CN102184540A - Sub-pixel level stereo matching method based on scale space - Google Patents

Sub-pixel level stereo matching method based on scale space Download PDF

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CN102184540A
CN102184540A CN2011101126198A CN201110112619A CN102184540A CN 102184540 A CN102184540 A CN 102184540A CN 2011101126198 A CN2011101126198 A CN 2011101126198A CN 201110112619 A CN201110112619 A CN 201110112619A CN 102184540 A CN102184540 A CN 102184540A
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门朝光
边继龙
李香
余鹏达
尚方
田泽宇
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Harbin Engineering University
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Abstract

The invention provides a sub-pixel level stereo matching method based on a scale space. The method comprises the following steps of: (1) establishing the scale space for a stereopair; (2) determining the size of a matching window for each point of a current level reference image in the scale space; (3) calculating a parallax searching range for each point of the level reference image according to the parallax of the former level; (4) calculating an integer-grade parallax of the current level in the scale space; and (5) calculating a sub-pixel level parallax through a sub-pixel level matching method based on binary search. The method of the invention uses the stereopair generated under the condition of small height ratio to match; a dispersed scale space is used in the matching process to improve the matching efficiency; a bonding phenomenon generated in the matching process is reduced by using a mixed window selecting strategy; and the sub-pixel level parallax is obtained by the sub-pixel level matching method based on the binary search so as to ensure high sub-pixel level precision, and greatly improve matching efficiency of the algorithm.

Description

Sub-pixel solid matching method based on metric space
Technical field
The present invention relates to computer vision, signal Processing, stereo mapping method, is a kind of sub-pixel solid matching method.
Background technology
The depth difference of three-dimensional scenic can produce geometric displacement on the view that different points of view obtains, three-dimensional coupling obtains the parallax of corresponding point with regard to being based on this principle by the view that mates two width of cloth or several different points of view, calculates the depth information of scenery again by principle of triangulation.Three-dimensional coupling is a hot issue in the computer vision field, and it has a wide range of applications in fields such as robot navigation, stereo mapping, photogrammetric measurement, remote sensing.
The stereogram that forms under the big base-height ratio condition of tradition can exist and more block, bigger radiation difference and geometric distortion and because the relative position variation that moving target in the scene produces, these factors have increased difficulty of matching to a certain extent, have caused a large amount of mistake couplings.
For weakening the adverse effect that above-mentioned factor produces coupling, the Stereo Matching Technology under the little base-height ratio condition is arisen at the historic moment.Base-height ratio is meant the ratio of photographic base and camera height, little base-height ratio then is meant in camera height one regularly, the time interval of taking pictures for twice is short, and promptly twice imaging time distance in the heart is less, factors such as the stereogram that forms under this condition can weaken that relative position between the scenery changes because motion produces, radiation difference and geometric distortion to the influence of mating to improve the accuracy that solid is mated.Depth information, base-height ratio and parallax satisfy dz=d ε/(b/h), under the given condition of parallax precision, base-height ratio is big more, depth error is more little, therefore, the base-height ratio that big more options are bigger in stereopsis to be reducing the increase that causes depth error owing to the parallax precision inadequately, but meanwhile, big base-height ratio has increased difficulty of matching again, has caused a large amount of mistake couplings.J.Delon in 2007 and B.Roug are at the 28th volume of " Journal of Mathematical Imaging and Vision ", delivered " Small Baseline Stereovision " paper on the 3rd phase, in this paper, proposed first based on little base-height ratio solid matching method, it is the adaptive definite window size of every bit in the reference picture that this method has proposed a kind of self-adapting window strategy, utilize " victor gets entirely " policy calculation every bit parallax again, utilize barycenter to proofread and correct to reduce " bonding " phenomenon in the three-dimensional coupling then, the last continuous expression form of calculating related coefficient in frequency domain obtains the sub-pixel parallax.It and difference of the present invention are to the present invention proposes hybrid window selection strategy and reduce " bonding " phenomenon in the three-dimensional coupling, and have proposed to obtain the sub-pixel parallax based on the sub-pixel matching process of binary search.
