CN115063434A - A low-low-light image instance segmentation method and system based on feature denoising - Google Patents
A low-low-light image instance segmentation method and system based on feature denoising Download PDFInfo
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Abstract
Description
技术领域technical field
本发明涉及一种在低弱光条件下对图像进行实例分割的方法和系统,具体涉及一种基于特征去噪的低弱光图像实例分割方法及系统,属于计算机视觉技术领域。The invention relates to a method and system for instance segmentation of images under low and low light conditions, in particular to a low and low light image instance segmentation method and system based on feature denoising, belonging to the technical field of computer vision.
背景技术Background technique
低弱光环境,即光线强度较低的环境,例如在夜间城市灯光、月光、星光条件下的环境等。在低弱光条件下采集的图像即为低弱光图像。此时,光线不足,图像传感器收集的光子较少,图像信号较弱,导致低弱光图像具有较强的噪声和较低的信噪比,场景信息丢失严重难以恢复。RAW图像是图像感应器将捕捉到的光源信号转化为数字信号的原始数据,是未经处理、未经压缩的格式。RAW图像相对于常用的JPEG格式的sRGB图像,保留了更多信息,具有更好的动态范围。Low low light environment, that is, the environment with low light intensity, such as the environment under night city lights, moonlight, starlight conditions, etc. An image captured under low-low-light conditions is a low-low-light image. At this time, the light is insufficient, the image sensor collects less photons, and the image signal is weak, resulting in low-low-light images with strong noise and low signal-to-noise ratio, and the scene information is seriously lost and difficult to recover. A RAW image is the raw data that the image sensor converts the captured light source signal into a digital signal, which is an unprocessed, uncompressed format. RAW images retain more information and have better dynamic range than sRGB images in the commonly used JPEG format.
实例分割,是一种能够从图像中提取语义信息的技术。该技术能够从自然光照条件下的图像中智能识别出感兴趣目标的类别、位置、大小和形状,并用类别标签、物体边界框,以及像素蒙版或多边形描述出来。该技术广泛用于图像编辑、智能安防、自动驾驶以及卫星图像判读,具有较高的实用价值和应用潜力。目前,主流的实例分割方法均基于深度学习和深度卷积神经网络,依赖于正常光图像数据集进行学习训练。由于缺少低弱光图像数据集以及相应的端到端方法和系统,导致其在应用于低弱光图像时,需要对图像进行去噪、增强等预处理。图像去噪,是指将带噪图像转换成干净图像,图像增强指将亮度较低的模糊图像转换从较亮的清晰图像。图像去噪、增强需要复杂的计算过程,从而增加了整个系统计算复杂度,且往往对低弱光图像效果较差,导致最终实例分割系统的速度、精度难以满足实际需要。Instance segmentation is a technique that can extract semantic information from images. The technology can intelligently identify the class, location, size, and shape of objects of interest from images under natural lighting conditions, and describe them with class labels, object bounding boxes, and pixel masks or polygons. This technology is widely used in image editing, intelligent security, autonomous driving and satellite image interpretation, and has high practical value and application potential. Currently, mainstream instance segmentation methods are based on deep learning and deep convolutional neural networks, and rely on normal light image datasets for learning and training. Due to the lack of low-low-light image datasets and corresponding end-to-end methods and systems, when it is applied to low-low-light images, it is necessary to perform image preprocessing such as denoising and enhancement. Image denoising refers to converting a noisy image into a clean image, and image enhancement refers to converting a blurred image with lower brightness from a brighter, clearer image. Image denoising and enhancement require complex calculation process, which increases the computational complexity of the entire system, and often has poor effect on low-low-light images, resulting in the speed and accuracy of the final instance segmentation system being difficult to meet the actual needs.
