CN106447714B - A kind of scene depth restoration methods based on signal decomposition - Google Patents
A kind of scene depth restoration methods based on signal decomposition Download PDFInfo
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Abstract
The invention belongs to field of image processings, provide a kind of scene depth restoration methods based on signal decomposition.The present invention is based on the priori knowledges that depth image signal is detachable, each section after being split by curved surface least square fitting and total variation filtering to depth signal models respectively, and the depth recovery model based on signal decomposition is constructed, respective algorithms are derived, solution obtains high quality depth image.The invention has program simple, it is easy to accomplish, the depth image of high quality can be obtained；This method is modeled respectively by each ingredient to depth signal, when avoiding using texture image deduction depth image, texture information can be mixed into depth image with the real structure feature of excavating depth image, so that the problem of depth value estimation inaccuracy；Using enhancing Lagrange and alternate method and solved, the complicated multivariable combined optimization problem with equality constraint is converted into be easy solution without constraining several subproblems.
Description
Technical field
The invention belongs to field of image processing, it is related to modeling depth information of scene using signal decomposition model, and derive
Respective algorithms acquire high quality depth map, and in particular to a kind of scene depth restoration methods based on signal decomposition.
Background technique
Scene depth is widely used in the various tasks of computer vision, including three-dimensional (3D) modeling, visualization and machine
Device people navigation etc.；Meanwhile it is also beneficial to the spatial reasoning and scene understanding of object.In fast-developing 3D cinematic industry
In, the acquisition of depth information of scene greatly simplifies the process that two-dimentional (2D) plane film is converted to three-dimensional film.Now
Scene depth acquisition modes majority uses depth camera, such as the Kinect camera of Microsoft, the RealSense phase of Intel Company
Machine etc. carries out the real-time perception of scene depth.But the Depth Imaging quality of depth camera is also difficult to meet application demand: point
Resolution is lower than the spatial resolution of mainstream industry camera, and noise is big, and image quality is influenced by extraneous light, and in depth jump area
Domain generates many cavities.The defect of these Depth Imagings brings very big obstacle to practical application.
Under normal conditions, depth camera can acquire the texture and depth information of scene simultaneously, and many scene depths are excellent
Change method i.e. improved using existing high quality texture information corresponding depth plot quality (J.Yang, X.Ye, K.Li,
C.Hou,and Y.Wang,“Color-guided depthrecovery from RGBD data using an adaptive
autoregressive model."IEEETIP,vol.23,no.8,pp.3443–3458,2014).The it is proposed base of such methods
In one it is assumed that i.e. depth image and corresponding texture image are highly relevant on characteristics of image and structure.But in reality
In the situation of border, colour and structural information contained by texture image will can not be found far more than depth image from cromogram
To a constant mapping relations of depth map, lead to depth value estimation inaccuracy.
It is observed that depth image is mainly made of region smooth paragraph by paragraph, and each piece of smooth region is by depth edge point
It leaves and.This signal can be split as the polynomial surface signal component of low order and the step signal ingredient of piecewise constant.Base
In this, modeled respectively by each ingredient to depth signal, can be with the real structure feature of excavating depth image, and then complete
The recovery of depth image.
Summary of the invention
The present invention is directed to overcome the deficiencies of the prior art and provide a kind of scene depth recovery side based on signal decomposition
Method.It is observed that depth image can be split as the polynomial surface signal component of low order and the step signal ingredient of piecewise constant.
Based on this priori knowledge, this method is by curved surface least square fitting and total variation (TV) filtering to two parts of signals ingredient point
It does not model, and constructs signal decomposition model, derive respective algorithms, solution obtains high quality depth image.
The technical scheme is that a kind of scene depth restoration methods based on signal decomposition, the method includes under
Column step:
The first step prepares primary data；
Primary data includes low quality depth map and the high-resolution color figure with visual angle.
Second step constructs observation model；
According to the decomposable priori of depth signal, real depth map f by low order polynomial surface signal z and piecewise constant
Step signal x constitute, it may be assumed that
F=x+z
Enable f0It is expressed as low quality depth map, the observation model that depth obtains can be expressed from the next:
f0=Kf+n
=K (x+z)+n
In formula, K indicates that observing matrix, n indicate the Gaussian noise of additivity.In the case where depth missing, f0Valid pixel
Number is less than real depth map f, is flat matrix, each element indicates the validity of corresponding position depth value in K；Only depositing
In the case where noise, K is unit square matrix.
