CN112750088B - Method for automatically correcting and stabilizing video image based on linear programming - Google Patents
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Abstract
The invention discloses a method for automatically correcting and stabilizing a video image based on linear programming, which comprises the steps of firstly separating an original video frame by frame to obtain a picture set, then taking an affine transformation matrix between two adjacent frames of the original video obtained by estimation as motion information, extracting a straight line segment in each frame, and estimating a vanishing point position and a horizontal line position in the vertical direction; then constructing a linear programming model, converting a transformation matrix for correcting each frame into a parameter to be optimized of the linear programming model, and obtaining projective transformation matrixes with the number equal to the number of video frames by solving the model; and then, the original video is transformed frame by frame, and the transformed frames are synthesized to obtain a new video. A series of projective transformation matrixes obtained by optimization can simultaneously complete distortion and image stabilization, the processed video has a better visual effect, the processing speed is high, and the obtained result has global optimality.
Description
Technical Field
The invention relates to a video image stabilizing and correcting technology, in particular to a method for automatically correcting and stabilizing a video image based on linear programming, which is an automatic video correcting and stabilizing method based on linear programming and applies geometric information of each frame of image and motion information between adjacent frames, and can quickly and automatically perform image stabilization and correction aiming at the video at the same time.
Background
Due to camera shake, inappropriate judder often occurs in the captured video. Moreover, the vertical structure such as a building is often inclined in the video due to the shooting angle of view, and the like, which all reduce the visual comfort of the video. Existing methods of video stabilization generally recover the original 3D path of the camera through a Motion recovery Structure (SfM), or describe a 2D path according to the position change of feature points or a transformation matrix between adjacent frames, and smooth this path to generate a stabilized version of the original video. However, these methods do not consider how to correct the vertical structures of the video that are inclined, and such correction can generally improve the visual effect of the video significantly.
Geometric information such as vanishing points and horizontal lines can be obtained from video images. Some image correction methods for a single image use the geometric information for image correction, however, such methods can only be modeled as non-convex optimization, the solution time is long, and the global optimality cannot be guaranteed. Some methods use vertical vanishing point information for video rectification technology, however, these methods do not consider the continuity between adjacent frames of video and the jitter of video, and the processed video has poor visual effect.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a method for automatically correcting and stabilizing video images based on linear programming, which applies geometric information of each frame of image and motion information between adjacent frames, carries out fast and automatic video image correction and stabilization on the video images based on the linear programming, estimates a projective transformation matrix for each frame of a section of input video and carries out photography transformation on the video frame by frame, and can simultaneously finish the correction and stabilization of the video, so that the processed video images have better visual effect.
In order to achieve the purpose, firstly, a video is separated frame by frame to obtain a picture set, an affine transformation matrix between two adjacent frames of the original video is estimated to be used as motion information, a straight line segment in each frame is extracted, and a vanishing point position and a horizontal line position in the vertical direction are estimated. And constructing a linear programming model taking the transformation matrix for correcting each frame as a parameter to be optimized according to the information. Then solving the model to obtain projective transformation matrixes with the number equal to the number of video frames. And finally, transforming the original video frame by frame, and synthesizing the transformed frames into a new video.
The technical scheme of the invention is as follows:
a method for automatically correcting and stabilizing video images based on linear programming comprises the following steps:
1) data preprocessing, comprising: separating video frames, extracting line segments from the images, estimating vanishing point positions and horizontal line information in the vertical direction of the video images, and estimating affine transformation matrix between two continuous frames of images
The video is separated into a picture set frame by frame, video reader in Matlab can be adopted to separate the video frames, and for each separated frame, a Line Segment Detector (LSD) method is used to extract Line segments from the video image. Estimating vanishing point positions in the vertical direction of the video images and horizontal line information by using a random sample consensus (RANSAC) according to a Manhattan hypothesis, and estimating an affine transformation matrix between two continuous frames of images of the original video;
2) and constructing an objective function and a constraint condition of the linear programming model.
All the frames obtained in the step 1) are used as original input frames, and for all the input frames, a projective transformation matrix from an output frame to the input frames is used as a parameter to be optimized. The objective function of the model is the sum of the optimization term for distortion and the optimization term for image stabilization. The optimization terms for the twist include the distance of the vertical infinity point and the vertical vanishing point before and after the transformation, the slope of the horizon, and the slope of the straight line segment in the image that is visually horizontal or vertical. The optimization term about the stabilized image is the residual error of the projective transformation matrix from the same original frame to the two adjacent frames after processing. All optimization items in the invention adopt L1 norm form, and the objective function is ensured to be linear.