Summary of the invention
The object of the present invention is to provide and a kind ofly can improve matching precision, can obtain the sub-pixel parallax of degree of precision, but also have the sub-pixel solid matching method based on metric space of lower space-time complexity.
The object of the present invention is achieved like this:
(1) makes up metric space for stereogram;
In this step, be left and right sides picture construction metric space in the stereogram according to disparity range, the formula that makes up metric space is as follows:
Figure BDA0000058935120000021
In the formula, u NN layer scalogram picture in the expression metric space, wherein, u 0(N=0) bottom layer image is an original image in the expression metric space;
(2) determine the match window size for the every bit of current level reference picture in the metric space;
In this step, determine this match window size according to every spot correlation density of current level reference picture in the metric space.Relevant density calculation formula is as follows:
Figure BDA0000058935120000023
In the formula,
Figure BDA0000058935120000024
The presentation video function, The presentation video function
Figure BDA0000058935120000026
Derivative, Expression is with x 0Be the support window at center, image function Norm
Figure BDA0000058935120000029
Computing formula as follows:
Figure BDA00000589351200000211
With its derivative
Figure BDA00000589351200000212
The inner product computing formula as follows:
Figure BDA00000589351200000213
The formula that calculates the match window size is as follows:
Figure BDA00000589351200000214
In the formula,
Figure BDA00000589351200000215
The expression reference picture, g is a Gaussian function, ↑ bPoor for noise criteria, λ is a matching precision,
Figure BDA00000589351200000216
Computing formula as follows:
Figure BDA00000589351200000217
(3) according to last layer level parallax be the every bit calculating parallax hunting zone of this level reference picture;
Be the every bit calculating parallax hunting zone of current level reference picture in the metric space, at first calculate the initial parallax of this level according to the integer level parallax of last layer level, the computing formula of initial parallax is as follows:
Figure BDA0000058935120000032
In the formula, d N(i j) is N level (i, j) the integer level parallax of position; Then, according to maximum disparity value d MaxCalculate the maximum disparity value d of this level N, max, its computing formula is as follows:
Figure BDA0000058935120000033
In the formula,
Figure BDA0000058935120000034
Expression is more than or equal to the smallest positive integral of x.
(4) the integer level parallax of current level in the calculating metric space;
In this step, according to the parallax hunting zone that obtains in match window size of determining for every bit in the step (2) and the step (3), at each definite match window position of hybrid window selection strategy, similarity according to NCC calculating match window in corresponding parallax hunting zone obtains pairing optimum parallax value under each the window's position, and chooses the final parallax of parallax conduct of similarity maximum in the parallax that is calculated under these the window's positions.
The NCC computing formula is as follows:
Figure BDA0000058935120000035
In the formula,
Figure BDA0000058935120000036
With
Figure BDA0000058935120000037
Represent the left and right sides image in the stereogram respectively, W kRepresent corresponding match window.
The pairing parallax computing formula of each the window's position is as follows:
Figure BDA0000058935120000038
In the formula, (optimal cost is expressed as accordingly for x, y) the optimum parallax of point under k match window in expression
Figure BDA00000589351200000310
The computing formula of final parallax is as follows:
Figure BDA00000589351200000311
In the formula,
Figure BDA00000589351200000312
Expression (x, final parallax y).
(5) utilize sub-pixel matching process to calculate the sub-pixel parallax based on binary search.