Third step constructs the constraint equation of the polynomial surface signal of low order；
Moving-polynomial smoother filter is suitable for Local approximation in polynomial signal, is fitted by the way of least square
Polynomial surface under noise observation；Using this characteristic, following constraint equation is constructed:
Wherein, P is vandermonde matrix, and t is multinomial coefficient, | | | |2For 2 norms.
4th step constructs the constraint equation of the step signal ingredient of piecewise constant；
Total variation filter linearly punishes the difference of adjacent element in signal, the signal of pairing approximation piecewise constant into
Row modeling, retains step ingredient therein；Using this characteristic, following constraint equation is constructed:
Wherein, D is difference matrix, | | | |1For 1 norm；Y is substitute variable, is acted on to replace out Dx out of 1 norm
Come, complicated energy equation is split into simple optimization problem.
5th step, according to second and third, the obtained observation model of four steps and constraint equation construct the depth based on signal decomposition
Restoration model.
5-1) by polynomial surface signal bondage equation and the step signal constraint equation of piecewise constant under observation model
Combine, constitute following equation:
S.t.y=Dx, f0=K (x+z)+n
Wherein, λ is balance factor.
5-2) by observation model constraint and polynomial surface signal bondage partial fusion to together, to reduce equality constraint,
Equation is as follows:
Variable z is substituted with Pt so that model is easier to restrain.
5-3) using the depth edge in high-resolution color figure auxiliary positioning depth map, depth edge priori is integrated to
In total variation item, final optimization method is obtained:
Wherein, ω is weight vectors, and whether corresponding pixel belongs to depth edge in indicator variable y.It ° is matrix by member
Plain multiplication operations.When depth map band noise, ω is complete 1 vector；When for depth missing the case where, ω is extracted in cromogram,
With ω come auxiliary positioning.
6th step derives 5-3) derivation algorithm of optimization method in step, obtain final high quality depth map；
6-1) using enhancing Lagrangian method, unconstrained problem is converted by the optimization problem of belt restraining, equation is as follows:
Wherein, μ is penalty factor, and Q is Lagrange multiplier matrix,<,>it is matrix inner products.
It 6-2) using method is alternated, fixes its dependent variable and optimizes current variable in turn, until algorithmic statement.Specific solution
Under entering:
X 6-2-1) is set0, Q0, t0, μ0, ρ0Initial value:, the number of iterations i=1, wherein x0、Q0、t0、μ0、ρ0Generation respectively
The initial value of table variable x, Q, t, μ, ρ.
Its dependent variable 6-2-2) is fixed, y-component is solved, can obtain:
yi+1=soft (Dxi+Qi/μi,ω/μi)
Its dependent variable 6-2-3) is fixed, x-component is solved, can obtain:
xi+1=(μiDTD+2λKTK)-1(μiDTyi+1-DTQi-2λKTKPti+2λKTf0)
Its dependent variable 6-2-4) is fixed, t component is solved, can obtain:
ti+1=((KP)T(KP))-1(KPT)(f0-Kxi+1)
Its dependent variable 6-2-5) is fixed, Q component is solved, can obtain:
Qi+1=Qi+μi(yi+1-Dxi+1)
Then 6-2-6) undated parameter μ carries out next iteration:
μi+1=ρ μi, i=i+1
6-2-7) repeat step 6-2-2) arrive step 6-2-6), until convergence, and calculate final high quality depth map.Side
Journey is as follows:
F=x+Pt
Above-mentioned second step and 5-3) in depth missing the case where lost for lack sampling or depth value.