The constraint condition of the model comprises two items, namely a cropping frame is kept in a visible range of an original image and the difference of each projective transformation matrix and an identity matrix is within a certain range. Since the method only performs deformation and cropping on each frame, in order to ensure that no black edge appears in the newly generated video, the cropping frame needs to be kept within the visible range of the original image, which is taken as a first constraint condition. Meanwhile, in order to ensure that the generated video does not contain large distortion, the difference between each projective transformation matrix and the identity matrix needs to be within a certain range, which is used as a second constraint condition, and specifically is as follows:
wherein, b 11 ,…,b 32 Projective transformation matrix B for t-th frame t 8 unknown parameters to be optimized.
3) Solving the model to obtain a projective transformation matrix corresponding to each original frame;
because the established model is a linear programming model, the solution can be quickly and accurately solved through a Matlab CVX optimization packet in specific implementation. And (5) carrying out inverse transformation on the solved result to obtain a projective transformation matrix corresponding to each original frame.
4) And (3) generating a new video: and transforming and cutting the original frame by applying the projective transformation matrixes, and synthesizing the processed video frame into a new video.
In specific implementation, video synthesis can be completed by using a video synthesizer tool of the VideoWriter class in Matlab.
Compared with the prior art, the invention has the following beneficial effects:
the invention provides a quick and simultaneous video correcting and image stabilizing method. The method utilizes the geometric information of vertical vanishing points, horizontal lines, long straight line segments and the like, and utilizes the motion information between adjacent frames, so that a series of projective transformation matrixes obtained by optimization can simultaneously complete two functions of correcting and stabilizing images, and the processed video has better visual effect. The invention uses one model to simultaneously complete the distortion and the image stabilization of the video, thereby avoiding the mutual influence caused by partial consideration. Meanwhile, the problem is modeled into a linear programming, and the solving speed and the global optimality of the result are ensured.
Drawings
Fig. 1 is a flow chart of a video rectification and image stabilization method provided by the present invention.
Fig. 2 is a schematic diagram of a symbol of a video rectification and image stabilization method provided by the present invention.
Wherein, I 1 ,…,I n Is a sequence of original video frames, I' 1 ,…,I′ n For the processed output video frame sequence, n is the frame number of the video. F t Affine transformation matrix representing the t +1 th to the t-th frame, B t Representing the projective transformation matrix from the processed t-th frame to the corresponding original frame. R t Representing the residual error of the transformation matrix from the same original frame to the two processed adjacent frames.
FIG. 3 is a schematic diagram of geometric information utilized in an embodiment of the present invention.
Fig. 4 is an image extracted from a video according to an embodiment of the present invention.
Fig. 5 is a result image obtained after video rectification and image stabilization according to the embodiment of the present invention.
Detailed Description
The invention will be further described by way of examples, without in any way limiting the scope of the invention, with reference to the accompanying drawings.
The invention provides a method for automatically correcting and stabilizing a video image based on linear programming. And constructing a linear programming model taking the transformation matrix for correcting each frame as a parameter to be optimized according to the information. Then solving the model to obtain projective transformation matrixes with the number equal to the number of video frames. And finally, transforming the original video frame by frame, and synthesizing the transformed frames into a new video. Fig. 1 shows a flow of a video rectification and stabilization method provided by the present invention.
As can be seen from fig. 1, the whole processing procedure of the system consists of four stages: data preprocessing, dynamic programming model construction, model solution and new video generation. Fig. 2 is a schematic illustration of a symbolic illustration describing an algorithm.
The first stage is as follows: data pre-processing
The method comprises the following steps: separating the video frame by frame, detecting the geometric information of each frame, including: straight line segment, vertical vanishing point and horizontal line (fig. 3 shows the geometric information result obtained by the specific implementation of the detection).
Extracting the video to be processed frame by frame to obtainAnd obtaining a picture set, and performing picture extraction by adopting a VideoReader class in Matlab, wherein FIG. 4 is a sample picture of a result of picture extraction in specific implementation. And for each frame of image obtained by extraction, performing straight line segment extraction by using an LSD algorithm. Under the Manhattan assumption, three vanishing point positions are obtained by a RANSAC method, wherein a straight line, namely a horizontal line, where two vanishing points in the horizontal direction are located, affine transformation matrixes between two continuous frames of images are simultaneously estimated, and F is used t Representing the transformation matrix from frame t +1 to frame t.
