CN106815596A - A kind of Image Classifier method for building up and device - Google Patents
A kind of Image Classifier method for building up and device Download PDFInfo
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- G06F18/21—Design or setup of recognition systems or techniques; Extraction of features in feature space; Blind source separation
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Abstract
The invention discloses a kind of Image Classifier method for building up and device, including:Samples pictures collection is obtained, samples pictures are concentrated comprising the positive sample containing target image and the negative sample without target image;Deformation process is carried out to the samples pictures that samples pictures are concentrated, the samples pictures collection after being expanded;According to the samples pictures collection after expansion and depth convolutional neural networks model, the grader for target image is obtained;Wherein, the output in depth convolutional neural networks model to convolutional layer is normalized.By the above method, only need the samples pictures collection that manual identification is limited, limited samples pictures collection is expanded again afterwards, so as to expand sample size, the accuracy of grader is improve, additionally, further increasing the accuracy of identification of grader using depth convolutional neural networks model, therefore, this programme can provide a kind of accuracy of identification the grader for target image higher.
Description
Technical field
The present invention relates to field of computer technology, more particularly to a kind of Image Classifier method for building up and device.
Background technology
Mark (LOGO) identification is one kind of image recognition, and whether target is included by feature contrast judgement image
LOGO, this is very important one side for enterprise's merchandise control, and enterprise trademark is judged for example, being recognized by LOGO
Whether falsely used by other people, recognized by LOGO and judge all many-sides such as the type of merchandise.
It is many for LOGO identifications using by the artificial method extracted feature, then train grader at present.But it is artificial
It is characterized in artificially to specify that the method for extraction is extracted to LOGO, for the identification of machine, it is understood that there may be the feelings such as coverage rate deficiency
Condition, further, since LOGO features need artificial extraction, allows for that during training grader sufficiently large Sample Storehouse cannot be obtained, because
The grader that this is obtained is not high for the accuracy rate of image recognition, has no idea to reach practical purpose.
To sum up, a kind of Image Classifier based on LOGO identifications of high-accuracy is still lacked at present.
The content of the invention
The present invention provides a kind of Image Classifier method for building up and device, be used to provide a kind of high-accuracy based on target
The Image Classifier of image recognition.
The embodiment of the present invention provides a kind of Image Classifier method for building up, including:
Samples pictures collection is obtained, samples pictures are concentrated comprising the positive sample containing target image and the negative sample without target image
This;
Deformation process is carried out to the samples pictures that samples pictures are concentrated, the samples pictures collection after being expanded;
According to the samples pictures collection after expansion and depth convolutional neural networks model, the classification for target image is obtained
Device;Wherein, the output in depth convolutional neural networks model to convolutional layer is normalized.
Alternatively, deformation process, including at least one of are carried out to the samples pictures that samples pictures are concentrated:
Mirror image switch, rotation, random cropping, brightness adjustment.
Alternatively, including:
Depth convolutional neural networks model is Googlenet models;
According to the samples pictures collection after expansion and depth convolutional neural networks model, the classification for target image is obtained
Device, including:
By in the Googlenet models of samples pictures input initialization;
Propagated forward obtains the loss function loss values of Googlenet models;
Googlenet model parameters are updated according to the backpropagation of loss values, until the loss values of Googlenet models meet
It is pre-conditioned, obtain the grader for target image.
Alternatively, the output in depth convolutional neural networks model to convolutional layer is normalized, including:
Output valve to every layer of convolutional layer in depth convolutional neural networks model is normalized.
The embodiment of the present invention provides a kind of image of the Image Classifier that method of offer according to embodiments of the present invention is set up
Recognition methods, including:
Obtain picture to be identified;
By picture to be identified be input into grader, obtain picture to be identified whether the classification results comprising target image.
The embodiment of the present invention provides a kind of Image Classifier and sets up device, including:
Acquisition module, for obtaining samples pictures collection, samples pictures are concentrated comprising the positive sample containing target image and are free of
The negative sample of target image;
Enlargement module, the samples pictures for being concentrated to samples pictures carry out deformation process, the sample graph after being expanded
Piece collection;
Processing module, for according to the samples pictures collection after expansion and depth convolutional neural networks model, obtaining and being directed to mesh
The grader of logo image;Wherein, the output in depth convolutional neural networks model to convolutional layer is normalized.
