Low-illumination image target detection method and device based on color channel conversion enhancement

Abstract

The invention discloses a low-illumination image target detection method and device based on color channel transformation enhancement, and belongs to the technical field of image processing and target detection, and the method comprises the steps: constructing an image target detection network based on color channel transformation enhancement, introducing learnable parameters into the network to transform pixel values of different color channels, carrying out image enhancement; calculating to obtain a detection result by using the enhanced image and the original image; and calculating the detection loss of the enhanced image and the original image, and judging whether to utilize regression loss to optimize the image enhancement process or not according to the detection loss. According to the method, the problem that the performance of a target detection algorithm is reduced due to factors such as low image contrast, fuzzy boundary and noise interference in a low-illumination scene is relieved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of image processing and target detection, and more particularly to a low-illumination image target detection method and device based on color channel transformation enhancement. BACKGROUND

[0002] Target detection, as an important basic task in the field of computer vision, aims to accurately identify target categories and location information from images, and plays an important role in automatic driving, environmental monitoring, national security and other fields. Due to the wide application demand and the continuous progress of software and hardware technology, deep learning-based target detection technology has attracted widespread attention from academia and industry, and has made great progress. However, the existing learning-based target detection algorithm is mainly optimized on standard datasets such as COCO and PASCAL VOC, and when processing low-illumination images such as night and backlight, the detection performance will be greatly reduced, thereby affecting the judgment ability and decision accuracy of the decision-making system.

[0003] In this context, it is of great theoretical value and practical significance to improve the robustness and generalization of detection algorithms in low-light scenes. Existing low-light enhancement networks can enhance low-light images to make them more consistent with human perception. However, the enhanced results inevitably differ from the actual high-light images in domain, and simply using the enhanced images for perception tasks cannot bring the best gain in visual perception tasks in low-light scenes. To address this problem, some researchers have tried to jointly optimize image enhancement and target detection networks during training. For example, Yin et al. proposed a pyramid enhancement network based on Laplace transform for target detection in low-light environments. Hashmi et al. proposed a feature enhancement method for target detection in low-light conditions, which enhances hierarchical features to improve detection performance. Some research also explores image adaptive solutions. For example, IA-YOLO and GDIP use differentiable image adaptive processing modules to adaptively adjust image contrast, white balance, and perform dehazing, smoothing, sharpening, and other operations to cope with target detection tasks in adverse environments. ERUP-YOLO simplifies the classic image processing filter into a pixel-level filter based on Bezier curves and a kernel-based local filter, and does not need to customize the filter combination for specific data. These methods use detection loss to jointly optimize the image adaptive enhancement module and the target detection network, making the processed image more suitable for detection task perception. In addition, MAET and DAINet train the model on low-light synthetic datasets and use multi-task learning and domain adaptation, respectively, to enable the network to extract illumination-invariant information from input images, thereby improving the performance of low-light image target detection. Overall, the current optimization methods for low-light scene target detection have pre-trained image enhancement networks, joint optimization of image enhancement networks, illumination-invariant feature extraction, and other optimization methods, which have achieved significant results. However, they do not fully consider the differences between different color channels. In addition, most existing "enhancement-detection" algorithms use enhanced images for detection tasks, which do not fully utilize the information of the original input images.

[0004] Prior art documents related to the technical background of the present application: [1] Yin X, Yu Z, Fei Z, et al. Yin, Xiangchen, et al. PE-YOLO: Pyramidenhancement network for dark object detection[C] / / Proceedings of theInternational Conference on Artificial Neural Networks, 2023: 163-174. [2] Hashmi KA, Kallempudi G, Stricker D, Afzal MZ. Featenhancer: Enhancing hierarchical features for object detection and beyond under low-light vision [C] / / Proceedings of the IEEE / CVF International Conference on Computer Vision, 2023: 6725-6735. [3] Liu W, Ren G, Yu R, et al. Image-Adaptive YOLO for Object Detection in Adverse Weather Conditions [C] / / Proceedings of the AAAI Conference on Artificial Intelligence, 2022, 36(2): 1792-1800. [4] Kalwar S, Patel D, Aanegola A, et al. GDIP: Gated differentiable image processing for object detection in adverse conditions [C] / / Proceedings of IEEE International Conference on Robotics and Automation, 2023: 7083-7089. [5] Ogino Y, Shoji Y, Toizumi T et al. ERUP-YOLO: Enhancing Object Detection Robustness for Adverse Weather Condition by Unified Image-Adaptive Processing [EB / OL]. arXiv preprint arXiv:2411.02799, 2024. [6]Cui Z, Qi G, Gu L, et al. Multitask aet with orthogonal tangent regularity for dark object detection[C] / / Proceedings of the IEEE / CVF International Conference on Computer Vision, 2021: 2553-2562. [7]Du Z, Shi M, Deng J. Boosting object detection with zero-shot day-night domain adaptation[C] / / Proceedings of the IEEE / CVF Conference on Computer Vision and Pattern Recognition, 2024: 12666-12676。 SUMMARY