The beneficial effects of the present invention are:
The present invention is based on the priori knowledges that depth image signal is detachable, pass through curved surface least square fitting and total variation
(TV) it filters each section after splitting depth signal to model respectively, and constructs the depth recovery model based on signal decomposition, push away
Respective algorithms are led, solution obtains high quality depth image, has the following characteristics that
1, program is simple, it is easy to accomplish, the depth image of high quality can be obtained；
2, this method is modeled respectively by each ingredient to depth signal, can be special with the real structure of excavating depth image
Texture information is mixed into depth image, when avoiding using texture image deduction depth image so that depth value is estimated by sign
The problem of inaccuracy；
3, algorithm uses enhancing Lagrange and alternates method and solved, by the complicated multivariable with equality constraint
Combined optimization problem be converted into be easy solution without constraining several subproblems.
Detailed description of the invention
Fig. 1 is implementation flow chart, by taking the low quality depth image block with noise as an example.
Fig. 2 is primary data；
In figure: (a) low quality depth map (b) high-resolution color figure
Fig. 3 is the recovery for the depth image block that lack sampling and depth value are lost.
Fig. 4 is the depth map restoration result of actual acquisition；Comparison is asked using the result that real depth map and each method acquire
Difference is shown, and light tone representative is not consistent with true value, and black representative is consistent with true value；
In figure: (a) colour-depth standards data set (b) the method for the present invention result (c) Steerable filter result (d) multiple spot
Filter result (e) autoregression model result.
Specific embodiment
The scene depth restoration methods of the invention based on signal decomposition are made in detail below with reference to embodiment and attached drawing
Explanation.
A kind of scene depth restoration methods based on signal decomposition, as shown in Figure 1, the method includes the following steps:
The first step prepares primary data；
Primary data includes low quality depth map (low resolution, containing missing, with noise) and the high-resolution coloured silk with visual angle
Chromatic graph, as shown in Figure 2.
Second step constructs observation model；
According to the decomposable priori of depth signal, real depth map f can be by the polynomial surface signal and perseverance paragraph by paragraph of low order
This two parts of fixed step signal are constituted, and are indicated respectively with z and x, it may be assumed that
F=x+z
Enable f0It is expressed as low quality depth map, the observation model that depth obtains can be expressed from the next:
f0=Kf+n
=K (x+z)+n
In formula, K indicates that observing matrix, n indicate the Gaussian noise of additivity.When there are depth missing the case where, i.e. lack sampling
Or depth value is lost, low quality depth map f0Valid pixel number be less than real depth map f, K be flat matrix, wherein each
Element indicates the validity of corresponding position depth value；When there is only in the case where noise, K is unit square matrix.
Third step constructs the constraint equation of polynomial surface signal component；
Moving-polynomial smoother filter is suitable for Local approximation in polynomial signal, and the mode for generalling use least square is come
The polynomial surface being fitted under noise observation；Using this characteristic, following constraint equation is constructed:
Wherein, P is Vandermonde (Vandermonde) matrix, and t is multinomial coefficient, | | | |2For 2 norms.By right
Depth signal observation, the polynomial surface that the top step number of vandermonde matrix P is 2 can completely represent the multinomial of depth map
Curved surface signal part.
4th step constructs the constraint equation of the step signal ingredient of piecewise constant；
Total variation (TV) filter linearly punishes the difference of adjacent element in signal, can be with pairing approximation piecewise constant
Signal modeled, retain step ingredient (edge) therein；Using this characteristic, following constraint equation is constructed:
Wherein, D is difference matrix, | | | |1For 1 norm；Y is substitute variable, is acted on to replace out Dx out of 1 norm
Come, complicated energy equation is split into simple optimization problem.
5th step, according to second and third, the obtained observation model of four steps and constraint equation construct the depth based on signal decomposition
Restoration model.
5-1) by polynomial surface signal bondage equation and the step signal constraint equation of piecewise constant under observation model
Combine, constitute following equation:
S.t.y=Dx, f0=K (x+z)+n
Wherein, λ is balance factor, value 0.1.
5-2) by observation model constraint and polynomial surface signal bondage partial fusion to together, to reduce equality constraint,
Equation is as follows:
Variable z is substituted with Pt so that model is easier to restrain.