And a second stage: constructing a linear programming model
The stage comprises the construction of an objective function of a linear programming model and the construction of a constraint condition. The invention takes the transformation matrix from each frame of the output video to the corresponding frame of the input video as the unknown quantity to be optimized, wherein, the projective transformation matrix B of the t-th frame t Expressed as:
wherein, b 11 ,…,b 32 For the 8 unknown parameters to be optimized in the matrix.
The linear programming objective function of the invention comprises two parts, wherein the first part is an optimization term positively correlated with image distortion, and the second part is an optimization term correlated with video image stabilization. The optimization terms positively correlated with the image distortion include: the optimization items are related to vanishing points in the vertical direction, the optimization items are related to horizontal lines, and the optimization items are related to straight line segments on the image;
the optimization items related to the vertical vanishing point specifically include:
wherein [ x ] p ,y p ,1] T Is the homogeneous coordinate of the vanishing point in the vertical direction in the t-th frame of the original video.
The optimization items related to the horizontal line are specifically as follows:
wherein [ n ] 1 ,n 2 ,n 3 ] T And the coordinates are the homogeneous coordinates of the horizontal line in the t-th frame of the original video.
And optimizing terms related to some straight line segments on the image, specifically:
wherein [ l 1 ,l 2 ,l 3 ] T Is a homogeneous coordinate of a visually desirable horizontal or vertical straight line segment in the tth frame of the original video. For a horizontal straight line segment, let e be 1; for a straight line segment in the vertical direction, let e be 0. For a plurality of straight-line segments, the number of the straight-line segments is reduced by applying non-maximum suppression (NMS), and the operation efficiency of the method is ensured.
The optimization term associated with video stabilization can be expressed as:
wherein R is t ＝|F t B t+1 -B t I represents the residual error of the transformation matrix from the same original frame to the processed two adjacent frames, | R t |、|R t+1 -R t I and R t+2 -2R t+1 +R t The | component represents the displacement, velocity and acceleration of the motion between adjacent frames after processing. Omega 1 ，ω 2 ，ω 3 For weight, 10, 1 and 100 are taken in the examples.
The final objective function is:
wherein, ω is 4 ，ω 5 ，ω 6 For weighting, in the examples, take10，10，1。
The constraint conditions of the model comprise the constraint of ensuring a cutting frame in an original image and the constraint of keeping the difference between a transformation matrix and an identity matrix within a certain range;
and ensuring the constraint of the cutting frame in the original image, which is specifically represented as:
where w and h are the width and height of the image.
Is the homogeneous coordinate of the four vertices of the image, where i is 1, …, 4.
The constraint that the difference between the transformation matrix and the identity matrix is kept within a certain range is specifically expressed as:
and a third stage: model solution
Because the established model is a linear programming model, the solution can be quickly and accurately carried out through a Matlab CVX optimization packet. For the results obtained
We find their inverse matrices
n is the frame number of the video.
A fourth stage: new video generation
For each frame I in the original video t Use of
Projective transformation is performed on the image, and the image is cut into the size same as that of the original video image, and fig. 5 is a result image obtained after projective transformation is performed. Finally all the obtained products are processedAnd synthesizing a new video by frames, namely the video obtained after the automatic correction and image stabilization of the video image based on the linear programming. The specific implementation may use the VideoWriter class in Matlab for video synthesis.
It is noted that the disclosed embodiments are intended to aid in further understanding of the invention, but those skilled in the art will appreciate that: various substitutions and modifications are possible without departing from the spirit and scope of the invention and appended claims. Therefore, the invention should not be limited by the disclosure of the embodiments, but should be defined by the scope of the appended claims.