[0005] The present application aims to overcome the shortcomings of the prior art, and provides a low-illumination image target detection method and device based on color channel transformation enhancement, which improves the detection effect.

[0006] The purpose of the present application is achieved by the following scheme: A low-illumination image target detection method based on color channel transformation enhancement, comprising the following steps: Constructing an image target detection network based on color channel transformation enhancement, which introduces learnable parameters to transform different color channel pixel values, and then performs image enhancement; using the enhanced image and the original image to calculate the detection result; Calculate the detection loss of the enhanced image and the original image, and determine whether to optimize the image enhancement process using the regression loss according to the detection loss.

[0007] Further, the image target detection network based on color channel transformation enhancement includes a color channel transformation image enhancement network; The color channel transformation image enhancement network includes a color conversion module and an image enhancement network; The processing flow of the color conversion module includes: performing color channel transformation on an input image, applying nonlinear operation, combining learned weights with each channel data of the image, and finely adjusting each color channel pixel value; the processing flow of the image enhancement network includes: inputting the output result of the color conversion module into the enhancement network for enhancement, the enhancement network adopts a convolution network in the form of encoding and decoding, and for the input image, first passes through a three-layer convolution network to extract multi-scale image features, and then uses the extracted multi-scale features to obtain an enhanced image through decoding.

[0008] Further, the image target detection network based on color channel transformation enhancement includes a low-illumination image target detection network; a loss function for cooperative optimization of the enhancement network and the target detection network is established , including an original image detection loss, an enhanced image detection loss, and a selective regression loss, and is defined as: ; Wherein, is the detection loss of the original input image , is the detection loss of the enhanced image , is the selective self-supervised regression loss, is a balance coefficient.

[0009] Further, the detection loss is defined as: ; Wherein, , and are a target category loss, a position loss, and a confidence loss, respectively, is a weight parameter of different losses.

[0010] Further, the enhanced image detection loss and the original image detection loss are used as the evaluation criteria, if the enhanced image detection loss is less than the original image detection loss, it indicates that the enhanced model can make the detection effect better; otherwise, it indicates that the detection effect of the enhanced image is not as good as that of the original input image, and further optimization is still needed.

[0011] Further, when the detection effect of the enhanced image is not as good as that of the original image, the selective self-supervised regression loss introduces an L1 loss, uses the original image as a self-supervised signal, and further optimizes the image enhancement network, and the loss is represented as: ; Wherein, is the enhanced image, and represent the detection loss of the enhanced image and the original input image, respectively.

[0012] Further, the original image comprises a low-illumination image acquired in a manner of an imaging sensor or image synthesis.

[0013] Further, the method further comprises a step of: when acquiring the low-illumination image, labeling a position of a target of interest in the image and annotating a category, for training of the low-illumination image target detection network based on the color channel transformation enhancement.

[0014] Further, the low-illumination image target detection network based on the color channel transformation enhancement is based on YOLOv3.

[0015] A low-illumination image target detection device based on color channel transformation enhancement comprises a processor and a memory, and the memory stores a computer program, which, when loaded by the processor, executes the method according to any one of the above.

[0016] The beneficial effects of the present application include: (1) The present application alleviates the problem of performance degradation of target detection algorithms caused by low image contrast, blurred boundaries, noise interference and other factors in low-illumination scenes, proposes a technical concept of combining enhanced image features and jointly optimizing the enhancement and detection network to utilize the enhancement to empower the detection task, and improves the detection effect, which is suitable for low-illumination environments in security monitoring, intelligent driving, night work and other scenes, and overcomes the problem of performance degradation of target detection algorithms caused by low image contrast, blurred boundaries, noise interference and other factors in low-illumination scenes.

