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OpenCV - Matrix Operations Part 3

2022-08-09 16:03:00 【why why】

OpenCV Comes with a large number of matrix processing functions,本文记录相关内容.

简介

OpenCV The member functions of the matrix class can perform many basic matrix operations,本文基于《学习 OpenCV3 》The content of Chapter 5 is organized Python OpenCV 矩阵操作函数.

内容列表

序号	函数	描述
1	cv2.phase()	Calculates the orientation of a 2D vector
2	cv2.polarToCart()	Angle and magnitude are known,Find the corresponding two-dimensional vector
3	cv2.pow()	Raises each element in the matrix to the exponentiation
4	cv2.randu()	Fills the given matrix with uniformly distributed random numbers
5	cv2.randn()	Fills the given matrix with normally distributed random numbers
6	cv2.randShuffle()	Shuffle matrix elements randomly
7	cv2.reduce()	Reduce a two-dimensional matrix to a vector by specific operations
8	cv2.repeat()	Copies the contents of one matrix to another
9	cv2.setIdentity()	Set the elements on the diagonal in the matrix to be 1,其他置0
10	cv2.solve()	求出线性方程组的解
11	cv2.solveCubic()	Find the real roots of the cubic equation
12	cv2.solvePoly()	Find the complex roots of a polynomial equation
13	cv2.sort()	Sorts the elements of any row or column in a matrix
14	cv2.sortIdx()	与 cv2.sort() 的目的相同,Except the matrix is unmodified,并返回索引
15	cv2.split()	Splits a multi-channel matrix into multiple single-channel matrices
16	cv2.sqrt()	Computes the element-wise square root of a matrix
17	cv2.subtract()	Implements element-wise subtraction of two matrices
18	cv2.trace()	Compute the trace of a matrix
19	cv2.transform()	Apply a matrix transformation on each element of the matrix
20	cv2.transpose()	矩阵的转置运算

矩阵操作

0. 基础引用

After that, we will demonstrate the above functions
All code references the following packages by default

import cv2
import numpy as np
import mtutils as mt
from mtutils import PIS

示例图片 img1.jpg 和 img2.jpg

查看 opencv 某函数 func Documentation works：

print(cv2.<func>.__doc__)

1. cv2.phase()

Calculates the orientation of a 2D vector

函数使用

cv2.phase(x, y)  --> dst

Calculates the azimuth for a Cartesian-polar transformation for a two-dimensional vector field（角度）部分.The vector field is composed of two independent single-channel matrices.Of course the two input matrices are the same size.（If you have a two channel matrix,那么调用cv2.phase()will do what you need.）然后,dstEvery element in x和yCalculate the arctangent of the two in the corresponding elements of .

代码示例

x = np.array([1, 0, -1], dtype='float32')
y = np.array([1, -1, 1], dtype='float32')
res = cv2.phase(x, y)

-->
res
array([[0.7852316],
       [4.712389 ],
       [2.3563612]], dtype=float32)

The above results are respectively \frac{\pi}{4}, \frac{3\pi}{2}, \frac{3\pi} { 4 }

2. cv2.polarToCart()

Angle and magnitude are known,Find the corresponding two-dimensional vector

函数使用

cv2.polarToCart(magnitude, angle, angleInDegrees=False)

cv2.polarToCart() 从向量场的极坐标中计算笛卡尔坐标(x,y).Input two matrices of the same size and type：幅度和角度,Specify the magnitude and angle of the vector at each point.Output similar two matrices,They are the same size and type as the input,and will contain the vector at each pointx和y投影.附加标志angleInDegreeswill make the values in the angle matrix in degrees,而不是弧度.

代码示例

mag = np.array(2**0.5)
angle = np.array(np.pi/4)
res = cv2.polarToCart(mag, angle)


-->
res
(array([[1.]]), array([[1.]]))

