CN110443782A - Chest x-ray piece model alignment schemes and device, storage medium - Google Patents
Chest x-ray piece model alignment schemes and device, storage medium Download PDFInfo
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- 238000012549 training Methods 0.000 claims abstract description 47
- 238000011976 chest X-ray Methods 0.000 claims abstract description 32
- 230000013011 mating Effects 0.000 claims abstract description 30
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Abstract
The embodiment of the present invention discloses a kind of chest x-ray piece model alignment schemes and device, storage medium, wherein method includes the following steps: that carrying out affine transformation to the offset chest x-ray piece inputted by affine transformation network obtains transformation chest x-ray piece, the training loss for calculating affine transformation network based on transformation chest x-ray piece and typical chest X-ray again, loses Reverse optimization affine transformation network using training.Using the present invention, by continuing to optimize trained affine transformation network, mating plate to be detected and the typical difference closed between piece are minimized, the accuracy that the disease detection model inspection based on the network can be made to go out chest disease is highly improved.
Description
Technical field
The present invention relates to thoracic cavity site disorders discrimination technology field more particularly to a kind of chest x-ray piece model alignment schemes
And device, storage medium.
Background technique
Thoracic cavity is easy to be influenced by various disease, and wherein Respiratory Medicine is mainly for diseases such as lung cancer, pulmonary tuberculosis, pneumonia
Make treatment diagnosis, and cardiothoracic surgery is the diagnoses and treatment for organs external structures such as lung and hearts.Timely judge thoracic cavity
Disease type is critically important to preventing that sb.'s illness took a turn for the worse and playing the role of.For example the discovery of lung cancer early stage can significantly improve patient's life
Deposit state.Lung cancer can directly be caused by lung tissue, can also be caused by the transfer at other positions of body.Corresponding CT scan
It says, the acquisition of chest x-ray piece is more convenient, and early stage, which first makees expected screening to chest x-ray piece, can alleviate the pressure of resource anxiety
And can effectively find the problem, the fixation and recognition chest x-ray piece symptom automated using deep learning tool reuses CT scan
Further differentiating with modes such as tissue samples (biopsy) not only can also be promoted with save medical resources to suspected patient screening
Efficiency.The developed countries such as the U.S. suggest needing aperiodically carrying out the screening of thoracic cavity site disorders to people at highest risk to alleviate it to the people
Many influences.Therefore the differentiation thoracic cavity site disorders of automation are significant to medical staff.But the multiplicity of thoracic cavity site disorders
The requirement of property and the characteristic easily obscured with surrounding tissue to computerized algorithm is very high.
Summary of the invention
The embodiment of the present invention provides a kind of chest x-ray piece model alignment schemes and device, storage medium, by by chest X
Mating plate sample can promote what disease detection model detected chest disease to the typical sample alignment for being more readily detected and identifying
Accuracy.
First aspect of the embodiment of the present invention provides a kind of chest x-ray piece model alignment schemes, it may include:
Affine transformation is carried out to the offset chest x-ray piece inputted based on affine transformation network and obtains transformation chest x-ray piece；
The training loss of affine transformation network is calculated based on transformation chest x-ray piece and typical chest X-ray；
Reverse optimization affine transformation network is lost using training.
Further, the above method further include:
Network alignment is carried out to the test chest x-ray piece inputted based on affine transformation network.
Further, above-mentioned that the offset chest x-ray piece progress affine transformation inputted is obtained based on affine transformation network
Convert chest x-ray piece, comprising:
Transformation parameter based on the offset chest x-ray piece that affine transformation e-learning is inputted；
Affine transformation is carried out to offset chest x-ray piece based on transformation parameter and obtains transformation chest x-ray piece.
Further, above-mentioned that transformation chest x-ray is obtained to offset chest x-ray piece progress affine transformation based on transformation parameter
Piece, comprising:
The affine coordinate of the inputted corresponding 3*3 of offset chest x-ray piece is extracted based on affine transformation network；
Transformation parameter is substituted into affine coordinate, transformation chest x-ray piece is obtained to offset chest x-ray piece progress affine transformation.