In this step, according to the integer level parallax that calculates in multiscale space, utilize binary search to calculate the sub-pixel parallax that is better than designated precision again, the computing formula of its binary search is as follows:
Figure BDA00000589351200000314
In the formula, A 〉=1 is an iterations, d A(x 0) expression x 0The sub-pixel parallax of the A time iteration of point, d 1(x 0) (A=1) expression x 0The integer parallax of point,
Figure BDA0000058935120000041
The expression reference windows
Figure BDA0000058935120000042
With match window
Figure BDA0000058935120000043
The standard cross-correlation coefficient, its computing formula is as follows:
Figure BDA0000058935120000044
Reduce computing time and improve matching efficiency under the prerequisite that guarantees matching precision, the present invention is embedded into three-dimensional matching process in the middle of the discrete metric space of " by slightly to smart ".Large scale image in the metric space provides the Global Information of image, and the small scale image provides the detailed information of image; The parallax of trying to achieve under large scale is approximate parallax, and the parallax of trying to achieve under small scale is accurate parallax.Based on the solid of metric space coupling in matching process, utilize exactly metric space at the middle and upper levels the approximate parallax of yardstick instruct this layer yardstick to mate and then try to achieve the process of this layer yardstick parallax.The size that supports window in matching process can influence matching precision, for obtaining in the reliable parallax support window certain grey scale change being arranged, supporting window in the non-texture region of image should be big as much as possible to comprise enough half-tone informations, should be enough little of to guarantee that parallax is constant in the window and support window in texture region.For this reason, the present invention has introduced the adaptive windows vocal imitation skill in matching process, and adaptive process has only changed window size and do not change its shape, and this can cause supporting window and cross over object boundary and produce " bonding " phenomenon.Cross over object boundary for avoiding supporting window in the matching process, the present invention proposes hybrid window selection strategy, hybrid window selection strategy not only can mate required grey scale change scope to satisfy by adaptive selection window size, but also the diversity that has increased the match window shape can improve matching precision to a certain extent to avoid the window crossing the boundary.
For obtaining the sub-pixel parallax, then need after obtaining integer level parallax, add the sub-pixel coupling.Traditional sub-pixel matching process mainly comprises image resampling method, fitting process and phase method.The image resampling method is to utilize interpolation technique that matching image is carried out interpolation to obtain high-definition picture, each location of pixels in the high-definition picture is represented the sub-pixel location of original image, utilize Stereo Matching Technology to determine the sub-pixel parallax again, this algorithm has realizes simple, precision advantages of higher, but its computation complexity is higher.Fitting process is to utilize the adjacent cost of the Optimum Matching cost and the left and right sides thereof, adopt fitting technique to obtain the continuous expression form of cost function, ask the extreme value place of its function again, this extreme point position is sub-pixel parallax position, this algorithm has to be realized simply, advantages such as complexity is low, but its sub-pixel precision is lower.Phase method is the displacement information that utilizes the phase information acquisition picture point of frequency domain, but the frequency alias effect can seriously influence the bearing accuracy of algorithm.For obtaining high-precision sub-pixel parallax, reduce the computation complexity of algorithm simultaneously, the present invention proposes the sub-pixel matching process based on binary search, this method not only can obtain the sub-pixel parallax of degree of precision, but also has lower space-time complexity.
The sub-pixel solid matching method that the present invention is based on metric space has used the stereogram that generates under the little base-height ratio condition to mate, in matching process, adopted discrete metric space to improve matching efficiency, and utilize hybrid window selection strategy to reduce " bonding " phenomenon that is produced in the matching process, used sub-pixel matching process to obtain the sub-pixel parallax at last based on binary search, this method not only can guarantee higher sub-pixel precision, but also has improved the matching efficiency of algorithm to a great extent.Compare with other matching process, advantage of the present invention is:
1, the present invention uses the stereogram of producing under the little base-height ratio condition to reduce because the mistake that factor caused couplings such as the relative position variation between the scenery, the radiation difference between stereogram and geometric distortions;
2, the present invention has been embedded into matching process in the middle of the discrete metric space, utilizes higher level's parallax to instruct subordinate to mate, and has reduced computing time, has improved matching efficiency;
3, the present invention proposes the hybrid window selection strategy that self-adapting window and multiwindow combine, this method has reduced " bonding " phenomenon that is produced in the matching process to a great extent, has improved the matching accuracy rate of integer level parallax;
4, the present invention proposes sub-pixel matching process based on binary search obtains the sub-pixel parallax and gives the error that three-dimensional reconstruction was brought to remedy little base-height ratio, this method not only can obtain higher sub-pixel precision, but also have lower space-time complexity: its time complexity O (A), space complexity is O (K 2).