去噪是指降低信号中的噪声,提高信号信噪比的过程。由于低弱光图像具有较强的噪声,这些噪声会导致用于实例分割的深度卷积神经网络在对图像进行特征提取的过程中受到严重扰动。因此,网络浅层提取的图像特征具有明显高频噪声,深层网络提取的图像特征对感兴趣目标语义响应较低,最终使得无法准确提取感兴趣目标的实例分割结果。自适应特征去噪,即根据输入特征的噪声情况自适应地降低图像噪声所导致的图像特征扰动,在减少网络浅层提取特征的高频噪声的同时保留更多有效特征信号,提高深层网络特征对感兴趣目标的语义响应。Denoising refers to the process of reducing the noise in the signal and improving the signal-to-noise ratio of the signal. Since low-low-light images have strong noise, these noises can cause deep convolutional neural networks for instance segmentation to be severely perturbed in the process of feature extraction from images. Therefore, the image features extracted by the shallow layer of the network have obvious high-frequency noise, and the image features extracted by the deep network have a low semantic response to the target of interest, which ultimately makes it impossible to accurately extract the instance segmentation results of the target of interest. Adaptive feature denoising, that is, adaptively reducing the disturbance of image features caused by image noise according to the noise of the input features, while reducing the high-frequency noise of the shallow extracted features of the network, while retaining more effective feature signals, and improving the deep network features. Semantic responses to objects of interest.
发明内容SUMMARY OF THE INVENTION
本发明的目的从现有夜间低弱光场景的图像智能识别需求出发,针对实例分割技术在低弱光条件下存在的计算复杂度高、性能低等缺点,创造性地提出一种基于特征去噪的低弱光图像实例分割方法及系统。本发明实现了端到端的快速高性能低弱光图像实例分割,无需对低弱光图像进行复杂的去噪、增强预处理,降低整个实例分割的计算复杂度。The purpose of the present invention is to propose a feature-based denoising method based on the existing requirements for intelligent image recognition of low and low light scenes at night, aiming at the shortcomings of instance segmentation technology in low and low light conditions, such as high computational complexity and low performance. Low-low-light image instance segmentation method and system. The invention realizes end-to-end fast and high-performance low-low-light image instance segmentation, does not need to perform complex denoising and enhancement preprocessing on the low-low-light image, and reduces the computational complexity of the entire instance segmentation.
本发明采用以下技术方案实现。The present invention is realized by the following technical solutions.
一种基于特征去噪的低弱光图像实例分割方法,包括以下步骤:A low-low-light image instance segmentation method based on feature denoising, comprising the following steps:
步骤101:合成仿真低弱光图像数据集。Step 101: Synthesize a simulated low-low-light image dataset.
步骤102:使用噪声扰动抑制损失函数以及实例分割任务损失函数,对实例分割深度卷积网络进行训练。Step 102: Use the noise disturbance suppression loss function and the instance segmentation task loss function to train the instance segmentation deep convolutional network.
步骤103:用训练好的深度卷积神经网络,对低弱光图像进行特征提取和特征去噪。无需对低弱光图像进行预处理。Step 103: Use the trained deep convolutional neural network to perform feature extraction and feature denoising on the low-low-light image. No preprocessing is required for low-low-light images.
步骤104:利用训练好的检测分割子网络,在去噪后的特征上进行目标检测分割,得到最终实例分割结果。Step 104: Use the trained detection and segmentation sub-network to perform target detection and segmentation on the denoised features to obtain a final instance segmentation result.
为实现本发明所述目的,本发明进一步提出了一种基于特征去噪的低弱光图像实例分割系统,包括仿真低弱光图像合成模块、噪声扰动抑制学习模块、图像特征提取和特征去噪模块、目标检测分割提取模块。In order to achieve the purpose of the present invention, the present invention further proposes a low-low-light image instance segmentation system based on feature denoising, including a simulation low-low-light image synthesis module, a noise disturbance suppression learning module, image feature extraction and feature denoising. Module, target detection segmentation and extraction module.
有益效果beneficial effect
本发明方法及系统,与现有技术相比,具有以下优点:Compared with the prior art, the method and system of the present invention have the following advantages:
1.本方法不依赖额外的低弱光图像去噪、增强以及其他处理模块,训练过程端到端进行,实现简单、性能高、鲁棒性强。1. This method does not rely on additional low-low-light image denoising, enhancement and other processing modules. The training process is carried out end-to-end, with simple implementation, high performance and strong robustness.
2.本方法应对低弱光的额外计算量开销极低,有利于实现低延迟,高速度的低弱光实例分割。2. This method has extremely low extra computational overhead for dealing with low and low light, which is beneficial to realize low-latency, high-speed low-low light instance segmentation.