Further, the above-mentioned training damage that affine transformation network is calculated based on transformation chest x-ray piece and typical chest X-ray
It loses, comprising:
Calculate the consistency loss of transformation chest x-ray piece and typical chest X-ray；
The perception loss of chest x-ray piece and typical chest X-ray is converted based on feature extraction network query function；
Loss is lost and perceived to consistency to be weighted to obtain the training loss of affine transformation network.
Further, the above method further include:
The decimal grid occurred in affine transformation is eliminated using bilinearity difference functions.
Second aspect of the embodiment of the present invention provides a kind of chest x-ray piece model alignment means, it may include:
Chest mating plate conversion module, it is affine for being carried out based on affine transformation network to the offset chest x-ray piece inputted
Transformation obtains transformation chest x-ray piece；
Training costing bio disturbance module, for calculating affine transformation network based on transformation chest x-ray piece and typical chest X-ray
Training loss；
Converting network optimization module, for using training loss Reverse optimization affine transformation network.
Further, above-mentioned apparatus further include:
Chest mating plate detection module, for carrying out network to the test chest x-ray piece inputted based on affine transformation network
Alignment.
Further, above-mentioned chest mating plate conversion module includes:
Transformation parameter unit, the transformation of the offset chest x-ray piece for being inputted based on affine transformation e-learning
Parameter；
Chest mating plate converter unit is converted for carrying out affine transformation to offset chest x-ray piece based on transformation parameter
Chest x-ray piece.
Further, above-mentioned chest mating plate converter unit includes:
Affine coordinate extracts subelement, corresponding for extracting inputted offset chest x-ray piece based on affine transformation network
3*3 affine coordinate；
Chest mating plate converts subelement, affine to offset chest x-ray piece progress for transformation parameter to be substituted into affine coordinate
Transformation obtains transformation chest x-ray piece.
Further, above-mentioned trained costing bio disturbance module includes:
Consistency costing bio disturbance unit, for calculating the consistency loss of transformation chest x-ray piece and typical chest X-ray；
Costing bio disturbance unit is perceived, for based on feature extraction network query function transformation chest x-ray piece and typical chest X-ray
Perception loss；
Training costing bio disturbance unit is weighted to obtain affine transformation network for losing consistency and perceiving loss
Training loss.
Further, above-mentioned apparatus further include:
Decimal grid cancellation module, for eliminating the decimal net occurred in affine transformation using bilinearity difference functions
Lattice.
The third aspect of the embodiment of the present invention provides a kind of computer storage medium, and computer storage medium is stored with a plurality of
Instruction, instruction are suitable for being loaded by processor and executing following steps:
Affine transformation is carried out to the offset chest x-ray piece inputted based on affine transformation network and obtains transformation chest x-ray piece；
The training loss of affine transformation network is calculated based on transformation chest x-ray piece and typical chest X-ray；
Reverse optimization affine transformation network is lost using training.
In embodiments of the present invention, affine transformation is carried out to the offset chest x-ray piece inputted by affine transformation network
Transformation chest x-ray piece is obtained, then calculates the training damage of affine transformation network based on transformation chest x-ray piece and typical chest X-ray
It loses, Reverse optimization affine transformation network is lost using training.By continuing to optimize trained affine transformation network, by light to be detected
Piece and the typical difference closed between piece minimize, and the disease detection model inspection based on the network is made to go out the accuracy of chest disease
Larger promotion is obtained.
Detailed description of the invention
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, to embodiment or will show below
There is attached drawing needed in technical description to be briefly described, it should be apparent that, the accompanying drawings in the following description is only this
Some embodiments of invention for those of ordinary skill in the art without creative efforts, can be with
It obtains other drawings based on these drawings.
Fig. 1 is a kind of flow diagram of chest x-ray piece model alignment schemes provided in an embodiment of the present invention；
Fig. 2 is chest x-ray piece model alignment configuration diagram provided in an embodiment of the present invention；
Fig. 3 is a kind of structural schematic diagram of chest x-ray piece model alignment means provided in an embodiment of the present invention；
Fig. 4 is the structural schematic diagram of chest mating plate conversion module provided in an embodiment of the present invention；
Fig. 5 is the structural schematic diagram of chest mating plate converter unit provided in an embodiment of the present invention；
Fig. 6 is the structural schematic diagram of trained costing bio disturbance module provided in an embodiment of the present invention；
Fig. 7 is the structural schematic diagram of another chest x-ray piece model alignment means provided in an embodiment of the present invention.