Description of drawings
Fig. 1 is the sub-pixel solid matching method process flow diagram based on metric space;
Fig. 2 is a multiscale space pyramid synoptic diagram;
Fig. 3 is hybrid window selection strategy synoptic diagram;
Fig. 4 is the sub-pixel coupling schematic diagram based on 3 * 3 windows;
Fig. 5 (a)-Fig. 5 (d) is experiment effect figure of the present invention, and first row Fig. 5 (a) is the reference picture in the stereogram, and secondary series Fig. 5 (b) is true disparity map, and the 3rd row Fig. 5 (c) is an integer level disparity map, and the 4th row Fig. 5 (d) is the sub-pixel disparity map.
Embodiment
For example technical scheme of the present invention is further described below in conjunction with accompanying drawing:
Fig. 1 has shown the process flow diagram of the sub-pixel solid matching method that the present invention is based on metric space, describes the specific implementation of each step in detail below in conjunction with this process flow diagram:
(1) makes up metric space for stereogram;
1. at first according to the maximum disparity value d of original stereogram MaxCalculate the maximum level N of metric space Max, its computing formula is as follows:
Figure BDA0000058935120000051
2. according to the maximum level N of metric space MaxBe respectively reference picture
Figure BDA0000058935120000052
Make up metric space with matching image u
Figure BDA0000058935120000053
And u N, its computing formula that makes up metric space is as follows:
Figure BDA0000058935120000054
Figure BDA0000058935120000055
Figure BDA0000058935120000061
Figure BDA0000058935120000062
In the formula, N layer reference picture in the expression metric space, wherein,
Figure BDA0000058935120000064
Expression original reference image
Figure BDA0000058935120000065
u NN layer matching image in the expression metric space, wherein, u 0(N=0) expression original match image.The height and the width of N layer yardstick reference picture and matching image are respectively 1/2 of former reference picture and matching image N, the construction process of its metric space as shown in Figure 2.
(2) determine the match window size for the every bit of current level reference picture in the metric space;
1. under the current level of metric space, at first calculate Gauss's norm according to standard deviation, its Gauss's norm calculation formula is as follows:
Figure BDA0000058935120000066
In the formula, the value of σ is 0.56.
2. the every bit for current level reference picture in the metric space calculates optimum window size, and the calculating of optimum window comes down to calculate the min-window value that satisfies inequality in the window size span, and its optimum window calculation formula is as follows:
Figure BDA0000058935120000067
In the formula,
Figure BDA0000058935120000068
The expression reference picture, g represents Gaussian function, ↑ bExpression Gaussian noise standard deviation, λ represents matching precision, The relevant density of expression reference picture, its computing formula is as follows:
Figure BDA00000589351200000610
(3) parallax according to the last layer level is the every bit calculating parallax hunting zone of this level reference picture;
1. the integer level parallax according to the last layer level is the every bit calculating initial parallax value of this level, and the computing formula of initial parallax is as follows:
Figure BDA00000589351200000611
Figure BDA00000589351200000612
In the formula, d N(i j) is N layer (i, j) the integer level parallax of position.
2. according to maximum disparity value d MaxCalculate the maximum disparity value d of this level N, max, its computing formula is as follows:
Figure BDA0000058935120000071
In the formula, Expression is more than or equal to the smallest positive integral of x.
(4) the integer level parallax of current level in the calculating metric space;
According to the parallax hunting zone of calculating in match window size of calculating in the step (2) and the step (3), at definite each the window's position (as shown in Figure 3) of hybrid window selection strategy, in corresponding parallax hunting zone, calculate the similarity of match window according to NCC, utilize " victor gets entirely " strategy to obtain the pairing optimum parallax of each the window's position again, and in these parallaxes, choose the final parallax of parallax conduct of similarity maximum.
1. at each the window's position, calculate the coupling cost according to window size and disparity range, its computing formula is as follows:
Figure BDA0000058935120000073
In the formula, u and
Figure BDA0000058935120000074
Represent the left and right sides image in the stereogram respectively, W kRepresent corresponding match window, C k(x, y, d) remarked pixel (x, y) under k window, the coupling cost when parallax is d.