3.本方法可以降低低弱光图像数据生成成本。基于数据驱动的深度卷积神经网络图像实例分割方法需要大量低弱光图像数据,而传统低弱光图像数据集收集制作需要大量人力物力,本方法无需人工收集数据,只需要利用现有的自然图像数据集即可合成高质量仿真低弱光图像数据集。3. The method can reduce the cost of generating low-low-light image data. The data-driven deep convolutional neural network image instance segmentation method requires a large amount of low-low-light image data, while the collection and production of traditional low-low-light image datasets requires a lot of manpower and material resources. This method does not require manual data collection, and only needs to use existing natural The image dataset can be synthesized into a high-quality simulated low-low-light image dataset.
附图说明Description of drawings
图1是本发明方法的流程图。Figure 1 is a flow chart of the method of the present invention.
图2是本发明方法仿真低弱光图像合成以及训练过程中噪声扰动抑制学习方法示意图。FIG. 2 is a schematic diagram of the method of the present invention for simulating low-low-light image synthesis and the noise disturbance suppression learning method in the training process.
图3是本发明方法所述自适应特征去噪下采样层内部细节示意图。FIG. 3 is a schematic diagram of the internal details of the adaptive feature denoising downsampling layer according to the method of the present invention.
图4是本发明方法所述可学习的低通滤波卷积块示意图。FIG. 4 is a schematic diagram of a learnable low-pass filtering convolution block according to the method of the present invention.
图5是本发明系统的流程图。Figure 5 is a flow chart of the system of the present invention.
具体实施方式Detailed ways
为了更好的说明本发明的目的和优点,下面结合附图对发明内容做进一步说明。In order to better illustrate the purpose and advantages of the present invention, the content of the invention will be further described below with reference to the accompanying drawings.
一种基于特征去噪的低弱光图像实例分割方法,包括以下步骤:A low-low-light image instance segmentation method based on feature denoising, comprising the following steps:
步骤101:合成仿真低弱光图像数据集。Step 101: Synthesize a simulated low-low-light image dataset.
目前,基于学习的实例分割方法主要依赖于高质量的数据集实现良好的性能,而目前缺少公开的低弱光图像数据集,且收集制作适用于实例分割的真实低弱光图像数据集制作周期长成本高,因此,本发明考虑合成仿真低弱光图像数据集来训练实例分割模型,以降低低弱光图像实例分割数据集的制作成本。At present, the learning-based instance segmentation methods mainly rely on high-quality datasets to achieve good performance, and there is currently a lack of public low-low-light image datasets, and the collection and production of real low-low-light image datasets suitable for instance segmentation production cycle The long-term cost is high. Therefore, the present invention considers synthesizing the low-low-light image data set to train the instance segmentation model, so as to reduce the production cost of the low-low-light image instance segmentation data set.
仿真低弱光图像数据的制作如图2所示,首先,可以利用Unprocess操作,将普通自然光照RGB图像转换成RAW图像数据。然后,使用仿真噪声注入来模拟低弱光条件下图像中的噪声。其中,注入的仿真噪声可以使用高斯噪声模型、高斯泊松混合噪声模型以及全元物理量噪声模型等生成,优选使用全元物理量噪声模型。全元物理量噪声模型需要针对传感器特性标定,以得到散粒噪声、读出噪声、偏色噪声、随机行噪声等物理噪声分量,实现更真实的噪声模拟,有利于达到更好的低弱光图像实例分割效果。通过这两步,即可将大规模的自然光照图像数据转化为仿真低弱光图像数据。本提出的方法适用于多种类型的低弱光图像(RAW图像,sRGB图像等),优选RAW图像。The production of simulated low and low light image data is shown in Figure 2. First, the Unprocess operation can be used to convert ordinary natural light RGB images into RAW image data. Then, simulated noise injection was used to simulate the noise in the image in low low light conditions. Wherein, the injected simulation noise can be generated using a Gaussian noise model, a Gaussian Poisson mixed noise model, a full-element physical quantity noise model, etc., preferably the full-element physical quantity noise model is used. The full-element physical quantity noise model needs to be calibrated according to the sensor characteristics to obtain physical noise components such as shot noise, readout noise, color cast noise, random line noise, etc., to achieve more realistic noise simulation, and to achieve better low-low light images. Instance segmentation effect. Through these two steps, large-scale natural light image data can be transformed into simulated low-low light image data. The proposed method is suitable for many types of low-low-light images (RAW images, sRGB images, etc.), preferably RAW images.