Alternatively, enlargement module, the samples pictures specifically for being concentrated to samples pictures carry out at least one following change
Shape treatment:Mirror image switch, rotation, random cropping, brightness adjustment.
Alternatively, the depth convolutional neural networks model that processing module is used is Googlenet models;
Processing module specifically for:
By in the Googlenet models of samples pictures input initialization;
Propagated forward obtains the loss function loss values of Googlenet models;
Googlenet model parameters are updated according to the backpropagation of loss values, until the loss values of Googlenet models meet
It is pre-conditioned, obtain the grader for target image.
Alternatively, processing module, specifically for the output valve to every layer of convolutional layer in depth convolutional neural networks model
It is normalized.
The embodiment of the present invention provides a kind of pattern recognition device, including:
Acquisition module, for obtaining picture to be identified;
Processing module, the grader for picture to be identified to be input into target image, obtains whether picture to be identified includes
The classification results of target image, wherein, the grader of target image is set up by Image Classifier provided in an embodiment of the present invention and filled
Put and obtain.
In sum, a kind of Image Classifier method for building up and device are the embodiment of the invention provides, including:Obtain sample
Pictures, samples pictures are concentrated comprising the positive sample containing target image and the negative sample without target image;To samples pictures collection
In samples pictures carry out deformation process, the samples pictures collection after being expanded;According to samples pictures collection and depth after expansion
Convolutional neural networks model, obtains the grader for target image;Wherein, to convolutional layer in depth convolutional neural networks model
Output be normalized.By the above method, the samples pictures collection that manual identification is limited is only needed, afterwards again to limited
Samples pictures collection is expanded, and so as to expand sample size, improves the accuracy of grader, additionally, using depth convolution
Neural network model further increases the accuracy of identification of grader, therefore, it is higher that this programme can provide a kind of accuracy of identification
The grader for target image.
Brief description of the drawings
Technical scheme in order to illustrate more clearly the embodiments of the present invention, below will be to that will make needed for embodiment description
Accompanying drawing is briefly introduced, it should be apparent that, drawings in the following description are only some embodiments of the present invention, for this
For the those of ordinary skill in field, without having to pay creative labor, it can also be obtained according to these accompanying drawings
His accompanying drawing.
Fig. 1 is a kind of Image Classifier method for building up schematic flow sheet provided in an embodiment of the present invention;
Fig. 2 is a kind of Googlenet model structures schematic diagram provided in an embodiment of the present invention;
Fig. 3 is a kind of image-recognizing method flow chart provided in an embodiment of the present invention;
Fig. 4 sets up apparatus structure schematic diagram for a kind of Image Classifier provided in an embodiment of the present invention;
Fig. 5 is a kind of pattern recognition device structural representation provided in an embodiment of the present invention.
Specific embodiment
In order that the object, technical solutions and advantages of the present invention are clearer, below in conjunction with accompanying drawing the present invention is made into
One step ground is described in detail, it is clear that described embodiment is only some embodiments of the invention, rather than whole implementation
Example.Based on the embodiment in the present invention, what those of ordinary skill in the art were obtained under the premise of creative work is not made
All other embodiment, belongs to the scope of protection of the invention.
Fig. 1 is a kind of Image Classifier method for building up schematic flow sheet provided in an embodiment of the present invention, as shown in figure 1, bag
Include following steps:
S101:Samples pictures collection is obtained, samples pictures are concentrated comprising the positive sample containing target image and without target image
Negative sample;
S102:Deformation process is carried out to the samples pictures that samples pictures are concentrated, the samples pictures collection after being expanded;
S103:According to the samples pictures collection after expansion and depth convolutional neural networks model, obtain for target image
Grader;Wherein, the output in depth convolutional neural networks model to convolutional layer is normalized.
In specific implementation process, target image is a fixed image, and the possible irregular, color and luster of form of the image can
Can be unintelligible etc..Target image can be the diversified forms such as logo, registration mark, certification mark, image artifacts.For
Whether the identification of target image refers to judging in picture to be identified comprising target image.