2. calculate pairing parallax under each the window's position, its computing formula is as follows:
Figure BDA0000058935120000075
In the formula,
Figure BDA0000058935120000076
(optimal cost is expressed as accordingly for x, y) the optimum parallax of point under k match window in expression
Figure BDA0000058935120000077
3. calculate final parallax, its computing formula is as follows:
Figure BDA0000058935120000078
In the formula,
Figure BDA0000058935120000079
Expression (x, final parallax y).
(5) utilize sub-pixel matching process to calculate the sub-pixel parallax based on binary search.
In this step,, utilize binary search to calculate the sub-pixel parallax that is better than designated precision according to the integer level parallax that in multiscale space, obtains.
1. at first utilize the linear interpolation formula to calculate the gray-scale value of match window and adjacent window apertures floating-point position, the left and right sides thereof, its left and right sides adjacent window apertures is by all pixels in the match window are distinguished direction translations to the left and right 1/2 ATwo windows that (A is an iterations) forms are called these three windows hereinafter: middle match window, the move to left match window and the match window that moves to right, and the gray scale computing formula of floating-point position is as follows in its match window:
Figure BDA00000589351200000710
In the formula, Expression rounds.
2. utilize NCC similarity measurement formula to calculate the similarity of reference windows and three match windows, its computing formula is as follows:
Figure BDA0000058935120000082
In the formula, Wherein A 〉=1 is an iterations, d A(x 0) expression x 0The sub-pixel parallax of the A time iteration of point, d 1(x 0) (A=1) expression x 0The integer level parallax of point,
Figure BDA0000058935120000084
Expression is with x 0Point is the reference windows at center,
Figure BDA0000058935120000085
Expression is with x 0+ m is the match window at center.
3. determine optimum sub-pixel parallax according to calculating three similarity values that obtain, computing formula is as follows:
Figure BDA0000058935120000086
Figure BDA0000058935120000087
The optimum sub-pixel parallax obtained is continued iterative search as new central point, and till reaching given solving precision, Fig. 4 has shown and uses 3 * 3 windows to carry out the sub-pix matching process of twice iteration.
Satisfy when the image sampling frequency under the situation of sampling thheorem, binary search can reach higher sub-pixel precision, and the sample frequency of image does not often satisfy sampling thheorem in the solid coupling of reality, and the precision of sub-pix is limited.Through experimental verification, this method can reach 1/20 sub-pixel precision, i.e. A=5.
Compare the present invention proposes the sub-pix method tangible improvement has all been arranged on time and space complexity with the sub-pix matching process of resampling method.When sub-pixel precision is 2 AThe time, the space complexity of resampling method is S 1=K 2* 2 A, and the space complexity of binary search is S 2=3*K 2, wherein K is for supporting window size; On time complexity, binary search is reduced to the linear session complexity with exponential time complexity, and the time complexity of resampling method is T=O (2 A), and the time complexity of binary search is T=O (A), this algorithm has had obvious improvement on time complexity.

Claims (6)

1. sub-pixel solid matching method based on metric space is characterized in that:
(1) makes up metric space for stereogram;
(2) determine the match window size for the every bit of current level reference picture in the metric space;
(3) according to last layer level parallax be the every bit calculating parallax hunting zone of this level reference picture;
(4) the integer level parallax of current level in the calculating metric space;
(5) utilize sub-pixel matching process to calculate the sub-pixel parallax based on binary search.
2. the sub-pixel solid matching method based on metric space according to claim 1 is characterized in that describedly for stereogram makes up in the metric space step, and the formula that makes up metric space is as follows:
u N ( x , y ) = Σ ( m , n ) ∈ S ( x , y ) u N - 1 ( m , n ) 4 ,
S(x，y)＝{(2x，2y)，(2x+1，2y)，(2x，2y+1)，(2x+1，2y+1)}
In the formula, u NN layer scalogram picture in the expression metric space, wherein, u 0, N=0, bottom layer image is an original image in the expression metric space.
