CN107133953A - A kind of intrinsic image decomposition method learnt based on partial differential equation - Google Patents
A kind of intrinsic image decomposition method learnt based on partial differential equation Download PDFInfo
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- 238000000034 method Methods 0.000 title claims abstract description 34
- 238000000354 decomposition reaction Methods 0.000 title claims abstract description 21
- 230000011514 reflex Effects 0.000 claims abstract description 8
- 238000002939 conjugate gradient method Methods 0.000 claims abstract description 7
- 238000013519 translation Methods 0.000 claims description 13
- 238000012549 training Methods 0.000 claims description 7
- 230000004069 differentiation Effects 0.000 claims description 6
- 230000008569 process Effects 0.000 claims description 4
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- 238000005286 illumination Methods 0.000 abstract description 7
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- 238000005457 optimization Methods 0.000 description 2
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
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Abstract
The present invention provides a kind of intrinsic image decomposition method learnt based on partial differential equation, and the present invention, independent of the prior-constrained of determination, and builds by the way of data-driven partial differential equation in the processing intrinsic Composition Estimation of image；The direction of search is determined using conjugate gradient method, relative to steepest descent method and Newton method, conjugacy is combined by this method with steepest descent method；One group of conjugate direction is constructed using the gradient at known point, and along this prescription to scanning for, obtains the minimal point of object function, to determine the optimal direction of search；This method can effectively realize that the image of different illumination conditions carries out reflex components and shade composition that eigen decomposition obtains the image.
Description
Technical field
The present invention relates to digital image processing field, more particularly, to a kind of based on the intrinsic of partial differential equation study
Picture breakdown method.
Background technology
The image that object in real world is presented in human eye depends on the intrinsic attribute of scene, the light of such as scene
According to, the shape of body surface, the material of body surface etc..Intrinsic image decomposition is a underlying issue in computer vision,
A given width input picture is, it is necessary to decomposite corresponding reflex components and shade composition.With the hair of digital image processing techniques
Exhibition, to image decompose obtaining its intrinsic composition, is played in computer vision and image processing field more and more important
Effect.Reflex components and shade that eigen decomposition obtains the image are carried out to the image with different illumination conditions under Same Scene
Composition is relatively difficult.
At present, on intrinsic image task resolution, traditional method is usually to design corresponding according to various prioris
Constrained optimization equation, acquisition reflex components and shade composition are solved by the optimization to target equation.Conventional a priori assumption
Have that the surface with the images of different illumination, input picture under Same Scene is smooth, the illumination of imaging surface color balancing, image
It is more natural etc..In addition, some current research algorithms are dependent on multiple input pictures, user's input or Depth cue
Extraneous information.Mainly for the input picture of the different illumination conditions under Same Scene, recover the anti-of input picture with this
Penetrate composition and shade composition.In place of above method comes with some shortcomings, existing method is typically based on a priori assumption, generally not
Possesses generality.
The content of the invention
The present invention provides a kind of intrinsic image decomposition method learnt based on partial differential equation, and this method, which can be realized, does not share the same light
Reflex components and shade composition that eigen decomposition obtains the image are carried out according to the image of condition.
In order to reach above-mentioned technique effect, technical scheme is as follows：
A kind of intrinsic image decomposition method learnt based on partial differential equation, is comprised the following steps：
S1：Input training data pair；
S2：Control function is initialized, because object function is non-convex, the convergence for minimizing process is initial towards depending on
The local minimum of change, step S3 is turned to when initialization procedure is not restrained, circulation is performed；Otherwise step S8 is turned to；
S3：Solve the optimal control equation constrained with PDE；
S4：Solve adjoint equation when adjoint function takes particular value；
S5：J=0,1 is calculated using following formula ..., the derivative of translation rotational invariants when 16：
Wherein, J is translation rotational invariants, and j is the number for translating rotational invariants, aj, bjIt is control function, λjAnd uj
It is positive weighting parameters,And φmIt is adjoint function, u is output image, and Ω is the rectangular area occupied by input picture, fΩ
Ω initial function, m=1,2 ..., M, M be the data sample logarithm of input, inv (u, v) represents to seek matrix (u, v)
Inverse, v is indicator function, and it is to collect the extensive information in image to be introduced into the purpose of indicator function, to instruct u differentiation.