5-3) using the depth edge (discontinuous place) in high-resolution color figure auxiliary positioning depth map, by depth edge
Priori is integrated in total variation item, obtains final optimization method:
Wherein, ω is weight vectors, and whether corresponding pixel belongs to depth edge in indicator variable y.It ° is matrix by member
Plain multiplication operations.The case where for depth map band noise, ω is complete 1 vector；For depth missing the case where, i.e., lack sampling or
Depth value is lost, and depth edge loss is more serious, needs ω to carry out auxiliary positioning, using canny edge detecting technology in colour
ω is extracted in figure.Lack sampling is illustrated in Fig. 3 and depth value lacks the depth image block restoration result of two kinds of situations.
6th step, according to 5-3) in optimization method derive corresponding derivation algorithm；
6-1) utilize enhancing Lagrangian method (Z.Lin, M.Chen, and Y.Ma, " The augmented
lagrange multiplier methodfor exact recovery of corrupted low-rank matrices,”
ArXiv preprintarXiv:1009.5055,2010), unconstrained problem is converted by the optimization problem of belt restraining, equation is such as
Under:
Wherein, μ is penalty factor, and Q is Lagrange multiplier matrix,<,>it is matrix inner products.
It 6-2) utilizes and alternates method (J.Yang and Y.Zhang, " Alternating direction
algorithms for 1-problemsin compressive sensing,”SIAM journal on scientific
Computing, vol.33, no.1, pp.250-278,2011), it fixes its dependent variable and optimizes current variable in turn, until algorithm
Convergence.Under specific solution enters:
Initial value: x 6-2-1) is set0=K-1f0, Q0=0, t0=0, μ0=0.05, ρ0=1.2, the number of iterations i=1,
Middle x0、Q0、t0、μ0、ρ0Respectively represent the initial value of x, Q, t, μ, ρ.
Its dependent variable 6-2-2) is fixed, y-component is solved, can obtain:
yi+1=soft (Dxi+Qi/μi,ω/μi)
Its dependent variable 6-2-3) is fixed, x-component is solved, can obtain:
xi+1=(μiDTD+2λKTK)-1(μiDTyi+1-DTQi-2λKTKPti+2λKTf0)
Its dependent variable 6-2-4) is fixed, t component is solved, can obtain:
ti+1=((KP)T(KP))-1(KPT)(f0-Kxi+1)
Its dependent variable 6-2-5) is fixed, Q component is solved, can obtain:
Qi+1=Qi+μi(yi+1-Dxi+1)
Then 6-2-6) undated parameter μ carries out next iteration:
μi+1=ρ μi, i=i+1
6-2-7) repeat step 6-2-2) arrive step 6-2-6), until convergence, and final high quality depth map is calculated, side
Journey is as follows:
F=x+Pt
The present embodiment is to the final restoration result of three groups of data and compared with other methods as shown in figure 4, wherein (a) figure
For colour-depth standards data set, (b) the method for the present invention as a result, (c) Steerable filter result (K.He, J.Sun, and
X.Tang, " Guided image filtering, " in Proc.ECCV, 2010, pp.1-14), (d) multiple spot filter result
(J.Lu,K.Shi,D.Min,L.Lin,and M.N.Do,“Cross-based localmultipoint filtering,”in
Proc.CVPR, 2012, pp.430-437.), (e) autoregression model result (J.Yang, X.Ye, K.Li, C.Hou, and
Y.Wang,“Color-guided depthrecovery from RGBD data using an adaptive
autoregressive model.”IEEETIP,vol.23,no.8,pp.3443–3458,2014)。
Claims (5)
1. a kind of scene depth restoration methods based on signal decomposition, characterized in that it comprises the following steps:
The first step prepares primary data, including low quality depth map and with the high-resolution color figure at visual angle；
Second step constructs observation model；According to the decomposable priori of depth signal, real depth map f is bent by the multinomial of low order
The face signal z and step signal x of piecewise constant is constituted, it may be assumed that
F=x+z
The observation model that depth obtains are as follows:
f0=Kf+n
=K (x+z)+n
In formula, f0For low quality depth map, K is observing matrix, and n is the Gaussian noise of additivity；In the case where depth missing, f0
Valid pixel number is less than real depth map f, is flat matrix, each element indicates the effective of corresponding position depth value in K
Property；There is only noise, K is unit square matrix；
Third step constructs the constraint equation of the polynomial surface signal of low order；
The polynomial surface being fitted by the way of least square under noise observation；Construct the pact of the polynomial surface signal of low order
Shu Fangcheng are as follows:
Wherein, P is vandermonde matrix, and t is multinomial coefficient, | | | |2For 2 norms；