In the specific implementation process of step S101, the mode and channel for obtaining samples pictures collection be not restricted, can be with
The acquisition samples pictures collection from internet is crawled by network, it is also possible to obtain samples pictures collection by way of artificial shooting,
Can also be obtained by other channels or mode, more multiple channel or mode can be combined to obtain enough samples
This picture is constituting samples pictures collection.In the samples pictures of samples pictures collection, the existing samples pictures comprising target image have again
Samples pictures not comprising target image.The grader of recognizable object image can be so obtained, such as comprising target image, point
Class device output 1, not comprising target image, grader output 0.Alternatively, samples pictures collection is manually marked, by sample graph
Piece collection is divided into the positive sample comprising target image and the negative sample not comprising target image.Alternatively, for the artificial mark of positive sample
It is 1 to note, and 0 is manually labeled as negative sample.Table one is a kind of annotation list provided in an embodiment of the present invention, as shown in Table 1,
Title and its corresponding path and markup information that samples pictures concentrate each samples pictures are have recorded in table one, wherein, path is used
To represent the storage location of samples pictures, mark is used for distinguishing samples pictures for positive sample or negative sample, such as Pic1 in table 1,
Its storage location is D:A B include target image in Pictures1, and Pic1, be one so its markup information is 1
Positive sample.
Table 1
Picture | Path | Mark |
… | … | … |
Pic1 | D:\A\B\Pictures1 | 1 |
Pic2 | D:\A\B\Pictures2 | 0 |
Pic3 | D:\A\B\Pictures3 | 1 |
… | … | … |
In the specific implementation process of step S102, deformed come exptended sample pictures by samples pictures.Can
The samples pictures that samples pictures are concentrated are carried out deformation process, including at least one of by selection of land:It is mirror image switch, rotation, random
Cutting, brightness adjustment.The grader that ensure that acquisition by exptended sample pictures is carrying out the accuracy of picture recognition.Need to refer to
Go out, should be tried one's best during deforming to samples pictures and avoid changing samples pictures mark feature, if i.e. sample
Picture contains target image, then the situation not comprising target image is sent out in the picture for avoiding being obtained after deformation process that should try one's best
It is raw, for example, only the samples pictures to the centrally located part of target image carry out cutting out treatment at random, without going to cut target image
Positioned at the samples pictures of marginal position.Mirror image switch and rotation process can't typically change the mark feature of samples pictures, because
This can carry out mirror image switch and selection operation to all of samples pictures.Brightness is excessively bright or can secretly influence subsequent pictures feature excessively
Extraction, therefore samples pictures only moderate to original brightness carry out brightness adjustment treatment.Alternatively, for the expansion of training set
The combination of various deformation treatment is should be to increase the picture categories of samples pictures concentration.By aforesaid operations, can be in original sample
The size of exptended sample pictures on the basis of this pictures, additionally, the mark for being to try to avoid changing original picture in expansion
Feature increased grader and set up efficiency from without manually being marked again to the Large Copacity sample set after expansion, reduce
Artificial and time cost.
In the specific implementation process of step S103, according to the samples pictures collection after expansion and depth convolutional neural networks mould
Type, obtains the grader for target image, and depth convolutional neural networks model here can be Googlenet models;Root
According to the samples pictures collection after expansion and depth convolutional neural networks model, the grader for target image is obtained, including:By sample
In the Googlenet models of this picture input initialization;Propagated forward obtains the loss function loss values of Googlenet models;
Googlenet model parameters are updated according to the backpropagation of loss values, until the loss values of Googlenet models meet default bar
Part, obtains the grader for target image.Certainly, the embodiment of the present invention can also use other depth convolutional neural networks moulds
Type.Deep learning classifier training has many models it is achieved that typical network architecture has:Alex network
(Alexnet) model, VGG models, Googlenet models, residual error network (Resnet) model, Alexnet models are easier to instruction
Get but final discrimination is not high enough;Other three kinds of network layers are deeper, and VGG model depths are 19 layers, Googlenet models
Depth is 22 layers, Resnet model depths are 152 layers, thus discrimination is more preferably, but is not easy training;VGG models and Resnet
The very big video card video memory of the training need of model, and Googlenet models are without Googlenet models show in limited
Just can realize preferably discrimination under the conditions of card video memory, and Googlenet models network parameter minimum about 50M, and VGG moulds
The network parameter of type is 500M, and the network parameter of Resnet models is 100M, and Googlenet models are more suitable for follow-up system portion
Administration.
