arrays_and_images.Rmd

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# Arrays as images, images as arrays

You have already seen (many) one-dimensional arrays.

Arrays can also be two-dimensional (or three, or four ...).

You can consider two-dimensional arrays as images, and images as arrays.

We start off with the imports that we need.

```{python}
# The standard library for working with arrays.
import numpy as np
# Standard library for plotting.
import matplotlib.pyplot as plt
```

Let’s make an array of numbers between 0 through 99:

```{python}
an_array = np.array([[ 0,  0,  0,  0,  0,  0,  0,  0],
                     [ 0,  0,  0,  9, 99, 99, 94,  0],
                     [ 0,  0,  0, 25, 99, 99, 79,  0],
                     [ 0,  0,  0,  0,  0,  0,  0,  0],
                     [ 0,  0,  0, 56, 99, 99, 49,  0],
                     [ 0,  0,  0, 73, 99, 99, 31,  0],
                     [ 0,  0,  0, 91, 99, 99, 13,  0],
                     [ 0,  0,  9, 99, 99, 94,  0,  0],
                     [ 0,  0, 27, 99, 99, 77,  0,  0],
                     [ 0,  0, 45, 99, 99, 59,  0,  0],
                     [ 0,  0, 63, 99, 99, 42,  0,  0],
                     [ 0,  0, 80, 99, 99, 24,  0,  0],
                     [ 0,  1, 96, 99, 99,  6,  0,  0],
                     [ 0, 16, 99, 99, 88,  0,  0,  0],
                     [ 0,  0,  0,  0,  0,  0,  0,  0]])
an_array.shape
```

Notice that this array has two elements in its shape — the number of *rows* and
the number of *columns*.

In fact this array represents a monochrome picture of a letter.

We can show arrays as images using the `plt.imshow` command from
[matplotlib](http://matplotlib.org/). Here is the default output:

```{python}
plt.imshow(an_array)
```

The image is weirdly colorful. That is because matplotlib is using the default
*colormap*. A colormap is a mapping from values in the array to colors. The
default Matplotlib colormap is called `viridis` and maps low numbers in the
image (0 in our case) to purple, and high numbers (99 in our case) to yellow.

We can see the relationship of the numbers to the colors by asking matplotlib
to show the colormap:

```{python}
plt.imshow(an_array)
plt.colorbar()
```

In our case, our image would make more sense as grayscale, so we use the
`gray` colormap, like this:

```{python}
plt.imshow(an_array, cmap='gray')
plt.colorbar()
```

A grayscale image is an array containing numbers giving the pixel intensity
values - in our case between 0 and 99.

Here we set `gray` to the default colormap for the rest of our plots:

```{python}
# Set 'gray' as the default colormap
plt.rcParams['image.cmap'] = 'gray'
```

This setting means that, by default, Matplotlib will use the `gray` colormap
for the *rest of this session*.

```{python}
# The default colormap is now gray.
plt.imshow(an_array)
plt.colorbar()
```

Matplotlib does not save this change, so we would have to rerun this command
for each session we want to change the default.  There are ways of making
[Matplotlib remember default
changes](https://matplotlib.org/stable/tutorials/introductory/customizing.html),
but we won't go into those here.

We can also plot *lines* in Matplotlib. For example, here are the values from
the row at position 8 in this array. Because Python indices start at 0, this is
the 9th row of the array.

```{python}
# Row position 8, all the columns.
an_array[8, :]
```

Actually, we can omit the second `:`, Numpy will assume we mean all the
columns, if we just specify the row:

```{python}
# Also, row position 8, all the columns.
an_array[8]
```

We might want to plot the values in row 8.  To do this, we use the `plt.plot`
function.  The first argument to this function is the `x` values for the plot,
and the second argument is the `y` values.  We will use the column positions as
for the `x` values:

```{python}
col_positions = np.arange(8)
col_positions
```

```{python}
# Specifying x and y values.
plt.plot(col_positions, an_array[8])
```

The x axis is the column position in the array (0 through 7) and the y axis is
the value of the array row at that position.

In fact, we can even omit the `x` values in this case, and Matplotlib will
assume we mean the x values to be `np.arange(8)`, where 8 is the length of the
`y` values array.

```{python}
# Just specifying the y values, we get the x values default.
plt.plot(an_array[8])
```

The plot shows us the 0 values at the edges of the bar of the “i”, and the ramp
up to the peak at the middle of the bar of the “i”, in columns number 3 and 4.

A transpose in numpy uses the `.T` method on the array. This has the effect
of flipping the rows and columns (in 2D):

```{python}
an_array.T
```

```{python}
# Defaults to gray colormap
plt.imshow(an_array.T)
```

We can also *reshape* the original array to a 1D array, by stacking all the
rows end to end.

Here's the original array:

```{python}
an_array
```

Here is the array, reshaped to 1D

```{python}
a_1d_array = np.reshape(an_array, 15 * 8)
a_1d_array
```

```{python}
a_1d_array.shape
```

Reshaping the array to one dimension is a common operation, so there is a
separate Numpy command for that, `np.ravel`:

```{python}
np.ravel(an_array)
```

One use of the 1D version of the array, is for making a histogram of the
distribution of values in the array:

```{python}
plt.hist(a_1d_array)
```

By default, the `plt.hist` function uses 50 bins, but you can specify how
many bins you want with the `bins` keyword:

```{python}
plt.hist(a_1d_array, bins=75)
```

As you can imagine, it's not hard to go back to the 2D shape, by splitting the
1D array back into 15 rows of 8 values each (and therefore 8 columns):

```{python}
array_back = np.reshape(a_1d_array, (15, 8))
array_back
plt.imshow(array_back)
```

In numpy, basic operations like multiplication, addition, comparison, are
always elementwise. For example, this multiplies every array value by 10:

```{python}
an_array * 10
```

Comparison is also elementwise. For example, this gives True for every value >
50, and False for every value <= 50:

```{python}
an_array > 50
```

Matplotlib will treat False as 0 and True as 1, so this is one way of
binarizing the image at a threshold (of 50 in this case):

```{python}
plt.imshow(an_array > 50)
```

We can slice arrays as we slice strings or lists. The difference for arrays is
that we can slice in any or all dimensions at the same time.  For example, to
get the dot of the “i” it looks (from the numbers at the sides of the ploat)
that we want to the top 4 rows, and the last 5 columns:

```{python}
an_array[0:4, 3:]
plt.imshow(an_array[0:4, 3:])
```