步骤102:使用噪声扰动抑制损失函数以及实例分割任务损失函数,对实例分割深度卷积网络进行训练。如图2所示,适用实例分割模型(Mask R-CNN、HTC、Cascade Mask R-CNN、YOLACT、PointRend等)。Step 102: Use the noise disturbance suppression loss function and the instance segmentation task loss function to train the instance segmentation deep convolutional network. As shown in Figure 2, instance segmentation models (Mask R-CNN, HTC, Cascade Mask R-CNN, YOLACT, PointRend, etc.) are applied.
具体地,总损失函数L(θ)表示为:Specifically, the total loss function L(θ) is expressed as:
L(θ)=LIS(x;θ)+αLIS(x′;θ)+βLDS(x,x′;θ) (1)L(θ)=L IS (x; θ)+αL IS (x'; θ)+βL DS (x,x'; θ) (1)
其中,LIS、LDS分别表示实例分割任务损失函数、噪声扰动抑制损失函数;x、x′分别表示仿真干净图像和仿真带噪图像;θ为模型参数;α、β为损失函数权重。其中,LIS根据实例分割所使用的不同模型进行调整;LDS表示为:Among them, L IS and L DS represent the instance segmentation task loss function and noise disturbance suppression loss function respectively; x and x′ represent the simulated clean image and simulated noisy image respectively; θ is the model parameter; α and β are the weights of the loss function. Among them, L IS is adjusted according to the different models used for instance segmentation; L DS is expressed as:
其中,f(i)为实例分割网络f第(i)层提取的特征。LDS可以利用在干净图像提取的干净图像特征作为引导,使模型在带噪图像上提取的特征尽可能接近干净图像特征,从而降低低弱光图像中较高水平的噪声对网络特征提取的干扰,有利于实现鲁棒的低弱光图像实例分割。Among them, f (i) is the feature extracted by the (i)th layer of the instance segmentation network f. LDS can use the clean image features extracted on clean images as a guide to make the features extracted by the model on noisy images as close to clean image features as possible, thereby reducing the interference of higher levels of noise in low-low-light images on network feature extraction. , which is beneficial to achieve robust low-low-light image instance segmentation.
在整个训练过程中,无需对低弱光图像进行处理,实例分割网络的特征提取网络、检测分割子网络通过端到端的方式一次性训练完成。During the whole training process, there is no need to process low-light images, and the feature extraction network and detection and segmentation sub-network of the instance segmentation network are completed by one-time training in an end-to-end manner.
步骤103:用训练好的实例分割深度卷积神经网络对低弱光图像进行实例分割,且无需对低弱光图像进行预处理。Step 103: Use the trained instance segmentation deep convolutional neural network to perform instance segmentation on the low-low-light image, and the low-low-light image does not need to be preprocessed.
普通实例分割模型仅能够对图像进行特征提取,而低弱光图像中较高强度的噪声会给提取的图像特征引入高频噪声,进而导致最终对感兴趣目标较低的响应度。Ordinary instance segmentation models can only perform feature extraction on images, and high-intensity noise in low-low-light images will introduce high-frequency noise into the extracted image features, resulting in lower responsivity to the target of interest.
本方法首先对图像进行特征提取。在特征提取过程中,利用自适应特征去噪下采样层和可学习的低通滤波卷积块,对特征进行去噪。去噪后的特征大大降低了低弱光图像中较高水平噪声造成的特征扰动,并且自适应特征去噪下采样层带来的额外计算量较少,可学习的低通滤波卷积块不额外增加计算量,有利于实现低延迟鲁棒的低弱光图像实例分割。This method first extracts features from the image. During feature extraction, features are denoised using adaptive feature denoising downsampling layers and learnable low-pass filtered convolution blocks. The denoised features greatly reduce the feature perturbation caused by higher levels of noise in low-low-light images, and the adaptive feature denoising downsampling layer brings less additional computation, and the learnable low-pass filter convolution block does not. The additional computational cost is beneficial to realize low-latency and robust low-light image instance segmentation.
自适应特征去噪下采样层,通过在卷积神经网络下采样过程,充分利用局部特征进行加权平均,降低了特征中的噪声水平。The adaptive feature denoising downsampling layer, through the downsampling process of the convolutional neural network, makes full use of the local features for weighted averaging, reducing the noise level in the features.
