overview
Perspective correction is an image processing technique that is used to perform perspective transformation on captured or scanned images to correct incorrect shapes and perspectives, so as to obtain correct rectangular shapes. This process requires the use of perspective transformation algorithms and linear interpolation techniques.
In the application scenario of perspective correction, algorithms such as machine learning and deep learning have high requirements on the source image, and some images may be placed incorrectly. Perspective correction can improve the accuracy of detection.
Implementation of the algorithm
Perspective correction algorithms usually need to use linear algebra and geometric transformation methods to achieve. The implementation steps of a common perspective correction algorithm:
- Determine the four points of the original image, and the four points of the target image. These eight points can be manually selected or automatically determined by an image processing algorithm.
- From these points, construct a perspective transformation matrix that maps the points of the original image to the points of the target image.
- Use this matrix to transform all pixels of the original image, usually by bilinear interpolation or higher-order interpolation methods.
- Output the transformed image as the target image.
It should be noted that when performing perspective correction, it is necessary to ensure that the size and proportion of the original image and the target image are consistent, otherwise distortion or deformation may occur. In addition, for some special images, such as images with perspective effects, it may be necessary to use more complex algorithms for correction.
Determine the parameters of the perspective transformation matrix?
Determining the parameters of the perspective transformation matrix requires the use of four point pairs, one parameter for every two point pairs. Therefore, at least four pairs of points are required to determine the parameters of the perspective transformation matrix.
Specifically, suppose the point on the original image is (x1, y1) and the point on the target image is (x2, y2). According to the perspective transformation matrix, the following equation can be obtained:
x2 = A * x1 + B * y1 + C
y2 = D * x1 + E * y1 + F
Among them, A, B, C, D, E, F are the parameters to be solved. To solve for these parameters, at least four pairs of points, ie four equations, are required. Therefore, at least four pairs of points need to be provided to solve the parameters of the perspective transformation matrix.
In practical applications, the least square method or other optimization algorithms are usually used to solve these parameters, so as to minimize the error between the transformed image and the target image.
The least squares method is used to solve the parameters of the perspective transformation matrix
Least squares is a mathematical optimization technique used to minimize the sum of squared errors between predicted and actual values. When solving the parameters of the perspective transformation matrix, the least squares method can solve the parameters by minimizing the square sum error between the points on the original image and the points on the transformed image.
Specifically, suppose there are n pairs of points, the point on the original image is (x1, y1), and the point on the target image is (x2, y2). According to the perspective transformation matrix, the following equation can be obtained:
x2 = A * x1 + B * y1 + C
y2 = D * x1 + E * y1 + F
Using the method of least squares, we can solve A, B, C, D, E, F such that the following error function is minimized:
E = ∑(x2 - (A * x1 + B * y1 + C))^2 + ∑(y2 - (D * x1 + E * y1 + F))^2
By solving the minimum value of this error function, the parameters of the perspective transformation matrix can be obtained. This process can be realized by mathematical optimization algorithms, such as gradient descent method, Gauss-Newton method and the like.
In practical applications, it is usually necessary to use a numerical calculation library or a special optimization algorithm library to realize the solution of the least squares method. For example, in Python, libraries such as NumPy, SciPy, etc. can be used to implement this process.