Specific embodiment
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete
Site preparation description, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.It is based on
Embodiment in the present invention, it is obtained by those of ordinary skill in the art without making creative efforts every other
Embodiment shall fall within the protection scope of the present invention.
Term " includes " in description and claims of this specification and above-mentioned attached drawing and " having " and they appoint
What is deformed, it is intended that covering non-exclusive includes that term " first " and " second " be not merely to difference name, represents number
The size or sequence of word.Such as it contains the process, method, system, product or equipment of a series of steps or units and does not limit
Due to listed step or unit, but optionally further comprising the step of not listing or unit, or optionally further comprising it is right
In other intrinsic step or units of these process, methods, product or equipment.
The present embodiments relate to chest x-ray piece model alignment means can be the end PC, or have data analysis
Other Medical Devices of processing capacity.
As shown in Figure 1, chest x-ray piece model alignment schemes at least may include following steps:
S101 carries out affine transformation to the offset chest x-ray piece inputted based on affine transformation network and obtains transformation chest X
Mating plate.
It is understood that above-mentioned affine transformation network can be ResNet18, by multiple identical buildingblock
It forms, the conventional part in buildingblock is (f (x)): CONV-BN-ReLU-CONV-BN, and output valve is f (x)+x.Its
Middle CONV represents convolutional layer, and BN (Batch Normalization) layer and line rectification unit (ReLU) can be done after CONV
Respective handling.
In the specific implementation, available the inputted offset chest x-ray piece of above-mentioned apparatus, is then based on affine transformation network
Affine transformation is carried out to the mating plate and obtains transformation chest x-ray piece.Optionally, above-mentioned apparatus can be based on affine transformation e-learning
The transformation parameter for deviating chest x-ray piece, such as the parameter θ in Fig. 2, it is to be understood that the parameter can be a parameter can also
To be one group of parameter, specifically determined according to transformation demand.It further, can be based on the transformation parameter to offset chest x-ray
Piece carries out affine transformation and obtains transformation chest x-ray piece.Preferably, offset chest x-ray piece can be extracted based on affine transformation network
The affine coordinate of corresponding 3*3 is as shown in Fig. 2, further, can substitute into affine coordinate for above-mentioned parameter θ, then carry out affine
Transformation.For example, affine transformation can be carried out by following formula:
Wherein, φA(I) the transformation chest x-ray piece after representation transformation, B be bilinear interpolation function, I be input picture i.e.
Chest x-ray piece is deviated,It is the first two columns in above-mentioned affine coordinate, G (I) is grid generation
Function, because grid will appear the possibility of decimal, it is possible to the decimal grid occurred in affine transformation is eliminated using B.
S102 calculates the training loss of affine transformation network based on transformation chest x-ray piece and typical chest X-ray.
Specifically, above-mentioned apparatus can calculate affine transformation network based on transformation chest x-ray piece and typical chest X-ray
Training loss, it should be noted that above-mentioned typical chest X-ray can be to be divided by averagely multiple and different normal samples
It is obtained up with the matched basis of key point.
In an alternative embodiment, above-mentioned apparatus can be as shown in Fig. 2, calculate transformation chest x-ray piece and typical chest X-ray
Consistency loss, specific calculation formula can be as follows:
Wherein, T is typical chest X-ray, | | | |2It is L2- norm, C, H, W are the dimension of feature or picture respectively.
Further, to minimize typical chest X-ray and converting the difference between chest x-ray piece, above-mentioned apparatus can be based on feature
Extract the perception loss of network query function transformation chest x-ray piece and typical chest X-ray, wherein feature extraction network equally can be with
It is ResNet18, specific calculation formula is as follows:
Wherein, N is feature extraction network.Further, above-mentioned apparatus can lose and be perceived to consistency loss and carry out
Weighting obtains the training loss of affine transformation network, specific formula is as follows:
Wherein, in order to weight two different losses, the preferred value of λ is 0.4.
S103 loses Reverse optimization affine transformation network using training.
It is understood that above-mentioned apparatus can using training loss the above-mentioned affine transformation network of Reverse optimization, when model
Alignment accuracy it is higher.Further, the test chest x-ray piece of the available input of above-mentioned apparatus, using trained alignment
Model to test chest x-ray piece carry out network alignment, then can will the image after alignment be sent into fixation and recognition network in make into
The study of one step.