Claims (9)
1. A video image automatic correcting and image stabilizing method based on linear programming comprises the steps of firstly separating an original video frame by frame to obtain a picture set, then taking an affine transformation matrix between two adjacent frames of the original video obtained through estimation as motion information, extracting a straight line segment in each frame, and estimating a vanishing point position and a horizontal line position in the vertical direction; then, a linear programming model is constructed, a transformation matrix for correcting each frame is used as a parameter to be optimized of the linear programming model, and projective transformation matrixes with the number equal to the number of video frames are obtained by solving the model; then, the original video is transformed frame by frame, and the transformed frames are synthesized to obtain a new video; the method comprises the following steps:
1) data preprocessing, comprising: performing video frame separation, extracting line segments from video images, estimating vanishing point positions and horizontal line information in the vertical direction of the video images, and estimating affine transformation matrixes between two adjacent frames of images of the original video;
2) constructing an objective function and a constraint condition of a linear programming model;
taking all frames obtained by separating the video frames in the step 1) as original input frames, and taking a projective transformation matrix from an output frame to the input frames as parameters to be optimized for all the input frames;
the objective function of the linear programming model is an optimization term for distortion and an optimization term for image stabilization E st Summing; the optimization terms all adopt an L1 norm form so as to ensure that the objective function is linear;
the optimization terms for twist include: optimization terms relating to vertical vanishing points
Optimization terms associated with horizontal lines
Optimization terms related to straight line segments on images
Wherein:
optimization terms relating to vertical vanishing points
The concrete expression is as follows:
wherein, [ x ] p ,y p ,1] T The coordinate is the homogeneous coordinate of a vanishing point in the vertical direction in the t-th frame of the original video;
optimization terms associated with horizontal lines
The concrete expression is as follows:
wherein [ n ] 1 ,n 2 ,n 3 ] T The homogeneous coordinate of a horizontal line in the t-th frame of the original video is obtained;
optimization terms associated with straight line segments on an image
The concrete expression is as follows:
wherein, [ l 1 ,l 2 ,l 3 ] T The homogeneous coordinate of a straight line segment in the original video t frame in the horizontal or vertical direction visually; for a horizontal straight line segment, let e be 1; for a straight line segment in the vertical direction, let e be 0; for a plurality of straight-line segments, reducing the number of the straight-line segments by applying a non-maximum value suppression NMS method to ensure the operation efficiency; b is a mixture of 11 ,…,b 32 Projective transformation matrix B for t-th frame t 8 unknown parameters to be optimized;
the objective function of the linear programming model is represented as:
wherein, ω is 4 ，ω 5 ，ω 6 Is a weight;
the constraints of the linear programming model include: keeping the cutting frame in the visible range of the original image and keeping the difference between each projective transformation matrix and the unit matrix in a set range;
3) solving through the model, and carrying out inverse transformation on the solved result to obtain a projective transformation matrix corresponding to each original frame;
4) and (3) generating a new video: and transforming and cutting the original frame according to the projective transformation matrix, and synthesizing the processed video frame to obtain a new video.
2. The method for automatically rectifying and stabilizing video images based on linear programming as claimed in claim 1, wherein the step 4) is performed by using a video synthesis tool to complete video synthesis; the video synthesis tool specifically adopts a VideoWriter class in Matlab.
3. The method for automatically correcting and stabilizing video images based on linear programming according to claim 1, wherein in the step 1) of data preprocessing, the video is separated into image sets frame by frame, and video readers in Matlab are particularly adopted for video frame separation; for each frame obtained by separation, a line segment detector LSD method is used to extract a line segment from the video image.
4. The method for automatically correcting and stabilizing the video image based on the linear programming as claimed in claim 3, wherein a random sample consensus algorithm RANSAC is specifically adopted to estimate the vertical vanishing point position and the horizontal line information of the video image, and estimate the affine transformation matrix between two adjacent frames of the original video.
5. The method for automatically rectifying and stabilizing video images based on linear programming as claimed in claim 1, wherein in step 2), said optimization terms regarding rectification include distances between vertical infinity points and vertical vanishing points before and after transformation, slopes of horizontal lines, and slopes of straight line segments in horizontal or vertical direction visually in the images; the optimization term about image stabilization is the residual error of the projective transformation matrix from the same original frame to two adjacent frames after processing.
6. The method for automatically rectifying and stabilizing video images based on linear programming as claimed in claim 1, wherein the constraint conditions of the model in step 2) are such that the difference between each projective transformation matrix and the identity matrix is within a set range, which is specifically expressed as:
wherein, b 11 ,…,b 32 Projective transformation matrix B for t-th frame t Of 8 unknown parameters to be optimized.
7. The method for automatically rectifying and stabilizing video images based on linear programming as claimed in claim 1, wherein the constraint condition of the model in step 2) is to keep the crop box within the visible range of the original image, which is specifically expressed as:
wherein w and h are the width and height of the image;
is the homogeneous coordinate of the four vertices of the image, where i is 1, …, 4.
8. The method for automatic distortion and stabilization of video images based on linear programming as claimed in claim 1, characterized in that the optimization term E associated with video stabilization st Expressed as:
wherein R is t ＝|F t B t+1 -B t I represents the residual error of the transformation matrix from the same original frame to the processed two adjacent frames, | R t |、|R t+1 -R t I and R t+2 -2R t+1 +R t The | component represents the displacement, speed and acceleration of the motion between the adjacent frames after the processing; omega 1 ，ω 2 ，ω 3 Are weights.
9. The method for automatically rectifying and stabilizing video images based on linear programming according to claim 1, wherein the model solution of step 3) is performed rapidly and accurately by using a Matlab CVX optimization package.
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