一、python中的多維陣列

參考部落格：NumPy 三維陣列以及高維陣列切片和索引

1,Indexing and slicing numpy arrays
https://www.pythoninformer.com/python-libraries/numpy/numpy-and-images/

In this section we will look at indexing and slicing. These work in a similar way to indexing and slicing with standard Python lists, with a few differences

Indexing an array
Indexing is used to obtain individual elements from an array, but it can also be used to obtain entire rows, columns or planes from multi-dimensional arrays.

Indexing in 1 dimension
We can create 1 dimensional numpy array from a list like this:

import numpy as np

a1 = np.array([1, 2, 3, 4])

print(a1) # [1, 2, 3, 4]

We can index into this array to get an individual element, exactly the same as a normal list or tuple:

print(a1[0]) # 1
print(a1[2]) # 3

Indexing in 2 dimensions
We can create a 2 dimensional numpy array from a python list of lists, like this:

import numpy as np

a2 = np.array([[1, 2, 3],
[4, 5, 6],
[7, 8, 9]])

Here is a diagram of the array:

We can index an element of the array using two indices - i selects the row, and j selects the column:

print(a2[2, 1]) # 8

Notice the syntax - the i and j values are both inside the square brackets, separated by a comma (the index is actually a tuple (2, 1), but tuple packing is used). The example picks row 2, column 1, which has the value 8. This compares with the syntax you might use with a 2D list (ie a list of lists):

v = [[1, 2, 3],
[4, 5, 6],
[7, 8, 9]]

print(v[2][1]) # 8

Picking a row or column
If we can supply a single index, it will pick a row (i value) and return that as a rank 1 array:

print(a2[2]) # [7, 8, 9]

That is quite similar to the what would happen with a 2D list. However, numpy allows us to select a single columm as well:

print(a2[:, 1]) # [2, 5, 8]

We are skipping ahead slightly to slicing, later in this tutorial, but what this syntax means is:

for the i value, take all values (: is a full slice, from start to end)
for the j value take 1
Giving this array [2, 5, 8]:

The array you get back when you index or slice a numpy array is a view of the original array. It is the same data, just accessed in a different order. If you change the view, you will change the corresponding elements in the original array.

Indexing in 3 dimensions
We can create a 3 dimensional numpy array from a python list of lists of lists, like this:

import numpy as np

a3 = np.array([[[10, 11, 12], [13, 14, 15], [16, 17, 18]],
[[20, 21, 22], [23, 24, 25], [26, 27, 28]],
[[30, 31, 32], [33, 34, 35], [36, 37, 38]]])

Here is a diagram of the array:

A 3D array is like a stack of matrices:

The first index, i, selects the matrix
The second index, j, selects the row
The third index, k, selects the column
Here is the same diagram, spread out a bit so we can see the values:

Here is how to index a particular value in a 3D array:

print(a3[2, 0, 1]) # 31

This selects matrix index 2 (the final matrix), row 0, column 1, giving a value 31.

Picking a row or column in a 3D array
You can access any row or column in a 3D array. There are 3 cases.

Case 1 - specifying the first two indices. In this case, you are choosing the i value (the matrix), and the j value (the row). This will select a specific row. In this example we are selecting row 2 from matrix 1:

print(a3[1, 2]) # [26 27 28]

Case 2 - specifying the i value (the matrix), and the k value (the column), using a full slice (:) for the j value (the row). This will select a specific column. In this example we are selecting column 1 from matrix 0:

print(a3[0, :, 1]) # [11 14 17]

Case 3 - specifying the j value (the row), and the k value (the column), using a full slice (:) for the i value (the matrix). This will create a row by taking the same element from each matrix. In this case we are taking row 1, column 2 from each matrix:

print(a3[:, 1, 2]) # [15, 25, 35]

Picking a matrix in a 3D array
If we only specify the i index, numpy will return the corresponding matrix. We will call this case 1. In this example we will request matrix 2:

print(a3[2]) # [[30 31 32]
# [33 34 35]
# [36 37 38]]

Case 2 if we specify just the j value (using a full slice for the i values), we will obtain a matrix made from the selected row taken from each plane. In this example we will take row 1:

print(a3[:, 1]) # [[13 14 15]
# [23 24 25]
# [33 34 35]]

Case 3 if we specify just the k value (using full slices for the i and j values), we will obtain a matrix made from the selected column taken from each plane. In this example we will take column 0: 注:取到的元素以行的形式排列

print(a3[:, :, 0]) # [[10 13 16]
# [20 23 26]
# [30 33 36]]

Slicing a 3D array

You can slice a 3D array in all 3 axes to obtain a cuboid subset of the original array:

import numpy as np

a3 = np.array([[[10, 11, 12], [13, 14, 15], [16, 17, 18]],
[[20, 21, 22], [23, 24, 25], [26, 27, 28]],
[[30, 31, 32], [33, 34, 35], [36, 37, 38]]])

print(a3[:2,1:,:2]) # [[ [13 14] [16 17] ]
# [ [23 24] [26 27] ]]

This selects:

planes :2 (the first 2 planes)
rows 1: (the last 2 rows)
columns :2 (the first 2 columns)
As shown here:

Full slices
You can, of course, use full slices : to select all planes, columns or rows. However, for trailing indices, simply omitting the index counts as a full slice. So for 2D arrays:

a2[1:3,:] # is the same as
a2[1:3]
For 3D arrays:

a3[1:,:2,:] # is the same as
a3[1:,:2]

a3[1:,:,:] # is the same as
a3[1:,:] # and is also the same as
a3[1:]

Slices vs indexing
As we saw earlier, you can use an index to select a particular plane column or row. Here we select row 1, columns 2:4:

import numpy as np

a2 = np.array([[10, 11, 12, 13, 14],
[15, 16, 17, 18, 19],
[20, 21, 22, 23, 24],
[25, 26, 27, 28, 29]])

print(a2[1,2:4]) # [17 18]

You can also use a slice of length 1 to do something similar (slice 1:2 instead of index 1):

print(a2[1:2,2:4]) # [[17 18]]

Notice the subtle difference. The first creates a 1D array, the second creates a 2D array with only one row.

Visit the PythonInformer Discussion Forum for numeric Python.

From Python Nested Lists to Multidimensional numpy Arrays

https://cognitiveclass.ai/blog/nested-lists-multidimensional-numpy-arrays

A Visual Intro to NumPy and Data Representation

http://jalammar.github.io/visual-numpy/

二、影象的結構

影象在python中並非按照[matrix,row,col]。

而是按照[row,col,matrix]的格式索引。個人認為兩者的邏輯結構應該是一樣的，只是索引方式不同，有待考究。