In embodiments of the present invention, affine transformation is carried out to the offset chest x-ray piece inputted by affine transformation network
Transformation chest x-ray piece is obtained, then calculates the training damage of affine transformation network based on transformation chest x-ray piece and typical chest X-ray
It loses, Reverse optimization affine transformation network is lost using training.By continuing to optimize trained affine transformation network, by light to be detected
Piece and the typical difference closed between piece minimize, and the disease detection model inspection based on the network is made to go out the accuracy of chest disease
Larger promotion is obtained.
Below in conjunction with attached drawing 3- attached drawing 6, chest x-ray piece model alignment means provided in an embodiment of the present invention are carried out detailed
It is thin to introduce.It should be noted that the attached chest x-ray piece model alignment means shown in fig. 6 of attached drawing 3-, for executing Fig. 1 of the present invention
With the method for embodiment illustrated in fig. 2, for ease of description, only parts related to embodiments of the present invention are shown, particular technique
What details did not disclosed, please refer to Fig. 1 of the present invention and embodiment shown in Fig. 2.
Fig. 3 is referred to, for the embodiment of the invention provides a kind of structural schematic diagrams of chest x-ray piece model alignment means.
As shown in figure 3, the model alignment means 1 of the embodiment of the present invention may include: chest mating plate conversion module 11, training costing bio disturbance
Module 12, converting network optimization module 13, chest mating plate detection module 14 and decimal grid cancellation module 15.Wherein, chest light
Piece conversion module 11 is as shown in figure 4, include transformation parameter unit 111 and chest mating plate converter unit 112, chest mating plate becomes
Unit 112 is changed as shown in figure 5, including that affine coordinate extracts subelement 1121 and chest mating plate transformation subelement 1122, training damage
Computing module 12 is lost as shown in fig. 6, including consistency costing bio disturbance unit 121, perception costing bio disturbance unit 122 and training loss
Computing unit 123.
Chest mating plate conversion module 11, for being imitated based on affine transformation network the offset chest x-ray piece inputted
It penetrates transformation and obtains transformation chest x-ray piece.
Training costing bio disturbance module 12, for calculating affine transformation net based on transformation chest x-ray piece and typical chest X-ray
The training loss of network
Converting network optimization module 13, for using training loss Reverse optimization affine transformation network.
It should be noted that before carrying out the transformation of chest x-ray piece, chest mating plate detection module 14, for being based on affine change
Switching network carries out network alignment to the test chest x-ray piece inputted.
It should be noted that above-mentioned chest mating plate conversion module 11 is specifically included with lower unit:
Transformation parameter unit 111, the change of the offset chest x-ray piece for being inputted based on affine transformation e-learning
Change parameter.
Chest mating plate converter unit 112 is become for carrying out affine transformation to offset chest x-ray piece based on transformation parameter
Change chest x-ray piece.
It should be noted that above-mentioned chest mating plate converter unit 112 specifically includes following subelement:
Affine coordinate extracts subelement 1121, for extracting inputted offset chest x-ray piece based on affine transformation network
The affine coordinate of corresponding 3*3.
Chest mating plate converts subelement 1122, carries out for transformation parameter to be substituted into affine coordinate to offset chest x-ray piece
Affine transformation obtains transformation chest x-ray piece.
It should be noted that above-mentioned trained costing bio disturbance module 12 is specifically included with lower unit:
Consistency costing bio disturbance unit 121, for calculating the consistency damage of transformation chest x-ray piece and typical chest X-ray
It loses.
Costing bio disturbance unit 122 is perceived, for based on feature extraction network query function transformation chest x-ray piece and typical chest X
The perception of mating plate is lost.
Training costing bio disturbance unit 123 is weighted to obtain affine transformation net for losing consistency and perceiving loss
The training loss of network.
It should be noted that during carrying out the transformation of chest x-ray piece, decimal grid cancellation module 15, for using
Bilinearity difference functions eliminate the decimal grid occurred in affine transformation.
It should be noted that the specific implementation of the embodiment of the present invention may refer to retouching in detail for above method embodiment
It states, details are not described herein again.