为了在降低特征噪声的同时,保留更多的目标特征。如图3所示,自适应特征去噪下采样层会对特征图的每个通道、每个位置自适应地预测不同低通滤波。经过自适应低通滤波处理后和2倍下采样的特征即为去噪后的特征:In order to retain more target features while reducing feature noise. As shown in Figure 3, the adaptive feature denoising downsampling layer adaptively predicts different low-pass filters for each channel and each position of the feature map. The features after adaptive low-pass filtering and 2 times downsampling are the features after denoising:
其中,X、Y分别为输入特征图和去噪后的特征图;W为自适应下采样层根据输入特征图预测的加权权重;(c,i,j)表示在特征图通道维度、宽维度、高维度上的坐标;S表示空间位置(i,j)周围的位置;φ()表示自适应下采样层的权重预测函数,为保证输出的权重是低通的,权重预测函数将预测的权重经过softmax进行归一化;表示预测Wc,i,j所依赖的局部特征位置;GP()表示全局池化(Global Pooling)操作。p、q分别表示卷积核上的横向、纵向坐标。Among them, X and Y are the input feature map and the denoised feature map respectively; W is the weighted weight predicted by the adaptive downsampling layer according to the input feature map; (c, i, j) represents the channel dimension and wide dimension of the feature map. , coordinates in high dimensions; S represents the position around the spatial position (i, j); φ() represents the weight prediction function of the adaptive downsampling layer. In order to ensure that the output weight is low-pass, the weight prediction function will predict The weights are normalized by softmax; Represents the local feature position on which the prediction W c,i,j depends; GP() represents the global pooling (Global Pooling) operation. p and q represent the horizontal and vertical coordinates on the convolution kernel, respectively.
可学习的低通滤波卷积块通过显式地利用一个带有可学习的低通滤波分支来提高普通卷积层对特征噪声的鲁棒程度,其结构如图4所示,包含两个分支,一个是和普通卷积一样的分支,另一个是由可学习的低通滤波和1×1卷积组成的分支。可学习的低通滤波权重可以从训练中得到,并经过softmax函数归一化保证其为低通滤波,它能够对特征进行局部平滑来降低特征中的噪声水平,并且通过1×1卷积将去噪后的特征融合进普通卷积分支。同时,可学习的低通滤波卷积块可以利用重参数化技术在推理时变成普通卷积层,因而不增加任何计算量。所述重参数化,是将卷积神经网络中多个并行的分支通过参数融合转化为等价的单分支结构。本实施例中,可学习的低通滤波卷积块重参数化为单个3×3卷积层的参数,通过下式得到:The learnable low-pass filtering convolution block improves the robustness of ordinary convolutional layers to feature noise by explicitly utilizing a branch with a learnable low-pass filtering. Its structure is shown in Figure 4 and contains two branches. , one is the same branch as ordinary convolution, and the other is a branch consisting of learnable low-pass filtering and 1×1 convolution. The learnable low-pass filter weight can be obtained from training and normalized by the softmax function to ensure that it is a low-pass filter, which can locally smooth the feature to reduce the noise level in the feature, and pass the 1×1 convolution. The denoised features are fused into the normal convolution branch. At the same time, the learnable low-pass filtered convolutional blocks can be transformed into ordinary convolutional layers during inference using reparameterization techniques, thus not adding any computational effort. The re-parameterization is to convert multiple parallel branches in the convolutional neural network into an equivalent single-branch structure through parameter fusion. In this embodiment, the learnable low-pass filter convolution block is re-parameterized into the parameters of a single 3×3 convolution layer, which is obtained by the following formula:
W′3×3[h,t,p,q]=W3×3[h,t,h,t]+(W1×1[h,t,1,1]*WLLPF[1,t,p,q]) (5)W′ 3×3 [h,t,p,q]=W 3×3 [h,t,h,t]+(W 1×1 [h,t,1,1]*W LLPF [1,t ,p,q]) (5)
其中,W′3×3为将可学习的低通滤波卷积块重参数化后的卷积层参数, C1、C2分别表示卷积层输入通道数、输出通道数,R表示实数;为可学习的低通滤波卷积块中的普通3×3卷积层参数;为1×1卷积层参数;为可学习的低通滤波器参数,可学习的低通滤波器对每个输入通道共享一套3×3的权重;h、t分别表示在输出通道、输入通道的坐标,并且h∈{1,2,…,C2},t∈{1,2,…,C1};p、q分别表示卷积核的横向、纵向坐标,p、q∈{1,2,3}。Among them, W′ 3×3 is the convolution layer parameter after reparameterization of the learnable low-pass filter convolution block, C 1 and C 2 respectively represent the number of input channels and output channels of the convolution layer, and R represents a real number; are the common 3×3 convolutional layer parameters in the learnable low-pass filtered convolutional block; is a 1×1 convolutional layer parameter; is a learnable low-pass filter parameter, and the learnable low-pass filter shares a set of 3 × 3 weights for each input channel; h and t represent the coordinates of the output channel and input channel, respectively, and h∈{1 ,2,…,C 2 }, t∈{1,2,…,C 1 }; p and q represent the horizontal and vertical coordinates of the convolution kernel, respectively, p, q∈{1,2,3}.