3. the sub-pixel solid matching method based on metric space according to claim 2 is characterized in that described every bit for current level reference picture in the metric space determines in the match window size step;
Relevant density calculation formula is as follows:
Figure FDA0000058935110000012
In the formula, u (x) presentation video function, u ' is the derivative of presentation video function u (x) (x),
Figure FDA0000058935110000013
Expression is with x 0Be the support window at center, the norm of image function u (x)
Figure FDA0000058935110000014
Computing formula as follows:
Figure FDA0000058935110000015
U (x) is as follows with its derivative u ' inner product computing formula (x):
Figure FDA0000058935110000016
The formula that calculates the match window size is as follows:
Figure FDA0000058935110000017
In the formula, The expression reference picture, g is a Gaussian function, σ bPoor for noise criteria, λ is a matching precision, Computing formula as follows:
Figure FDA0000058935110000021
4. the sub-pixel solid matching method based on metric space according to claim 3 is characterized in that describedly according to last layer level parallax for the method that the every bit of this level reference picture calculates the parallax hunting zone being:
At first calculate the initial parallax of this level according to the integer level parallax of last layer level, the computing formula of initial parallax is as follows:
d N-1(i，j)＝2·d N(m，n)，
(i，j)∈{(2m，2n)，(2m+1，2n)，(2m，2n+1)，(2m+1，2n+1)}
In the formula, d N(i j) is N level (i, j) the integer level parallax of position;
Then, according to maximum disparity value d MaxCalculate the maximum disparity value d of this level N, max, its computing formula is as follows:
In the formula,
Figure FDA0000058935110000023
Expression is more than or equal to the smallest positive integral of x;
5. the sub-pixel solid matching method based on metric space according to claim 4 is characterized in that the method for the integer level parallax of current level in the described calculating metric space is:
According to the parallax hunting zone that obtains in match window size of determining for every bit in the step (2) and the step (3), at each definite match window position of hybrid window selection strategy, similarity according to NCC calculating match window in corresponding parallax hunting zone obtains pairing optimum parallax value under each the window's position, and chooses the final parallax of parallax conduct of similarity maximum in the parallax that is calculated under these the window's positions;
The NCC computing formula is as follows:
C k ( x , y , d ) = Σ ( i , j ) ∈ W k u ( x + i , y + j ) · u · ( x + i + d , y + j ) Σ ( i , j ) ∈ W k u ( x + i , y + j ) 2 · Σ ( i , j ) ∈ W k u · ( x + i + d , y + j ) 2
In the formula, u (x, y) and
Figure FDA0000058935110000025
Represent the left and right sides image in the stereogram respectively, W kRepresent corresponding match window;
The pairing parallax computing formula of each the window's position is as follows:
d k ( x , y ) = arg d max C k ( x , y , d )
In the formula, d k(x, (optimal cost is expressed as C accordingly for x, y) the optimum parallax of point under k match window in y) expression K, opt(x, y);
The computing formula of final parallax is as follows:
d opt ( x , y ) = arg d k ( x , y ) max C k , opt ( x , y )
In the formula, d Opt(x, y) expression (x, final parallax y);
6. the sub-pixel solid matching method based on metric space according to claim 5, it is characterized in that in the sub-pixel matching process calculating sub-pixel parallax step of described utilization based on binary search, according to the integer level parallax that in multiscale space, calculates, utilize binary search to calculate the sub-pixel parallax that is better than designated precision again, the computing formula of its binary search is as follows:
d A + 1 ( x 0 ) = arg m ∈ S max N x 0 ( m )
S＝{d A(x 0)，d A(x 0)+1/2 A，d A(x 0)-1/2 A}
In the formula, A 〉=1 is an iterations, d A(x 0) expression x 0The sub-pixel parallax of the A time iteration of point, d 1(x 0) (A=1) expression x 0The integer parallax of point,
Figure FDA0000058935110000033
The expression reference windows
Figure FDA0000058935110000034
With match window
Figure FDA0000058935110000035
The standard cross-correlation coefficient, its computing formula is as follows:
Figure FDA0000058935110000036
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