0066] Further, the image is enhanced by cross double filtering:

[0067]

[0068] ω(p)=∑ q∈Ω s(||p-q||)r(|I(q)-I(p)|)c(q)

[0069] where D` is the input image, p is the input pixel value, D is the output image, q is the output pixel value, Ω is the set of pixels around p, ω(p) is the normalization parameter, s is the spatial filter kernel, r is the range filter kernel, I is the estimation object, and c is the edge value.

[0070] Then input the preprocessed image into the detection network for forward propagation inference to obtain detection results at each scale. Many of these detection results are repeated, so non-maximum suppression is used as a post-processing algorithm to filter out repeated results. For example, the detection result is as followsFigure 3 The schematic diagram shows that the method can accurately identify the target, and the total detection time of the target is 0.825 seconds.

[0071] To verify that the method can quickly and accurately identify the target, the following selects the traditional convolutional neural network and the method to identify the target vehicle.

[0072] The experiment uses a 480*720 pixel camera to collect, and runs two methods on the python platform respectively for testing, and the test results are shown in the following table.

[0073] Table 2: Comparison of results of identifying 10 target vehicles by using traditional convolutional neural network algorithm and the method respectively.

[0074] Method Successful vehicle identification Total identification time Conventional convolutional neural network algorithm 8 vehicles 9.35s The present method 10 vehicles 8.58s

[0075] It can be seen that the recognition time of the embodiment is improved by 8% than the traditional convolutional network, and 10 target vehicles can be completely identified.

[0076] As used in this application, the terms "component," "module," "system" and the like are intended to refer to a computer-related entity, either hardware, firmware, a combination of hardware and software, software, or software in execution. For example, a component can be, but is not limited to being, a process running on a processor, a processor, an object, an executable, a thread of execution, a program, and / or a computer. By way of illustration, both an application running on a computing device and the computing device can be a component. One or more components can reside within a process and / or thread of execution and a component can be localized, partially and / or entirely, in one computer or distributed between two or more computers. In addition, these components can execute from various computer readable media having various data structures stored thereon. The components can communicate by way of local and / or remote processes such as in accordance with a signal having one or more data packets (e.g., data from one component interacting with another component in a local system, distributed system, and / or across a network such as the Internet with other systems via the signal). The disclosure also contemplates a component that performs one or more tasks for the benefit of (and / or to facilitate) one or more other components.

[0077] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present application, not limit the present application. Although the present application has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present application can be modified or replaced by equivalent, without departing from the spirit and scope of the technical solutions of the present application, which should be covered in the scope of the claims of the present application.

Claims

1. A fast target detection method based on depthwise separable convolution, characterized in that: Multi-target detection applied to the field of automatic driving The method comprises the following steps, A fast target detection network based on deep separable convolution is constructed; The proposed detection network is trained on the training set using back propagation until the detection network converges; The trained detection network is used to detect test images; The final result is outputted; The fast target detection network comprises a base network part, a feature pyramid and a multi-target detection, four layers of features of different scales are used to detect targets of different scales, and the four layers of features are further fused to add deep features to shallow features; The base network part comprises a base network convolution list, the base network convolution list comprises a general convolution layer conv1, a deep separable convolution DwConv, and Block[5*5, 60, s1]*3 represents three basic convolution modules connected in series repeatedly; The base network convolution list further comprises six convolution layers stage1-stage6; In stage2-stage4, 5*5 convolution is applied, and in stage5-stage6 convolution layer, 3*3 deep separable convolution is used; A deep convolution of 5*5 is used to increase the receptive field range of the convolution layer, and two basic convolution modules are used for stage2 to extract sufficient image detail features; Four output features of stage3-stage6 are used for target detection; The theoretical receptive field size of the fast target detection network at four convolution feature layers is 139, 491, 715 and 1035 respectively, which is approximately 4 times the size of the current target scale, and sufficient image information can be extracted to complete target positioning and classification.

2. The fast object detection method based on depthwise separable convolution of claim 1, wherein: The method further comprises the following steps, A deep separable convolution with a step of 2 is used instead of maximum value pooling downsampling.

3. The fast object detection method based on depthwise separable convolution of claim 2, wherein: The multi-target detection part also uses deep separable convolution to output the position coordinates and category probability of the target, four layers of features are used for target prediction, and the basic scale sizes of the anchor points are 32, 64, 128 and 256 respectively, and the aspect ratio sizes of the anchor boxes are 1:1, 1:2 and 2:

1.

4. The fast object detection method based on depthwise separable convolution of claim 3, wherein: The detection network training comprises the following steps, The base network part is pre-trained in a classification task; A softmax classification layer is added behind stage6; The pre-trained base network part is used to continue fine-tuning training on a specific data set.

5. The fast object detection method based on depthwise separable convolution of claim 4, wherein: The picture detection comprises the following steps, The trained detection network is applied in an actual scene; Images collected by a camera are preprocessed; The image size is scaled to 320*320 and then the image is normalized; The image is normalized to zero mean and variance of 1; The preprocessed image is input into the detection network for forward propagation inference to obtain detection results at different scales.

6. The fast object detection method based on depthwise separable convolution of claim 5, wherein: The preprocessing comprises, The image is binarized according to the following formula: wherein D p is the pixel gray value of the image after the binarization processing, and dp is the pixel gray value of the image captured by the camera. The image is enhanced by cross double filtering.

7. The fast object detection method based on depthwise separable convolution of claim 6, wherein: The cross double filtering comprises, w(p)=∑s(|Ip-qI|)r(II(q)-I(p)I)c(q) q∈Ω Wherein, D' is the input image, p is the input pixel value, D is the output image, q is the output pixel value, Ω is the pixel set around p, w(p) is the normalization parameter, s is the spatial filter kernel, r is the range filter kernel, I is the estimation object, and c is the edge value.

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