Fig. 2 is a kind of Googlenet model structures schematic diagram provided in an embodiment of the present invention, as shown in Fig. 2
Googlenet models include 1 convolution module, 9 starting inception modules, 3 softmax modules, wherein, every 3
One softmax module of inception wired in parallel.Table 2 is the Googlenet model parameter presets shown in Fig. 2, such as He of table 2
Shown in Fig. 2, preceding two groups of convolution (conv) parameter and the parameter that maximum pond (maxpool) parameter is convolution module in Fig. 2 in table 2,
Afterwards for 9 inception parameters and its between maximum pond parameter, the effect in maximum pond is to reduce model dimension.
Table 2
As shown in Fig. 2 every 3 inception modules are connected with a softmax module, the effect master of softmax modules
If during model training, loss function (loss) value of detection model, the effect of the first two softmax is to prevent
Depth is too deep, and last softmax module is to the problem that can not accurately be detected compared with shallow-layer module.
Alternatively, before model training, the samples pictures collection of acquisition is divided into training set, checking collection in proportion and is tested
Collection, ratio here can empirically or actual demand is determined.Training set is used to train grader, and checking collection is for verifying
Whether model restrains, and test set is used for the discrimination of the grader for testing last acquisition.Alternatively, the species of test set picture should
Relatively checking collection more horn of plenty, the confidence level of such test result is just enough high.
Alternatively, also needed to initialize Google models before model training, first for parameter to be trained is assigned
One initial value, alternatively, training ginseng is treated in using standard deviation for 0.1 Ze Weier (Xavier) algorithm random initializtion model
Number, it can be ensured that model can finally restrain.
Alternatively, by training set and (batch) treatment in batches of checking collection, such as training batch is 256, and checking batch is
64.The detailed process for carrying out classifier training using Googlenet models as shown in Figure 2 is:Propagated forward, by training set
The samples pictures of one batch are input into Googlenet models after being normalized to fixed size, after circulation input preset times, such as follow
Ring is input into 1000 times, obtains sorter model now, by a checking batch input for batch sorter model now,
Circulation input preset times, such as 100 times, the predicted value of acquisition sorter model output, and and actual comparison, obtain this time-division
The loss values and accuracy rate of class device model;Afterwards, judge whether the loss values and accuracy rate of sorter model restrain, if not
Convergence, then proceed backpropagation, using gradient descent method according to the size more new model weights of gradient and learning rate;Update
After weights, change next group training batch and repeat propagated forward and backpropagation until loss values and accuracy rate tend towards stability;Sentence
Whether loss values after disconnected stabilization are less than default loss threshold values and whether accuracy rate is higher than default accuracy rate threshold value, if it is not,
Then sorter model failure to train, need to change training pattern, if so, then continuing to judge whether learning rate now is higher than default
Learning rate threshold value;If so, then returning to training set sample input step, above-mentioned circulation is repeated, if it is not, then exporting grader now
Model, that is, obtain target image grader.Alternatively, loss values herein are the loss that three softmax modules are obtained respectively
The weight calculation result of value, the softmax module numbers of plies are deeper, and its weight is higher, for example, being surveyed for the softmax of most shallow-layer
The loss values for obtaining, weight during its calculating is 0.3, and weight during for its calculating of middle softmax modules is 0.3, for
The softmax modules of bottommost layer, weight during its calculating is 1.
Alternatively, the output valve to every layer of convolutional layer in depth convolutional neural networks model is normalized.Can
Trained with acceleration model and restrained, improve discrimination.
Fig. 3 is a kind of image-recognizing method flow chart provided in an embodiment of the present invention, and module used by image recognition is through upper
The target image grader of embodiment acquisition is stated, as shown in figure 3, comprising the following steps:
S301:Obtain picture to be identified;
S302:By picture to be identified be input into grader, obtain picture to be identified whether the classification results comprising target image.
In sum, a kind of Image Classifier method for building up is the embodiment of the invention provides, including:Obtain samples pictures
Collection, samples pictures are concentrated comprising the positive sample containing target image and the negative sample without target image;Samples pictures are concentrated
Samples pictures carry out deformation process, the samples pictures collection after being expanded;According to samples pictures collection and depth convolution after expansion
Neural network model, obtains the grader for target image;Wherein, to the defeated of convolutional layer in depth convolutional neural networks model
Go out to be normalized.By the above method, the samples pictures collection that manual identification is limited is only needed, afterwards again to limited sample
Pictures are expanded, and so as to expand sample size, improve the accuracy of grader, additionally, using depth convolutional Neural
Network model further increases the accuracy of identification of grader, therefore, this programme can provide a kind of accuracy of identification pin higher
To the grader of target image.