[0017] (2) The present application improves the flexibility of the enhancement strategy by designing a learnable color channel transformation enhancement module to obtain better detection features, and jointly optimizes the enhancement module and the detection network using a detection loss to enable the enhancement network to be optimized in a direction conducive to the detection task, and proposes a selective self-supervised regression loss to perform self-supervised regression optimization on the enhancement network according to the detection results, further improving the detection effect. BRIEF DESCRIPTION OF DRAWINGS

[0018] In order to more clearly illustrate the technical solutions of the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiment or prior art description. Obviously, the drawings in the following description are only some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained without creative labor.

[0019] Figure 1 FIG. 1 is a structural schematic diagram of a low-illumination image target detection network based on color channel transformation enhancement of the present application; Figure 2 FIG. 2 is a structural schematic diagram of a color channel transformation image enhancement network of the present application; Figure 3A schematic diagram of the workflow of the color channel transformation module; Figure 4 A comparison chart of the effects of the method of the present application and other existing methods. DETAILED DESCRIPTION

[0020] All features disclosed in the embodiments disclosed in the specification, or all steps in the methods or processes impliedly disclosed, can be combined and / or extended, replaced, unless mutually exclusive features and / or steps are otherwise indicated.

[0021] The specific implementation process of the present application is as follows: The present application aims to solve the following technical problems: the existing learning-based target detection algorithm is mainly optimized on standard data sets such as COCO and PASCAL VOC, and when processing low-illumination images such as night and backlight, the detection performance will be greatly reduced, thereby affecting the judgment ability and decision accuracy of the decision system.

[0022] In view of the above technical problems, the present application proposes the following ideas: based on color channel transformation enhancement to realize low-illumination image target detection, by jointly optimizing the enhancement and detection network, using enhancement processing to promote the detection task. By designing a learnable color channel transformation enhancement module, the flexibility of the enhancement strategy is improved, and better detection features are obtained; the detection loss is used to jointly optimize the enhancement module and the detection network, so that the enhancement network can be optimized in the direction conducive to the detection task; a selective self-supervised regression loss is proposed, and the enhancement network is optimized by self-supervised regression according to the detection result, so as to further improve the detection effect.

[0023] Furthermore, during the training phase, the present invention first adjusts the three color channels of the input image through a color conversion module, and then inputs them into an enhancement network to strengthen the image information representation. The enhanced image and the original image are then input into the detection network to obtain prediction results, and the detection loss is calculated to jointly optimize the detection network. This process uses the detection loss to jointly optimize both the enhancement network and the detection network, making the enhancement network more suitable for the detection network's perception. Finally, based on the detection loss of the enhanced image and the original image, it is determined whether to use regression loss to optimize the image enhancement network. During the inference phase, the trained enhancement network is first used to adaptively enhance the input image, making it more suitable for the detection network's perception. Then, the enhanced image is input into the detection network to obtain detection results including target category, location, and confidence level, achieving accurate identification and localization of targets in the image. The advantages of this scheme are that a color channel conversion step is introduced before the image enhancement module. By cleverly introducing learnable parameters to adjust the pixel values ​​of the three color channels of the input image for nonlinear transformation, the model's adaptability to different lighting conditions and scenes is greatly improved, giving the model more flexible adjustment space when dealing with complex and varied low-light images. At the same time, the selective self-supervised regression loss determines whether to calculate the regression loss for the original image and the enhanced image separately based on the detection results, which fully ensures that the enhanced image results closely match the inherent needs of the detection task, maximizes the role of the enhanced image in assisting the detection network, and thus improves the detection effect of low-light images.