In embodiments of the present invention, affine transformation is carried out to the offset chest x-ray piece inputted by affine transformation network
Transformation chest x-ray piece is obtained, then calculates the training damage of affine transformation network based on transformation chest x-ray piece and typical chest X-ray
It loses, Reverse optimization affine transformation network is lost using training.By continuing to optimize trained affine transformation network, by light to be detected
Piece and the typical difference closed between piece minimize, and the disease detection model inspection based on the network is made to go out the accuracy of chest disease
Larger promotion is obtained.
The embodiment of the invention also provides a kind of computer storage medium, the computer storage medium can store more
Item instruction, described instruction are suitable for being loaded by processor and executing the method and step such as above-mentioned Fig. 1 and embodiment illustrated in fig. 2, specifically
Implementation procedure may refer to illustrating for Fig. 1 and embodiment illustrated in fig. 2, herein without repeating.
The embodiment of the present application also provides another chest x-ray piece model alignment means.As shown in fig. 7, chest x-ray piece
Model alignment means 20 may include: at least one processor 201, such as CPU, at least one network interface 204, user interface
203, memory 205, at least one communication bus 202 can also include optionally display screen 206.Wherein, communication bus 202
For realizing the connection communication between these components.Wherein, user interface 203 may include touch screen, keyboard or mouse etc..
Network interface 204 optionally may include standard wireline interface and wireless interface (such as WI-FI interface), pass through network interface 204
It can establish and communicate to connect with server.Memory 205 can be high speed RAM memory, be also possible to non-labile storage
Device (non-volatile memory), for example, at least a magnetic disk storage, memory 205 include in the embodiment of the present invention
flash.Memory 205 optionally can also be that at least one is located remotely from the storage system of aforementioned processor 201.Such as Fig. 7 institute
Show, as may include operating system, network communication module, user interface in a kind of memory 205 of computer storage medium
Module and program instruction.
It should be noted that network interface 204 can connect receiver, transmitter or other communication modules, other communications
Module can include but is not limited to WiFi module, bluetooth module etc., it will be understood that chest X-ray model in the embodiment of the present invention
Alignment means also may include receiver, transmitter and other communication modules etc..
Processor 201 can be used for calling the program instruction stored in memory 205, and be aligned chest x-ray piece model
Device 20 executes following operation:
Affine transformation is carried out to the offset chest x-ray piece inputted based on affine transformation network and obtains transformation chest x-ray piece；
The training loss of affine transformation network is calculated based on transformation chest x-ray piece and typical chest X-ray；
Reverse optimization affine transformation network is lost using training.
In some embodiments, device 20 be also used to based on affine transformation network to the test chest x-ray piece inputted into
The alignment of row network.
In some embodiments, device 20 is imitating the offset chest x-ray piece inputted based on affine transformation network
It is specific to execute following operation when penetrating transformation and obtaining transformation chest x-ray piece:
Transformation parameter based on the offset chest x-ray piece that affine transformation e-learning is inputted；
Affine transformation is carried out to offset chest x-ray piece based on transformation parameter and obtains transformation chest x-ray piece.
In some embodiments, device 20 is becoming offset chest x-ray piece progress affine transformation based on transformation parameter
It is specific to execute following operation when changing chest x-ray piece:
The affine coordinate of the inputted corresponding 3*3 of offset chest x-ray piece is extracted based on affine transformation network；
Transformation parameter is substituted into affine coordinate, transformation chest x-ray piece is obtained to offset chest x-ray piece progress affine transformation.
In some embodiments, device 20 is calculating affine transformation net based on transformation chest x-ray piece and typical chest X-ray
It is specific to execute following operation when the training loss of network:
Calculate the consistency loss of transformation chest x-ray piece and typical chest X-ray；
The perception loss of chest x-ray piece and typical chest X-ray is converted based on feature extraction network query function；
Loss is lost and perceived to consistency to be weighted to obtain the training loss of affine transformation network.
In some embodiments, device 20 is also used to occur in affine transformation using the elimination of bilinearity difference functions small
Number grid.