步骤104:利用训练好的检测分割子网络,在去噪后的特征上进行目标检测分割,得到最终实例分割结果。Step 104: Use the trained detection and segmentation sub-network to perform target detection and segmentation on the denoised features to obtain a final instance segmentation result.
为实现本发明所述目的,本发明进一步提出了一种基于自适应特征去噪的端到端低弱光图像实例分割系统,如图5所示,包括仿真低弱光图像合成模块10、噪声扰动抑制学习模块20、图像特征提取和特征去噪模块30、目标检测分割提取模块40。In order to achieve the purpose of the present invention, the present invention further proposes an end-to-end low-low-light image instance segmentation system based on adaptive feature denoising, as shown in FIG. Disturbance suppression learning module 20 , image feature extraction and feature denoising module 30 , target detection segmentation extraction module 40 .
其中,仿真低弱光图像合成模块10,用于建立用于训练实例分割模型的仿真低弱光图像数据集。该模块可以将输入的自然光照图像数据集合成为仿真低弱光图像数据集。Among them, the simulated low and low light image synthesis module 10 is used to establish a simulated low and low light image data set for training the instance segmentation model. This module can assemble the input natural light image data into a simulated low and low light image data set.
噪声扰动抑制学习模块20,用于引导实例分割模型学习鲁棒的图像特征,使其能够降低低弱光图像中较高水平噪声造成的特征扰动。该模块利用仿真低弱光图像数据集使用噪声扰动抑制学习训练模型,输出得到训练好的实例分割模型。The noise disturbance suppression learning module 20 is used to guide the instance segmentation model to learn robust image features, so that it can reduce the feature disturbance caused by higher level noise in low and low light images. This module uses the simulated low and low light image data set to learn the training model using noise disturbance suppression, and outputs the trained instance segmentation model.
图像特征提取和特征去噪模块30,利用自适应的低通滤波降低实例分割网络中图像特征的噪声水平,在带噪的低弱光图像上提取出稳定干净的图像特征,以实现鲁棒的低弱光图像实例分割。The image feature extraction and feature denoising module 30 uses adaptive low-pass filtering to reduce the noise level of image features in the instance segmentation network, and extracts stable and clean image features on the noisy low-light image to achieve robust Instance segmentation of low-low-light images.
目标检测分割提取模块40,能够从去噪后的图像特征中识别提取出感兴趣目标的类别位置大小形状,得到最终的低弱光图像实例分割结果。The target detection, segmentation and extraction module 40 can identify and extract the category, position, size, and shape of the target of interest from the denoised image features, and obtain the final low-low-light image instance segmentation result.
上述模块之间的连接关系如下:The connection relationship between the above modules is as follows:
仿真低弱光图像合成模块10的输出端与噪声扰动抑制学习模块20的输入端相连。The output end of the simulated low and low light image synthesis module 10 is connected to the input end of the noise disturbance suppression learning module 20 .
噪声扰动抑制学习模块20的输出端与图像特征提取和特征去噪模块30的输入端相连。The output end of the noise disturbance suppression learning module 20 is connected to the input end of the image feature extraction and feature denoising module 30 .
图像特征提取和特征去噪模块30的输出端与目标检测分割提取模块40的输入端相连。The output end of the image feature extraction and feature denoising module 30 is connected to the input end of the target detection, segmentation and extraction module 40 .
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