Based on identical technology design, the embodiment of the present invention also provides a kind of Image Classifier and sets up device, and the device can
Perform above method embodiment.Fig. 4 sets up apparatus structure schematic diagram for a kind of Image Classifier provided in an embodiment of the present invention, such as
Shown in Fig. 4, setting up device 400 includes:Acquisition module 401, enlargement module 402 and processing module 403, wherein:
Acquisition module 401, for obtaining samples pictures collection, samples pictures concentration is comprising the positive sample containing target image and not
Negative sample containing target image;
Enlargement module 402, the samples pictures for being concentrated to samples pictures carry out deformation process, the sample after being expanded
Pictures;
Processing module 403, for according to the samples pictures collection after expansion and depth convolutional neural networks model, being directed to
The grader of target image;Wherein, the output in depth convolutional neural networks model to convolutional layer is normalized.
Alternatively, enlargement module 402, the samples pictures specifically for being concentrated to samples pictures carry out at least one following
Deformation process:Mirror image switch, rotation, random cropping, brightness adjustment.
Alternatively, the depth convolutional neural networks model that processing module 403 is used is Googlenet models;
Processing module 403 specifically for:
By in the Googlenet models of samples pictures input initialization;
Propagated forward obtains the loss function loss values of Googlenet models;
Googlenet model parameters are updated according to the backpropagation of loss values, until the loss values of Googlenet models meet
It is pre-conditioned, obtain the grader for target image.
Alternatively, processing module 403, specifically for the output to every layer of convolutional layer in depth convolutional neural networks model
Value is normalized.
Based on identical technology design, the embodiment of the present invention also provides a kind of pattern recognition device, on the device is executable
State image-recognizing method embodiment.Fig. 5 is a kind of pattern recognition device structural representation provided in an embodiment of the present invention, such as Fig. 5
Shown, identifying device 500 includes:Acquisition module 501 and processing module 502, wherein:
Acquisition module 501, for obtaining picture to be identified;
Processing module 502, the grader for picture to be identified to be input into target image, obtains whether picture to be identified wraps
Classification results containing target image, wherein, the grader of target image is set up by Image Classifier provided in an embodiment of the present invention
Method is obtained.
In sum, a kind of Image Classifier method for building up and device are the embodiment of the invention provides, including:Obtain sample
Pictures, samples pictures are concentrated comprising the positive sample containing target image and the negative sample without target image;To samples pictures collection
In samples pictures carry out deformation process, the samples pictures collection after being expanded;According to samples pictures collection and depth after expansion
Convolutional neural networks model, obtains the grader for target image;Wherein, to convolutional layer in depth convolutional neural networks model
Output be normalized.By the above method, the samples pictures collection that manual identification is limited is only needed, afterwards again to limited
Samples pictures collection is expanded, and so as to expand sample size, improves the accuracy of grader, additionally, using depth convolution
Neural network model further increases the accuracy of identification of grader, therefore, it is higher that this programme can provide a kind of accuracy of identification
The grader for target image.
The present invention is the flow with reference to method according to embodiments of the present invention, equipment (system) and computer program product
Figure and/or block diagram are described.It should be understood that every first-class during flow chart and/or block diagram can be realized by computer program instructions
The combination of flow and/or square frame in journey and/or square frame and flow chart and/or block diagram.These computer programs can be provided
The processor of all-purpose computer, special-purpose computer, Embedded Processor or other programmable data processing devices is instructed to produce
A raw machine so that produced for reality by the instruction of computer or the computing device of other programmable data processing devices
The device of the function of being specified in present one flow of flow chart or multiple one square frame of flow and/or block diagram or multiple square frames.
These computer program instructions may be alternatively stored in can guide computer or other programmable data processing devices with spy
In determining the computer-readable memory that mode works so that instruction of the storage in the computer-readable memory is produced and include finger
Make the manufacture of device, the command device realize in one flow of flow chart or multiple one square frame of flow and/or block diagram or
The function of being specified in multiple square frames.