[0024] In more specific implementation details, this invention designs a low-light image target detection network based on color channel transformation enhancement, and the above method operates based on this network. For example... Figure 1 As shown, the network includes the following functional networks: (1) a color channel transformation image enhancement network; and (2) a target detection network. The color channel transformation image enhancement network and the target detection network are co-optimized, and the color channel transformation image enhancement network is suitable for the fusion and collaboration of mainstream detection networks. The design ideas of the specific modules are introduced below: (1) Color Channel Transformation Image Enhancement Network Low-light images suffer from low contrast, blurred boundaries, and noise interference, all of which negatively impact detection performance. Therefore, a low-light image enhancement network is proposed for adaptive image enhancement, with the following structure: Figure 2 As shown. The low-light image enhancement network of the present invention includes a color conversion module and an image enhancement network composed of a convolutional network. The processing flow of the color conversion module is as follows. Figure 3 As shown. For the input image This module is Each of the three color channels is assigned a learnable weight. These weights are broadcast to the same dimensions as the image space to ensure compatibility with the image data. Then, the image pixel values are weighted by a non-linear operation. The specific process can be represented as: ; wherein, represents the pixel value of the input image in the color channel . row

[0025] After adjusting the image illumination curve by the color conversion module, the image is input into the enhancement network. The network structure is shown in Figure 2 , which adopts a convolutional network in the form of encoding and decoding. The specific network parameters are shown in Table 1, where C, K, and S represent the output channel number, the convolution kernel size, and the convolution step, respectively. For the input image, first, a three-layer convolutional network is used to extract multi-scale image features, and the specific process is as follows: ; wherein, represents a convolution module with a kernel of and a step of , represents a Relu activation function. represents the encoded multi-scale features, represents the feature space scale downsampling multiple.

[0026] The extracted multi-scale features are used for decoding to obtain the enhanced image . Specifically, first, the deep features are upsampled using deconvolution, then are concatenated along the channel dimension, and further convolution and ReLU activation function are used to extract and nonlinearly transform the fused features. Then, the above process is repeated to upsample the concatenated features using deconvolution, and then concatenate with the shallow features . Finally, a layer of convolutional network is used to fuse feature information and adjust the channel number to obtain the enhanced image. The above process can be represented by the formula: ; ; wherein, represents the feature concatenation along the channel dimension, represents the output feature of the decoding DCR module, refers to the deconvolution operation process.

[0027] Figure 1 ​In and is the detection loss of the original image, and is the detection loss of the enhanced image, is the selective self-supervised regression loss.

[0028] (2) Target detection network The low-light enhanced image is input into the target detection network for target detection and recognition to obtain target category, position, and other information. The structure of the target detection network is not strictly limited and can be applicable to mainstream end-to-end detection models. Unlike the establishment of conventional detection models, in order to make the enhanced network optimize in a direction more suitable for the perception of the detection network, the original image detection result is combined as an auxiliary to establish a loss function for the cooperative optimization of the enhanced network and the target detection network, including the original image detection loss, the enhanced image detection loss, and the selective regression loss, which are defined as follows: ; wherein, is the detection loss of the original input image , is the detection loss of the enhanced image , is the selective self-supervised regression loss. is the balance coefficient.

[0029] The detection loss can be defined as: ; wherein, , and are the target category loss, position loss, and confidence loss in the conventional detection, is the weight parameter of different losses.

[0030] The introduction of the selective self-supervised regression loss is to make the output result of the enhanced network more suitable for the subsequent detection task. Specifically, the detection loss of the enhanced image and the original image is used as the evaluation standard. If the detection loss of the enhanced image is less than that of the original image, it indicates that the enhanced model can make the detection effect better. Otherwise, it indicates that the detection effect of the enhanced image is not as good as that of the original input image and still needs to be further optimized. When the detection effect of the enhanced image is not as good as that of the original image, the selective self-supervised regression loss introduces the L1 loss, uses the original image as a self-supervised signal, and further optimizes the image enhancement network. The loss is represented as: ; wherein, is the enhanced image, and represent the detection loss of the enhanced image and the original input image, respectively.

[0031] The operation steps of the method of this invention based on the above-designed network are as follows: mainly including two parts: model training and model inference. The usage process is described in detail below: S1: Acquire a large number of low-light images and target labels through imaging sensors or image synthesis, and divide them into training set and test set; S2: Construct a low-light image target detection network based on color channel transformation enhancement, including a color channel transformation image enhancement network and an object detection network. The innovation of this network lies in the color channel transformation image enhancement network, which introduces learnable parameters to transform different color channels, improving the flexibility of the enhancement strategy and enhancing the model's adaptability to different lighting conditions and scenes. The workflow of the color channel transformation image enhancement network is as follows: 1) Input image Perform color channel transformation, apply non-linear calculations, and apply the learned weights. By combining the data from each channel of the image, the pixel values ​​of each color channel of the image are finely adjusted; 2) The output of the color conversion module is input into the enhancement network for enhancement. First, it passes through a three-layer convolutional network to extract multi-scale image features. Then, the enhanced image is obtained through decoding. .