S6：The direction of search is determined using conjugate gradient method；
S7：Golden section search is performed along the direction of search, and constantly updates system function, next circulation is carried out, directly
To j=16, it is trained；
S8：Terminate circulation, output system function；
S9：Prepare application data, data picture feature is background black, and object is single and prominent；
S10：Using obtained system function, to give data to carry out eigen decomposition application, obtain the reflex components of image
With shade composition.
Further, by solving (1) formula to control function a in the step S2j(t), t=0, Δ t, 1-
Δ t is initialized, and now fixes bj(t), j=0,1,16,
Fa (t)=d (1)
Wherein, ajAnd b (t)j(t) it is control function, a (t)={ aj} and b (t)={ b (t)j(t) } it is defined on Q
Function set, is respectively intended to control u and v differentiation, fuAnd fvIt is u and v initial function respectively.
Further, j-th of translation rotational invariants is calculated by introducing the adjoint equation of (2) formula in the step S3
Gateaux derivative, therefore local optimumWithCalculated and obtained by the algorithm based on gradient, for um
And vm, work as m=1, (2) formula solved during 2 ..., M：
Wherein, T is the time that PDE systems complete Vision information processing and output result, and Q is Ω × (0, T), and Γ is
Further, adjoint equation during adjoint function particular value is solved in the step S4：
ForAnd φm, m=1, during 2 ..., M, solution adjoint equation, whereinAnd φmAdjoint equation such as (3) formula：
Wherein, OmIt is desired output image, p, q belongs to the part of { (0,0), (0,1), (0,2), (1,1), (2,0) }
The indexed set of change.
Further, the derivative of translation rotational invariants during formula (4) calculating j=0,1 ..., 16 is utilized；Pass through public affairs
Formula (4) calculates j=0,1 ..., the derivative of the translation rotational invariants of control function when 16WithIn adjoint equation
With the help of, for ajAnd b (t)j(t), J derivative is as follows in each iteration：
Wherein, adjoint functionAnd φmIt is the answer of equation (3).
Further, golden section search is performed along the direction of search in the step S7, and constantly updates system function,
Carry out next circulation；
Golden section search is performed along the direction of search, control function a is updatedjAnd b (t)j(t), j=0,1 ..., 16, after
Continue next circulation, until j=16, be trained.
Further, in the step S8, circulation, output system function are terminatedWith
Compared with prior art, the beneficial effect of technical solution of the present invention is：
The present invention in the processing intrinsic Composition Estimation of image independent of the prior-constrained of determination, and using data-driven
Mode builds partial differential equation；The direction of search is determined using conjugate gradient method, relative to steepest descent method and Newton method, the party
Conjugacy is combined by method with steepest descent method；One group of conjugate direction is constructed using the gradient at known point, and along this prescription
To scanning for, the minimal point of object function is obtained, to determine the optimal direction of search；This method can effectively realize different illumination
The image of condition carries out the reflex components and shade composition that eigen decomposition obtains the image.
Brief description of the drawings
Fig. 1 is flow chart of the method for the present invention.
Embodiment
Accompanying drawing being given for example only property explanation, it is impossible to be interpreted as the limitation to this patent；
In order to more preferably illustrate the present embodiment, some parts of accompanying drawing have omission, zoomed in or out, and do not represent actual product
Size；
To those skilled in the art, it is to be appreciated that some known features and its explanation, which may be omitted, in accompanying drawing
's.
Technical scheme is described further with reference to the accompanying drawings and examples.
Embodiment 1
As shown in figure 1, a kind of intrinsic image decomposition method learnt based on partial differential equation, is comprised the steps of：
1), the training stage：
Step 1：Input training data pair；
The training data of input to being MIT-Intrinsic Images storehouses in image, training input data include 20 classes
Picture, the picture of the different illumination of 10 Same Scenes is included per class, totally 220 pictures, and training output data is correspondence input figure
The shade composition that piece is gathered.