3. cv2.pow()

Raises each element in the matrix to the exponentiation

data = np.reshape(np.arange(20), [4, 5])
res = cv2.pow(data, 2)


-->
res
array([[  0,   1,   4,   9,  16],
       [ 25,  36,  49,  64,  81],
       [100, 121, 144, 169, 196],
       [225, 256, 289, 324, 361]], dtype=int32)

4. cv2.randu()

Fills the given matrix with uniformly distributed random numbers 注意： The function is modified inline,The input data is directly transformed into a random matrix

函数使用

cv2.randu(data, low, high)

Generated inline lowhigh A matrix of uniformly distributed random numbers between

示例代码

data = np.zeros([5, 5])
cv2.randu(data, low=2, high=3) 

-->
data
array([[2.16117805, 2.03818934, 2.42586133, 2.84612762, 2.88760448],
       [2.26471239, 2.27078305, 2.95266639, 2.6751313 , 2.81021636],
       [2.18396021, 2.0944562 , 2.81590329, 2.52451766, 2.38083885],
       [2.41199476, 2.25553534, 2.9448959 , 2.90012348, 2.45789156],
       [2.84130697, 2.28030013, 2.3854357 , 2.45190146, 2.87543355]])

5. cv2.randn()

Fills the given matrix with normally distributed random numbers 注意： The function is modified inline,The input data is directly transformed into a random matrix

函数使用

cv2.randn(data, mean, stddev)

Generated inline with mean为均值,stddev A matrix of normally distributed random numbers with standard deviations

示例代码

data = np.zeros([5, 5])
cv2.randn(data, mean=5, stddev=1) 

-->
data
array([[6.27751625, 6.43329835, 4.49584228, 3.92785478, 6.10956049],
       [5.49447021, 4.10116905, 4.46068269, 4.88458967, 4.05134571],
       [5.52288508, 5.11468363, 5.03454646, 4.02846879, 5.8627224 ],
       [6.25682068, 4.23800135, 5.5566175 , 7.2824192 , 7.58638453],
       [6.67061222, 4.90155111, 6.18168759, 3.01809192, 6.19408202]])

6. cv2.randShuffle()

Shuffle matrix elements randomly

data = np.reshape(np.arange(25), [5, 5])
cv2.randShuffle(data) 

-->
data
array([[14,  5,  1, 13,  2],
       [23, 20, 21,  3,  8],
       [22,  4, 16,  7,  6],
       [18, 17, 19, 24, 15],
       [10, 11,  9, 12,  0]])

7. cv2.reduce()

Reduce a two-dimensional matrix to a vector by specific operations

函数使用

cv2.reduce(src, dim, reduceOp=cv2.REDUCE_SUM) --> vec

简化是指使用一些reduceOp所代表的组合规则,对输入矩阵src的每一行（或列）system transformation,直到只剩一行（或列）为止,make it a vectorvec.参数dim决定如何进行简化.

参数说明

src

接受参数为 float 类型的一维、二维数据

reduceOp

参数	含义
cv2.REDUCE SUM	计算向量的总和
cv2.REDUCE AVG	计算向量的平均值
cv2.REDUCE MAX	计算向量中的最大值
cv2.REDUCE MIN	计算向量中的最小值

dim

参数	含义
0	合并为1行
1	合并为1列

示例代码

data = np.reshape(np.arange(25, dtype='float32'), [5, 5])
res = cv2.reduce(data, 0, rtype=cv2.REDUCE_SUM)


-->
res
array([[50., 55., 60., 65., 70.]], dtype=float32)

8. cv2.repeat()

Copies the contents of one matrix to another

函数使用

cv2.repeat(src, nx, ny)

将src 数据 x 方向重复 nx 次, y 方向重复 ny 次

示例代码

data = np.reshape(np.arange(4, dtype='float32'), [2, 2])
res = cv2.repeat(data, 2, 3)

-->
res
array([[0., 1., 0., 1., 0., 1.],
       [2., 3., 2., 3., 2., 3.],
       [0., 1., 0., 1., 0., 1.],
       [2., 3., 2., 3., 2., 3.]], dtype=float32)

9. cv2.setIdentity()

Set the elements on the diagonal in the matrix to be 1,其他置0

mtx = np.random.random([5,6])
res = cv2.setIdentity(mtx)

-->
res
array([[1., 0., 0., 0., 0., 0.],
       [0., 1., 0., 0., 0., 0.],
       [0., 0., 1., 0., 0., 0.],
       [0., 0., 0., 1., 0., 0.],
       [0., 0., 0., 0., 1., 0.]])