[0032] S3: The low-light image target detection network based on color channel transformation enhancement is trained using the training set. The trained model can detect and recognize targets in input low-light images, obtaining information such as target category and location. Furthermore, the trained model is tested using test data. The innovation of the above detection model training lies in achieving a loss function that is collaboratively optimized between the enhancement network and the target detection network, including the original image detection loss. Enhanced image detection loss and selective regression loss Among them, the selective self-supervised regression loss determines whether it is necessary to calculate the regression loss separately for the original image and the enhanced image based on the detection results, ensuring that the enhanced image results closely match the inherent needs of the detection task and maximizing the role of the enhanced image in assisting the detection network.

[0033] In other embodiments of the present invention, a low-light image target detection method based on color channel transformation enhancement is provided according to a specific application scenario, and the method specifically performs the following steps: First, acquire low-light images, mark the locations of targets of interest in the images with rectangles and annotate their categories, and use this information to train a low-light image target detection model enhanced by color channel transformation.

[0034] Then, a low-illumination image target detection model based on color channel transformation enhancement is built. The environment required for model building and model training is prepared. In this embodiment, the coding and running environment of PyTorch is used to realize the low-illumination image target detection model based on color channel transformation enhancement. The model is based on an end-to-end target detection and recognition network structure, mainly composed of a backbone network, a connection neck, a detection head and the like. In this embodiment, YOLOv3 is used as the basic detection network.

[0035] Then, the three color channels of the input image are adjusted by the color conversion module, and the enhanced image information is input into the enhancement network. The color conversion module assigns learnable weights to the three color channels, and uses nonlinear operations to combine the weights and image channel data to weight the image pixel values, effectively optimizing the image color features and enhancing the model's adaptability to different lighting conditions and scenes. In this embodiment, the enhancement network structure and parameters are as shown in Table 1. Figure 2

[0036] Further, the enhanced image is input into the detection model for target detection, and the enhancement network and the detection network are jointly optimized through the detection loss, so that the enhancement processing better supports the detection task. In this embodiment, YOLOv3 is used as the basic detection model, and the training loss includes image detection loss, enhanced image detection loss and selective regression loss.

[0037] The labeled low-illumination image is input into the low-illumination image target detection model based on color channel transformation enhancement for training. In the base class model training stage, the YOLOv3 network pre-trained on the COCO dataset is used for optimization. The linear learning rate is used, and the initial learning rate is 0.01, and the last round is reduced to 0.001. The batch size is set to 8 in the first stage training, and the batch size is set to 1 in the second stage training. The SGD optimizer is used, the momentum hyperparameter is set to 0.937, the weight decay hyperparameter is set to 0.0005, and the input image size is fixed to 640x640. The trained model is saved, and the test image is input into the test to obtain the final target comprehensive detection and recognition result.

[0038] ​The low-illumination image target detection model based on color channel transformation enhancement fully and effectively utilizes the enhancement processing to support low-illumination target detection, introduces learnable parameters to transform different color channels, can improve the flexibility of the enhancement strategy, and jointly optimizes the enhancement module and the detection network, so that the enhancement network can be optimized in a direction conducive to the detection task, and based on the selective self-supervised regression loss, the detection result is used for self-supervised regression optimization of the enhancement network, and the detection effect is improved. For the problem of detection effect decline caused by low image contrast, blurred boundary and noise interference in low-illumination scene, the model can well solve the problem, such as Figure 4 As shown in the figure, C2TEOD is the result of the method of the application, and the others are the results of the comparison method. Among them, YOLOv3 is the basic detection algorithm, SCI-YOLOv3 uses the SCI image enhancement network to pre-process the image, thereby improving the image brightness. IAYOLO is a joint optimization of the image adaptive enhancement module and the detection network to improve the night image detection effect. YOLA enhances the robustness of the detection algorithm in the night scene by learning the illumination invariant feature representation.

