# Image Shifting using NumPy from Scratch

Image shifting is simply shifting each pixel of the image to a new position. This is a method of pixel shift used in digital cameras to produce super-resolution images. We can think of a pixel as a point in the coordinate axis to be shifted in any direction. When we implement this on all the pixels of the image then we can say the image is shifted.

Credits of Cover Image - Photo by James Lewis on Unsplash

In this blog article, we will try to shift the image as we shift the point in the coordinate axis completely using NumPy operations. The image is always considered as a `2D` plane, hence we shall also consider a `2D` coordinate axis having `X` as the horizontal axis and `Y` as the vertical axis. The coordinate axis is divided into `4` quadrants namely -

• Q1 → Quadrant where both `X` and `Y` are positive.
• Q2 → Quadrant where `X` is negative and `Y` is positive.
• Q3 → Quadrant where both `X` and `Y` are negative.
• Q4 → Quadrant where `X` is positive and `Y` is negative. We assume that our original image to be at origin i.e., (0, 0). To visualize this, we can imagine something like the below - Now, let's say we want to shift the image at coordinates (3, 4). Basically, the origin of the image has to be shifted from (0, 0) to (3, 4) something like the below - Likewise, based on the coordinate points, we need to shift the image. Let's try to understand and implement from scratch using the module NumPy starting from a `2D` matrix because images are just large matrices.

### Time to Code

The packages that we mainly use are:

• NumPy
• Matplotlib
• OpenCV → It is only used for reading the image (in this article). ### `import` the Packages

``````import numpy as np
import cv2
import json
from matplotlib import pyplot as plt
``````

### `2D` Matrix

We will be creating a `5 X 5` matrix having random numbers.

``````>>> import random
>>>
>>> mat = [[random.randint(5, 100) for i in range(5)] for j in range(5)]
>>> mat = np.matrix(mat)
>>> print(mat)
[[ 46  13  68  54  12]
[  7  68  32  46  26]
[ 46  43  58  27 100]
[ 64  59  76 100  41]
[ 35  62  56  44   7]]
>>>
``````

For instance, let us assume that we are shifting the image in `Q1`, for sure the image has to move left side towards the `X` axis and topside towards the `Y` axis. In that case, the size of the image increases. Basically, we are padding the image left side as per the `x` coordinate depth and the bottom side as per the `y` coordinate depth. The same has to be replicated when we are shifting the image in the rest of the quadrants `Q2`, `Q3`, and `Q4`.

In order to do so, we need to create a padding function using NumPy methods.

``````def pad_vector(vector, how, depth, constant_value=0):
vect_shape = vector.shape[:2]
if (how == 'upper') or (how == 'top'):
pp = np.full(shape=(depth, vect_shape), fill_value=constant_value)
pv = np.vstack(tup=(pp, vector))
elif (how == 'lower') or (how == 'bottom'):
pp = np.full(shape=(depth, vect_shape), fill_value=constant_value)
pv = np.vstack(tup=(vector, pp))
elif (how == 'left'):
pp = np.full(shape=(vect_shape, depth), fill_value=constant_value)
pv = np.hstack(tup=(pp, vector))
elif (how == 'right'):
pp = np.full(shape=(vect_shape, depth), fill_value=constant_value)
pv = np.hstack(tup=(vector, pp))
else:
return vector
return pv
``````

The above function is used to pad the image. The arguments used are as follows:

1. vector → a matrix in which the padding is done.
2. how → this takes four values that decide the quadrants where the image needs to be shifted.

• lower or bottom
• upper or top
• right
• left
3. depth → the depth of the padding.
4. constant_value → signifies `black` color and `0` is the default value.

Note - For the padding-right and padding-left, we use the method `hstack()`. In the same way, for the padding-top and padding-bottom, we use the method `vstack()`. These two are the NumPy methods.

• hstack() → horizontal stack
• vstack() → vertical stack

First, we create a padding matrix whose values are zero. And based on the direction of the shift we make use of these methods.