4th step constructs the constraint equation of the step signal of piecewise constant；
Total variation filter is linearly punished that the signal of pairing approximation piecewise constant is built to the difference of adjacent element in signal
Mould retains step ingredient therein；Construct the constraint equation of the step signal of piecewise constant are as follows:
Wherein, D is difference matrix, | | | |1For 1 norm；Y is substitute variable, is come out for replacing Dx out of 1 norm；
5th step constructs the depth restoration model based on signal decomposition, comprising the following steps:
5-1) by the polynomial surface signal bondage equation of low order and the step signal constraint equation of piecewise constant in observation model
Under combine, constitute following equation:
S.t.y=Dx, f0=K (x+z)+n
Wherein, λ is balance factor；
5-2) by observation model constraint and polynomial surface signal bondage partial fusion to together, to reduce equality constraint, equation
It is as follows:
Variable z is substituted with Pt so that model is easier to restrain；
5-3) using the depth edge in high-resolution color figure auxiliary positioning depth map, depth edge priori is integrated to full change
In poor item, final optimization method is obtained:
Wherein, ω is weight vectors, is used to indicate whether corresponding pixel in variable y belongs to depth edge；It ° is matrix by member
Plain multiplication operations；When depth map band noise, ω is complete 1 vector；When for depth missing the case where, ω is extracted in cromogram,
With ω come auxiliary positioning；
6th step derives 5-3) derivation algorithm of optimization method in step, obtain final high quality depth map.
2. a kind of scene depth restoration methods based on signal decomposition according to claim 1, which is characterized in that the 6th step
The derivation algorithm for deriving optimization method, obtains high quality depth map, comprising the following steps:
6-1) using enhancing Lagrangian method, unconstrained problem is converted by the optimization problem of belt restraining, equation is as follows:
Wherein, μ is penalty factor, and Q is Lagrange multiplier matrix,<,>it is matrix inner products；
It 6-2) using method is alternated, fixes its dependent variable and optimizes current variable in turn, until algorithmic statement；Calculate final height
Quality depth figure, equation are as follows:
F=x+Pt.
3. a kind of scene depth restoration methods based on signal decomposition according to claim 1 or 2, which is characterized in that the
In three steps, the top step number of vandermonde matrix P is 2.
4. a kind of scene depth restoration methods based on signal decomposition according to claim 1 or 2, which is characterized in that the
Two steps and 5-3) described in depth missing the case where lost for lack sampling or depth value.
5. a kind of scene depth restoration methods based on signal decomposition according to claim 3, which is characterized in that second step
And 5-3) described in depth missing the case where lost for lack sampling or depth value.
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| CN102722863A (en) * | 2012-04-16 | 2012-10-10 | 天津大学 | Super-resolution reconstruction method for depth map by adopting autoregressive model |
| CN103218771A (en) * | 2013-03-07 | 2013-07-24 | 天津大学 | Parameter self-adaptation selecting method based on autoregressive model depth recovery |
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| CN102722863A (en) * | 2012-04-16 | 2012-10-10 | 天津大学 | Super-resolution reconstruction method for depth map by adopting autoregressive model |
| CN103218771A (en) * | 2013-03-07 | 2013-07-24 | 天津大学 | Parameter self-adaptation selecting method based on autoregressive model depth recovery |
Non-Patent Citations (3)
| Title |
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| Color-Guided Depth Recovery From RGB-D Data Using an Adaptive Autoregressive Model;Jingyu Yang et al.;《IEEE Transactions On Image Processing》;20140831;第23卷(第8期);第3443-3458页 |
| High Quality Depth Map Upsampling for 3D-TOF Cameras;Jaesik Park et al.;《2011 IEEE International Conference on Computer Vision》;20111231;第1623-1630页 |
| Image Guided Depth Upsampling using Anisotropic Total Generalized Variation;David Ferstl et al.;《2013 IEEE International Conference on Computer Vision》;20131231;第993-1000页 |
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