[0039] Table 1. Enhancement network structure and parameter table

[0040] The units described in the embodiments of the application can be implemented in software or hardware, and the described units can also be arranged in a processor. In some cases, the names of these units do not constitute a limitation on the units themselves.

[0041] According to an aspect of the embodiments of the present application, a computer program product or computer program is provided, which includes computer instructions stored in a computer readable storage medium. The processor of the computer device reads the computer instructions from the computer readable storage medium, and the processor executes the computer instructions to make the computer device execute the methods provided in the various optional implementation manners described above.

[0042] As another aspect, the embodiments of the present application also provide a computer readable medium, which can be included in the electronic device described in the above embodiments, or can exist separately without being assembled into the electronic device. The computer readable medium carries one or more programs, which, when executed by the electronic device, make the electronic device implement the methods described in the above embodiments.

Claims

1. A low-light image target detection method based on color channel transformation enhancement, characterized in that, The method comprises the following steps: An image target detection network based on color channel transformation enhancement is constructed, which introduces learnable parameters to transform different color channel pixel values, and then performs image enhancement; A detection result is calculated using the enhanced image and the original image; A detection loss of the enhanced image and the original image is calculated, and whether to optimize the image enhancement process using a regression loss is determined according to the detection loss.

2. The low-light image object detection method based on color channel transformation enhancement of claim 1, wherein, The image target detection network based on color channel transformation enhancement comprises a color channel transformation image enhancement network. The color channel transformation image enhancement network comprises a color conversion module and an image enhancement network. The processing flow of the color conversion module comprises: performing color channel transformation on an input image, applying nonlinear operation, combining learned weights with image channel data, and finely adjusting each color channel pixel value of the image. The processing flow of the image enhancement network comprises: inputting the output result of the color conversion module into the enhancement network for enhancement, and the enhancement network adopts a convolution network in the form of encoding and decoding, which first extracts multi-scale image features through three convolution networks for the input image, and then obtains an enhanced image through decoding using the extracted multi-scale features.

3. The color channel transformation enhancement based low-light image object detection method according to any one of claims 1 or 2, characterized in that, The image target detection network based on color channel transformation enhancement comprises a low-illumination image target detection network; a loss function for cooperative optimization of the enhancement network and the target detection network is established , comprising an original image detection loss, an enhanced image detection loss and a selective regression loss, and is defined as: ； wherein, is a detection loss for the original input image is a detection loss for the enhanced image is a detection loss for the original input image is a detection loss for the enhanced image is a selective self-supervised recurrent loss, is a balancing coefficient.

4. The low-light image object detection method based on color channel transformation enhancement of claim 3, wherein, The detection loss is defined as: ； wherein, , and are target class loss, position loss and confidence loss, respectively, are weight parameters for different losses.

5. The low-light image object detection method based on color channel transformation enhancement of claim 4, wherein, The detection loss of the enhanced image and the original image is used as a judgment standard, if the detection loss of the enhanced image is less than that of the original image, it indicates that the enhanced model can make the detection effect better, otherwise it indicates that the detection effect of the enhanced image is not as good as that of the original input image, and further optimization is still needed.

6. The low-light image object detection method based on color channel transformation enhancement of claim 5, wherein, When the detection effect of the enhanced image is not as good as that of the original image, the selective self-supervised regression loss is introduced, the original image is used as a self-supervised signal to further optimize the image enhancement network, and the loss is represented as: ； wherein, is the enhanced image, and respectively denote the detection loss for the enhanced image and the original input image.

7. The low-light image object detection method based on color channel transformation enhancement of claim 1, wherein, The original image comprises a low-light image obtained by an imaging sensor or image synthesis.

8. The low-light image target detection method based on color channel transformation enhancement of claim 7, wherein, Further comprising the step of: when obtaining a low-light image, labeling the position of a target of interest in the image and annotating the category, for training of the low-light image target detection network based on color channel transformation enhancement.

9. The low-light image object detection method based on color channel transformation enhancement of claim 8, wherein, The low-light image target detection network based on color channel transformation enhancement is realized based on YOLOv3.

10. A low-illumination image target detection device based on color channel transformation enhancement, characterized in that, A processor and a memory are included, and the memory stores a computer program, when the computer program is loaded by the processor, the method of any one of claims 1-9 is executed.

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