10. cv2.solve()

求出线性方程组的解

函数用法

cv2.solve(src1, src2, flags)

其中 src1 为 A, src2 为 B
flags

取值	含义
cv2.DECOMP_LU	高斯消元法(LU分解)
cv2.DECOMP_SVD	奇异值分解(SVD)
cv2.DECOMP_CHOLESKY	对于对称正定矩阵
cv2.DECOMP_EIG	特征值分解,只用于对称矩阵
cv2.DECOMP_OR	QR因式分解
cv2.DECOMP_NORMAL	可选附加标志;表示要求解标准方程

The first five parameters in the table are mutually exclusive,But the last parametercv2.DECOMP_NORMALCan be combined with any of the first five(例如,通过逻辑OR).如果使用该参数,那么cv2.solve() 将尝试解决标准方程：hsT·Ihs·dst=lhsT·rhs, 而不是一般方程Ihs·dst=rhs.

示例代码

A = np.array([[1,2], [2,1]], dtype='float32')
B = np.array([[0], [1]], dtype='float32')
res = cv2.solve(A, B)

-->
res
(True, array([[ 0.6666667 ]...e=float32))
special variables
function variables
0:True
1:array([[ 0.6666667 ],
       [-0.33333334]], dtype=float32)
special variables
[0:2] :[array([0.6666667], d...e=float32), array([-0.33333334],...e=float32)]
dtype:dtype('float32')

Equation solved successfully, x = \frac {2}{3}, y=-\frac{1}{3}

11. cv2.solveCubic()

Find the real roots of the cubic equation

函数用法

cv2.solveCubic(coeffs)

Given a cubic polynomial represented by three or four element vector coefficients,cv2.solveCubic()将计算该多项式的实根.如果coeffs有四个元素,则Compute the roots of the following polynomial：

如果coeffs只有三个元素,则Compute the roots of the following polynomial：

The returned result will have one or three elements,具体取决于多项式具有多少个实根.

示例代码

coeffs = np.array([1,1,-12,0], dtype='float32')
res = cv2.solveCubic(coeffs)


-->
res
(3, array([[-4.0000000e+...e=float32))
special variables
function variables
0:3
1:array([[-4.0000000e+00],
       [ 3.0000000e+00],
       [ 8.3266727e-16]], dtype=float32)
special variables
[0:3] :[array([-4.], dtype=float32), array([3.], dtype=float32), array([8.3266727e-16...e=float32)]
special variables
function variables

得到 x3+x2-12x=0 three solutions {-4, 3, 0}

12. cv2.solvePoly()

Find the complex roots of a polynomial equation

函数使用

cv2.solvePoly(coeffs)

给定以系数向量表示的任意阶数的多项式,cv2.solvePoly()将尝试计算该多项式的根.给定系数矩阵,Compute the roots of the following polynomial：

示例代码

coeffs = np.array([4, 0, 1], dtype='float32')
res = cv2.solvePoly(coeffs)


-->
res
(0.0, array([[[ 0., -2.]],...e=float32))
special variables
function variables
0:0.0
1:array([[[ 0., -2.]],

       [[ 0.,  2.]]], dtype=float32)
special variables
[0:2] :[array([[ 0., -2.]], ...e=float32), array([[0., 2.]], dt...e=float32)]
special variables

解得 x^2+4=0 The solutions of the equations are imaginary numbers 2j,-2j

13. cv2.sort()

Sorts the elements of any row or column in a matrix

函数使用

cv2.sort(src, flags)

可以通过使用cv2.SORT_EVERY_ROW或cv2.SORT_EVERY_COLUMN Flags to sort on each row or column.Sorting can be ascending or descending,分别由cv2.SORT_ASCENDING或cv2.SORT_DESCENDING标志指定.One logo from each group needs to be selected.