In embodiments of the present invention, affine transformation is carried out to the offset chest x-ray piece inputted by affine transformation network
Transformation chest x-ray piece is obtained, then calculates the training damage of affine transformation network based on transformation chest x-ray piece and typical chest X-ray
It loses, Reverse optimization affine transformation network is lost using training.By continuing to optimize trained affine transformation network, by light to be detected
Piece and the typical difference closed between piece minimize, and the disease detection model inspection based on the network is made to go out the accuracy of chest disease
Larger promotion is obtained.
Those of ordinary skill in the art will appreciate that realizing all or part of the process in above-described embodiment method, being can be with
Relevant hardware is instructed to complete by computer program, the program can be stored in computer-readable storage medium
In, the program is when being executed, it may include such as the process of the embodiment of above-mentioned each method.Wherein, the storage medium can be magnetic
Dish, CD, read-only memory (Read-Only Memory, ROM) or random access memory (Random Access
Memory, RAM) etc..
The above disclosure is only the preferred embodiments of the present invention, cannot limit the right model of the present invention with this certainly
It encloses, therefore equivalent changes made in accordance with the claims of the present invention, is still within the scope of the present invention.
Claims (10)
1. a kind of chest x-ray piece model alignment schemes characterized by comprising
Affine transformation is carried out to the offset chest x-ray piece inputted based on affine transformation network and obtains transformation chest x-ray piece；
The training loss of the affine transformation network is calculated based on the transformation chest x-ray piece and typical chest X-ray；
Using affine transformation network described in the training loss Reverse optimization.
2. the method according to claim 1, wherein the method also includes:
Network alignment is carried out to the test chest x-ray piece inputted based on the affine transformation network.
3. the method according to claim 1, wherein it is described based on affine transformation network to the offset chest inputted
Portion's X-ray carries out affine transformation and obtains transformation chest x-ray piece, comprising:
Transformation parameter based on the offset chest x-ray piece that affine transformation e-learning is inputted；
Affine transformation is carried out to the offset chest x-ray piece based on the transformation parameter and obtains transformation chest x-ray piece.
4. according to the method described in claim 3, it is characterized in that, described be based on the transformation parameter to the offset chest X
Mating plate carries out affine transformation and obtains transformation chest x-ray piece, comprising:
The affine coordinate of the inputted corresponding 3*3 of offset chest x-ray piece is extracted based on affine transformation network；
The transformation parameter is substituted into the affine coordinate, transformation chest is obtained to offset chest x-ray piece progress affine transformation
X-ray.
5. the method according to claim 1, wherein described be based on the transformation chest x-ray piece and typical chest X
Mating plate calculates the training loss of the affine transformation network, comprising:
Calculate the consistency loss of the transformation chest x-ray piece and typical chest X-ray；
Perception loss based on transformation chest x-ray piece and typical chest X-ray described in feature extraction network query function；
Consistency loss and the perception loss are weighted to obtain the training loss of the affine transformation network.
6. the method according to claim 1, wherein the method also includes:
The decimal grid occurred in affine transformation is eliminated using bilinearity difference functions.
7. a kind of chest x-ray piece model alignment means characterized by comprising
Chest mating plate conversion module, for carrying out affine transformation to the offset chest x-ray piece inputted based on affine transformation network
Obtain transformation chest x-ray piece；
Training costing bio disturbance module, for calculating the affine transformation based on the transformation chest x-ray piece and typical chest X-ray
The training loss of network；
Converting network optimization module, for using affine transformation network described in the training loss Reverse optimization.
8. device according to claim 7, which is characterized in that described device further include:
Chest mating plate detection module, for carrying out network to the test chest x-ray piece inputted based on the affine transformation network
Alignment.
9. device according to claim 7, which is characterized in that the chest mating plate conversion module includes:
Transformation parameter unit, the transformation parameter of the offset chest x-ray piece for being inputted based on affine transformation e-learning；
Chest mating plate converter unit is obtained for carrying out affine transformation to the offset chest x-ray piece based on the transformation parameter
Convert chest x-ray piece.
10. a kind of computer storage medium, which is characterized in that the computer storage medium is stored with a plurality of instruction, the finger
It enables and is suitable for being loaded by processor and executing following steps:
Affine transformation is carried out to the offset chest x-ray piece inputted based on affine transformation network and obtains transformation chest x-ray piece；
The training loss of the affine transformation network is calculated based on the transformation chest x-ray piece and typical chest X-ray；
Using affine transformation network described in the training loss Reverse optimization.
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