Step 2：Control function is initialized, because object function is non-convex, the convergence direction for minimizing process is depended on
The local minimum of initialization, step 3 is turned to when initialization procedure is not restrained, circulation is performed；Otherwise step 8 is turned to；
By solving (1) formula to control function aj(t), t=0, Δ t, 1- Δs t is initialized, and is now fixed
bj(t), j=0,1,16,
Fa (t)=d (1)
Wherein, u is output image, and v is indicator function, and it is the extensive letter searched in image to be introduced into the purpose of indicator function
Breath, in order to correctly instruct u differentiation.Because object function is non-convex, the convergence for minimizing process is first towards depending on
The local minimum of beginningization, when control function is not restrained, turns to step 3, performs circulation, otherwise turn to step 8.
Step 3：Solve the optimal control equation constrained with PDE；
By introducing the adjoint equation of (2) formula, the gateaux derivative of j-th of translation rotational invariants is calculated, therefore part is most
The figure of meritWithIt can be calculated and obtained by the algorithm based on gradient, for umAnd vm, work as m=1,2 ..., M
When solve (2) formula：
Wherein Ω is the rectangular area occupied by input picture, and T is that PDE systems complete Vision information processing and output result
Time, and be u and v initial function respectively.For computational problem and it is related to deduction mathematically, the present invention will be around it
Fill the null value of several pixel wides.Due to chronomere can be changed, T=1, and it is fixed as being defined on one group of letter on Q
Number, is respectively intended to control u and v differentiation.
Step 4：Solve adjoint equation when adjoint function takes particular value；
ForAnd φm, m=1, during 2 ..., M, solution adjoint equation, whereinAnd φmAdjoint equation such as (3) formula：
Step 5：J=0,1 is calculated using formula (4), the derivative of translation rotational invariants when 16；
J=0,1 is calculated by formula (4), the derivative of the translation rotational invariants of control function when 16
WithWith the help of adjoint equation, for ajAnd b (t)j(t), J derivative is as follows in each iteration：
Wherein, λjAnd ujIt is positive weighting parameters, adjoint functionAnd φmIt is the answer of equation (3).
Step 6：The direction of search is determined using conjugate gradient method；
Determine the direction of search using conjugate gradient method, wherein conjugate gradient method is mutually to tie conjugacy with steepest descent method
Close.One group of conjugate direction is constructed using the gradient at known point, and along this prescription to scanning for, obtains the pole of object function
Dot, to determine the optimal direction of search.
Step 7：Golden section search is performed along the direction of search, and constantly updates system function, next circulation is carried out；
Golden section search is performed along the direction of search, system function a is updatedjAnd b (t)j(t), j=0,1 ..., 16, after
Continue next circulation, until j=16, be trained；
Step 8：Terminate circulation, output system function.
2), the application stage：
Step 9：Prepare application data, data picture feature is background black, and object is single and prominent；
Step 10：To give data carry out eigen decomposition application, obtain the reflex components and shade composition of image.
The same or analogous part of same or analogous label correspondence；
Position relationship is used for being given for example only property explanation described in accompanying drawing, it is impossible to be interpreted as the limitation to this patent；
Obviously, the above embodiment of the present invention is only intended to clearly illustrate example of the present invention, and is not pair
The restriction of embodiments of the present invention.For those of ordinary skill in the field, may be used also on the basis of the above description
To make other changes in different forms.There is no necessity and possibility to exhaust all the enbodiments.It is all this
Any modifications, equivalent substitutions and improvements made within the spirit and principle of invention etc., should be included in the claims in the present invention
Protection domain within.
Claims (7)
1. a kind of intrinsic image decomposition method learnt based on partial differential equation, it is characterised in that comprise the following steps：
S1：Input training data pair；
S2：Control function is initialized, because object function is non-convex, the convergence of process is minimized towards depending on initialization
Local minimum, step S3 is turned to when initialization procedure is not restrained, circulation is performed；Otherwise step S8 is turned to；
S3：Solve the optimal control equation constrained with PDE；
S4：Solve adjoint equation when adjoint function takes particular value；
S5：J=0,1 is calculated using following formula ..., the derivative of translation rotational invariants when 16：
Wherein, J is translation rotational invariants, and j is the number for translating rotational invariants, aj, bjIt is control function, λjAnd ujIt is positive
Weighting parameters,And φmIt is adjoint function, u is output image, and Ω is the rectangular area occupied by input picture, fΩIt is Ω
Initial function, m=1,2 ..., M, M for input data sample logarithm, inv (u, v) represent matrix (u, v) is inverted, v refers to
Show function, it is to collect the extensive information in image to be introduced into the purpose of indicator function, to instruct u differentiation.