Let's test the above function.

``````>>> pmat = pad_vector(vector=mat, how='left', depth=3)
>>> print(pmat)
[[  0   0   0  46  13  68  54  12]
[  0   0   0  7   68  32  46  26]
[  0   0   0  46  43  58  27 100]
[  0   0   0  64  59  76 100  41]
[  0   0   0  35  62  56  44   7]]
>>>
``````

We can clearly see that the function padded the matrix left side with the depth level `3`. If we were to plot the same (convert the padded matrix into an image), we get -

``````>>> plt.axis("off")
>>> plt.imshow(pmat, cmap='gray')
>>> plt.show()
`````` Whereas the original image is - With this, we can conclude the image is shifted to the left side towards the `X` axis with the `x` coordinate 3. The same technique is applied to the real image. Let's try to replicate the same for the image.

We shall have a function to read the image both in grayscale and RGB format.

``````def read_this(image_file, gray_scale=False):
image_src = cv2.imread(image_file)
if gray_scale:
image_src = cv2.cvtColor(image_src, cv2.COLOR_BGR2GRAY)
else:
image_src = cv2.cvtColor(image_src, cv2.COLOR_BGR2RGB)
return image_src
``````

Let's make another function called `shifter()` which actually shifts the image along the `Y` axis irrespective of the quadrant.

``````def shifter(vect, y, y_):
if (y > 0):
image_trans = pad_vector(vector=vect, how='lower', depth=y_)
elif (y < 0):
image_trans = pad_vector(vector=vect, how='upper', depth=y_)
else:
image_trans = vect
return image_trans
``````

Now that we have the `shifter()` function, we will need to use this in another function that can shift anywhere in the coordinate axis. Here, we consider `X` and `Y` axes.

``````def shift_image(image_src, at):
x, y = at
x_, y_ = abs(x), abs(y)

if (x > 0):
left_pad = pad_vector(vector=image_src, how='left', depth=x_)
image_trans = shifter(vect=left_pad, y=y, y_=y_)
elif (x < 0):
right_pad = pad_vector(vector=image_src, how='right', depth=x_)
image_trans = shifter(vect=right_pad, y=y, y_=y_)
else:
image_trans = shifter(vect=image_src, y=y, y_=y_)

return image_trans
``````
• When `x` and `y` coordinates are greater than 0, pad the image left side and bottom side.

• When `x` is greater than 0 and `y` is less than 0, pad the image left side and topside.

• When `x` is less than 0 and `y` is greater than 0, pad the image right side and bottom side.

• When `x` and `y` coordinates are less than 0, pad the image right side and topside.

• When `x` and `y` coordinates exactly equal to 0, do not disturb the image.

There is one problem yet to translate or shift the image. An image can be of two types - grayscale and colored. For grayscale, there won't be any problem. But for the colored image, we need to separate RGB pixels, apply the shift function, and then finally combine the pixels. Hence the below function.

``````def translate_this(image_file, at, with_plot=False, gray_scale=False):
if len(at) != 2: return False

image_src = read_this(image_file=image_file, gray_scale=gray_scale)

if not gray_scale:
r_image, g_image, b_image = image_src[:, :, 0], image_src[:, :, 1], image_src[:, :, 2]
r_trans = shift_image(image_src=r_image, at=at)
g_trans = shift_image(image_src=g_image, at=at)
b_trans = shift_image(image_src=b_image, at=at)
image_trans = np.dstack(tup=(r_trans, g_trans, b_trans))
else:
image_trans = shift_image(image_src=image_src, at=at)

if with_plot:
cmap_val = None if not gray_scale else 'gray'
fig, (ax1, ax2) = plt.subplots(nrows=1, ncols=2, figsize=(10, 20))

ax1.axis("off")
ax1.title.set_text('Original')

ax2.axis("off")
ax2.title.set_text("Translated")

ax1.imshow(image_src, cmap=cmap_val)
ax2.imshow(image_trans, cmap=cmap_val)
return True
return image_trans
``````

Now that it all set, let's test the above function:

For color image

``````translate_this(
image_file='lena_original.png',
at=(60, 60),
with_plot=True
)
`````` Clearly, the image is shifted to the origin (60, 60) i.e., in the first quadrant (Q1).

For grayscale image

``````translate_this(
image_file='lena_original.png',
at=(-60, -60),
with_plot=True,
gray_scale=True
)
`````` Clearly, the image is shifted to the origin (-60, -60) i.e., in the third quadrant (Q3).

Well, that's it for this article. From this, we tried to understand how the image shifting process is done.

Here I take leave. If you have liked it consider visiting this page to read more on Image Processing. And make sure to buy coffee for me from here or just hit the button below. 