These computer program instructions can be also loaded into computer or other programmable data processing devices so that in meter
Series of operation steps is performed on calculation machine or other programmable devices to produce computer implemented treatment, so as in computer or
The instruction performed on other programmable devices is provided for realizing in one flow of flow chart or multiple flows and/or block diagram one
The step of function of being specified in individual square frame or multiple square frames.
, but those skilled in the art once know basic creation although preferred embodiments of the present invention have been described
Property concept, then can make other change and modification to these embodiments.So, appended claims are intended to be construed to include excellent
Select embodiment and fall into having altered and changing for the scope of the invention.
Obviously, those skilled in the art can carry out various changes and modification without deviating from essence of the invention to the present invention
God and scope.So, if these modifications of the invention and modification belong to the scope of the claims in the present invention and its equivalent technologies
Within, then the present invention is also intended to comprising these changes and modification.
Claims (10)
1. a kind of Image Classifier method for building up, it is characterised in that including:
Samples pictures collection is obtained, the samples pictures are concentrated comprising the positive sample containing target image and the negative sample without target image
This;
Deformation process is carried out to the samples pictures that the samples pictures are concentrated, the samples pictures collection after being expanded;
According to the samples pictures collection after the expansion and depth convolutional neural networks model, dividing for the target image is obtained
Class device;Wherein, the output in the depth convolutional neural networks model to convolutional layer is normalized.
2. the method for claim 1, it is characterised in that the samples pictures that the samples pictures are concentrated are carried out at deformation
Reason, including at least one of:
Mirror image switch, rotation, random cropping, brightness adjustment.
3. the method for claim 1, it is characterised in that including:
The depth convolutional neural networks model is Googlenet models;
According to the samples pictures collection after the expansion and depth convolutional neural networks model, dividing for the target image is obtained
Class device, including:
By in the Googlenet models of the samples pictures input initialization;
Propagated forward obtains the loss function loss values of the Googlenet models;
The Googlenet model parameters are updated according to the loss values backpropagation, until the Googlenet models
Loss values meet pre-conditioned, obtain the grader for the target image.
4. the method for claim 1, it is characterised in that to the defeated of convolutional layer in the depth convolutional neural networks model
Go out to be normalized, including:
Output valve to every layer of convolutional layer in the depth convolutional neural networks model is normalized.
5. the image-recognizing method of the Image Classifier that a kind of method of basis as described in any one of Claims 1-4 is set up, its
It is characterised by, including:
Obtain picture to be identified;
The picture to be identified is input into the grader, obtain the picture to be identified whether comprising the target image point
Class result.
6. a kind of Image Classifier sets up device, it is characterised in that including:
Acquisition module, for obtaining samples pictures collection, the samples pictures are concentrated comprising the positive sample containing target image and are free of
The negative sample of target image;
Enlargement module, for carrying out deformation process to the samples pictures that the samples pictures are concentrated, the sample graph after being expanded
Piece collection;
Processing module, for according to the samples pictures collection after the expansion and depth convolutional neural networks model, obtaining and being directed to institute
State the grader of target image;Wherein, the output in the depth convolutional neural networks model to convolutional layer is normalized place
Reason.
7. device as claimed in claim 6, it is characterised in that
The enlargement module, specifically for being carried out to the samples pictures that the samples pictures are concentrated at least one following deformation
Reason:Mirror image switch, rotation, random cropping, brightness adjustment.
8. device as claimed in claim 6, it is characterised in that
The depth convolutional neural networks model that the processing module is used is Googlenet models;
The processing module specifically for:
By in the Googlenet models of the samples pictures input initialization;
Propagated forward obtains the loss function loss values of the Googlenet models;
The Googlenet model parameters are updated according to the loss values backpropagation, until the Googlenet models
Loss values meet pre-conditioned, obtain the grader for the target image.
9. device as claimed in claim 6, it is characterised in that
The processing module, is carried out specifically for the output valve to every layer of convolutional layer in the depth convolutional neural networks model
Normalized.
10. a kind of pattern recognition device, it is characterised in that including:
Acquisition module, for obtaining picture to be identified;
Whether processing module, the grader for the picture to be identified to be input into target image, obtain the picture to be identified
Classification results comprising the target image, wherein, the grader of the target image is as described in any one of claim 6 to 9
Image Classifier is set up device and is obtained.
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