S6：The direction of search is determined using conjugate gradient method；
S7：Golden section search is performed along the direction of search, and constantly updates system function, next circulation is carried out, until j=
16, it is trained；
S8：Terminate circulation, output system function；
S9：Prepare application data, data picture feature is background black, and object is single and prominent；
S10：Using obtained system function, to give data to carry out eigen decomposition application, obtain the reflex components and the moon of image
Shadow composition.
2. the intrinsic image decomposition method according to claim 1 learnt based on partial differential equation, it is characterised in that described
By solving (1) formula to control function a in step S2j(t), t=0, Δ t ..., 1- Δ t is initialized, and now fixes bj
(t), j=0,1 ..., 16,
Fa (t)=d (1)
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By introducing the adjoint equation of (2) formula in step S3, the gateaux derivative of j-th of translation rotational invariants is calculated, therefore part is most
The figure of meritWithCalculated and obtained by the algorithm based on gradient, for umAnd vm, work as m=1, solved during 2 ..., M
(2) formula：
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4. the intrinsic image decomposition method according to claim 2 learnt based on partial differential equation, it is characterised in that described
Adjoint equation during adjoint function particular value is solved in step S4：
ForAnd φm, m=1, during 2 ..., M, solution adjoint equation, whereinAnd φmAdjoint equation such as (3) formula：
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</msub>
<mrow>
<mo>(</mo>
<mi>u</mi>
<mo>,</mo>
<mi>v</mi>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mo>&part;</mo>
<msub>
<mi>u</mi>
<mrow>
<mi>p</mi>
<mi>q</mi>
</mrow>
</msub>
</mrow>
</mfrac>
</mrow>
<mrow>
<msub>
<mi>&sigma;</mi>
<mrow>
<mi>p</mi>
<mi>q</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>v</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mo>&part;</mo>
<msub>
<mi>F</mi>
<mi>v</mi>
</msub>
</mrow>
<mrow>
<mo>&part;</mo>
<msub>
<mi>u</mi>
<mrow>
<mi>p</mi>
<mi>q</mi>
</mrow>
</msub>
</mrow>
</mfrac>
<mo>=</mo>
<msubsup>
<mi>&Sigma;</mi>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mn>16</mn>
</msubsup>
<msub>
<mi>b</mi>
<mi>j</mi>
</msub>
<mfrac>
<mrow>
<mo>&part;</mo>
<msub>
<mi>inv</mi>
<mi>j</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>v</mi>
<mo>,</mo>
<mi>u</mi>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mo>&part;</mo>
<msub>
<mi>u</mi>
<mrow>
<mi>p</mi>
<mi>q</mi>
</mrow>
</msub>
</mrow>
</mfrac>
</mrow>
<mrow>
<msub>
<mover>
<mi>&sigma;</mi>
<mo>~</mo>
</mover>
<mrow>
<mi>p</mi>
<mi>q</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>u</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mo>&part;</mo>
<msub>
<mi>F</mi>
<mi>u</mi>
</msub>
</mrow>
<mrow>
<mo>&part;</mo>
<msub>
<mi>u</mi>
<mrow>
<mi>p</mi>
<mi>q</mi>
</mrow>
</msub>
</mrow>
</mfrac>
<mo>=</mo>
<msubsup>
<mi>&Sigma;</mi>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mn>16</mn>
</msubsup>
<msub>
<mi>a</mi>
<mi>j</mi>
</msub>
<mfrac>
<mrow>
<mo>&part;</mo>
<msub>
<mi>inv</mi>
<mi>j</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>u</mi>
<mo>,</mo>
<mi>v</mi>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mo>&part;</mo>
<msub>
<mi>u</mi>
<mrow>
<mi>p</mi>
<mi>q</mi>