示例代码

data = cv2.randShuffle(np.reshape(np.arange(36), [6,6]))
res = cv2.sort(data, flags=cv2.SORT_EVERY_ROW)

-->
res
array([[ 1,  4,  8, 12, 30, 35],
       [ 0,  5, 10, 11, 15, 22],
       [ 3,  7, 16, 20, 25, 29],
       [19, 21, 23, 24, 31, 34],
       [ 9, 14, 18, 28, 32, 33],
       [ 2,  6, 13, 17, 26, 27]], dtype=int32)

14. cv2.sortIdx()

与 cv2.sort() 的目的相同,Except the matrix is unmodified,并返回索引

data = cv2.randShuffle(np.reshape(np.arange(36), [6,6]))
res = cv2.sortIdx(data,  flags=cv2.SORT_EVERY_ROW)


-->
res
array([[0, 1, 3, 2, 5, 4],
       [3, 2, 4, 5, 1, 0],
       [0, 2, 4, 5, 3, 1],
       [1, 5, 3, 2, 0, 4],
       [4, 1, 3, 0, 2, 5],
       [1, 2, 0, 5, 4, 3]], dtype=int32)

15. cv2.split()

Splits a multi-channel matrix into multiple single-channel matrices

image = mt.cv_rgb_imread('img1.jpg')
res = cv2.split(image)
PIS(image, *res)

16. cv2.sqrt()

Computes the element-wise square root of a matrix

data = cv2.randShuffle(np.reshape(np.arange(16, dtype='float32'), [4, 4]))
res = cv2.sqrt(data) 

-->
res
array([[3.3166249, 3.       , 2.6457512, 1.4142135],
       [2.4494898, 3.6055512, 2.       , 1.7320508],
       [3.4641016, 1.       , 0.       , 3.1622777],
       [2.828427 , 3.7416575, 2.236068 , 3.8729835]], dtype=float32)

17. cv2.subtract()

Implements element-wise subtraction of two matrices

mat_1 = np.ones([3,3])
mat_2 = np.zeros([3,3])
cv2.setIdentity(mat_2)
res = cv2.subtract(mat_1, mat_2) 


-->
res
array([[0., 1., 1.],
       [1., 0., 1.],
       [1., 1., 0.]])

18. cv2.trace()

Compute the trace of a matrix

mat_1 = np.ones([3,4], dtype='float32')
res = cv2.trace(mat_1)

-->
res
(3.0, 0.0, 0.0, 0.0)

19. cv2.transform()

Apply a matrix transformation on each element of the matrix

函数使用

cv2.transform(src, mtx)

函数cv2.transform()Can be used to compute arbitrary linear image transformations.它将多通道输入矩阵src视为向量的集合,你可以将其视为“channel space”,Then multiply these vectors by “小”矩阵mt×,以实现此channel space中的转换.

示例代码

image = mt.cv_rgb_imread('img1.jpg')
mtx = cv2.flip(cv2.setIdentity(np.zeros([3, 3], dtype='float32')), flipCode=0)
gbr = cv2.transform(image, mtx)
PIS(image, gbr)

20. cv2.transpose()

矩阵的转置运算

mat = np.reshape(np.arange(16, dtype='float32'), [4, 4])
res = cv2.transpose(mat)

-->
res
array([[ 0.,  4.,  8., 12.],
       [ 1.,  5.,  9., 13.],
       [ 2.,  6., 10., 14.],
       [ 3.,  7., 11., 15.]], dtype=float32)