</mrow>
</msub>
</mrow>
</mfrac>
</mrow>
<mrow>
<msub>
<mover>
<mi>&sigma;</mi>
<mo>~</mo>
</mover>
<mrow>
<mi>p</mi>
<mi>q</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>v</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mo>&part;</mo>
<msub>
<mi>F</mi>
<mi>v</mi>
</msub>
</mrow>
<mrow>
<mo>&part;</mo>
<msub>
<mi>u</mi>
<mrow>
<mi>p</mi>
<mi>q</mi>
</mrow>
</msub>
</mrow>
</mfrac>
<mo>=</mo>
<msubsup>
<mi>&Sigma;</mi>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mn>16</mn>
</msubsup>
<msub>
<mi>b</mi>
<mi>j</mi>
</msub>
<mfrac>
<mrow>
<mo>&part;</mo>
<msub>
<mi>inv</mi>
<mi>j</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>v</mi>
<mo>,</mo>
<mi>u</mi>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mo>&part;</mo>
<msub>
<mi>u</mi>
<mrow>
<mi>p</mi>
<mi>q</mi>
</mrow>
</msub>
</mrow>
</mfrac>
</mrow>
<mrow>
<msub>
<mi>u</mi>
<mrow>
<mi>p</mi>
<mi>q</mi>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<msup>
<mo>&part;</mo>
<mrow>
<mi>p</mi>
<mo>+</mo>
<mi>q</mi>
</mrow>
</msup>
<mi>u</mi>
</mrow>
<mrow>
<mo>&part;</mo>
<msup>
<mi>x</mi>
<mi>p</mi>
</msup>
<mo>&part;</mo>
<msup>
<mi>y</mi>
<mi>q</mi>
</msup>
</mrow>
</mfrac>
<mo>,</mo>
<msub>
<mi>v</mi>
<mrow>
<mi>p</mi>
<mi>q</mi>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<msup>
<mo>&part;</mo>
<mrow>
<mi>p</mi>
<mo>+</mo>
<mi>q</mi>
</mrow>
</msup>
<mi>v</mi>
</mrow>
<mrow>
<mo>&part;</mo>
<msup>
<mi>x</mi>
<mi>p</mi>
</msup>
<mo>&part;</mo>
<msup>
<mi>y</mi>
<mi>q</mi>
</msup>
</mrow>
</mfrac>
</mrow>
Wherein, OmIt is desired output image, p, q belongs to the localized variation of { (0,0), (0,1), (0,2), (1,1), (2,0) }
Indexed set.
5. the intrinsic image decomposition method according to claim 4 learnt based on partial differential equation, it is characterised in that utilize
Formula (4) calculates j=0,1 ..., the derivative of translation rotational invariants when 16；J=0,1 is calculated by formula (4) ...,
The derivative of the translation rotational invariants of control function when 16WithWith the help of adjoint equation, for ajAnd b (t)j
(t), J derivative is as follows in each iteration：
Wherein, adjoint functionAnd φmIt is the answer of equation (3).
6. the intrinsic image decomposition method according to claim 5 learnt based on partial differential equation, it is characterised in that described
Golden section search is performed along the direction of search in step S7, and constantly updates system function, next circulation is carried out；
Golden section search is performed along the direction of search, control function a is updatedjAnd b (t)j(t), j=0,1 ..., 16, under continuation
One circulation, until j=16, is trained.
7. the intrinsic image decomposition method according to claim 6 learnt based on partial differential equation, it is characterised in that described
In step S8, circulation, output system function are terminatedWith
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| US20160171755A1 (en) * | 2013-08-08 | 2016-06-16 | Adobe Systems Incorporated | Automatic geometry and lighting inference for realistic image editing |
| CN106355601A (en) * | 2016-08-31 | 2017-01-25 | 上海交通大学 | Intrinsic image decomposition method |
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| CN104700109A (en) * | 2015-03-24 | 2015-06-10 | 清华大学 | Method and device for decomposing hyper-spectral intrinsic images |
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