Concept of Sampling

Sampling is done only on an independent variable. For example, if we digitize x-axis in sampling.

Sampling is divided into two parts:

• upsampling
• downsampling

There are variations in the sampled signal which is due to noise. To reduce the noise more samples are taken which means more data or pixel which result in a better image with less noise present in it.

In an image, pixel is the smallest element which is represented in the form of a matrix.

In sampling, the number of samples taken in X-axis is continuous and refers to a number of pixels in that image.

Oversampling

As we have seen above, there are two types of sampling, up-sampling, and down-sampling.

Up-sampling is also known as oversampling.

In an image, oversampling means using a high-resolution image sensor as compare to camera output image resolution.

One of the oversampling applications in image processing is known as zooming.

Zooming

Increasing pixel quantity is known as Zooming. When we zoom in an image, more detail can be seen.

Increasing the number of pixels is done using oversampling.

Zooming has two steps:

1. In a new location, new pixels are created.
2. And assignment of the gray level to a new location.

Another, way to zoom an image is by zooming optically using the motor movement of the lens, and then the image is captured.

Optical Zoom vs. digital Zoom

Zooming methods

There are three types of methods used in zooming; they are as follows:

1. Pixel replication or (Nearest neighbor interpolation)
2. Zero-order hold method
3. Zooming K times

Pixel replication

Pixel replication is also known as Nearest neighbor interpolation. In this method, a copy is produced of the neighboring pixels. This algorithm works the same as zooming.

Working:

In this method, new pixels are generated from the originally given pixel. Each pixel is copied from its neighboring pixel n time row and column-wise, and we get a zoomed image.

For example, we have 2 row and 2 columns of an image. And we zoom the image twice.

ROW WISE ZOOMING:

When an image is zoom row-wise, it copies the pixels from row to the new cell

COLUMN SIZE ZOOMING:

Next step is to copy the pixel column-wise to the new adjacent column.

As we can see that the original image was having2 rows and 2 columns, but after zooming the image, it is converted into 4 rows and 4 columns.

Advantages

It is very simple, and we have to copy the pixels.

Disadvantages

When we zoom an image, the output is very blurry. As a result, we have a full blurred image.

Zero order hold

It is another method of zooming. Zero order hold is also known as zoom in twice, as it can only be zoomed twice.

Working

In this method, two adjacent elements are taken from the row, then elements are added, and the result is divided by two. The result is placed in between the elements.

For example:

Row Wise Zooming

When an image is zooming in row-wise, then rows are added (5+6) =11 and then it is divided by 2. We will get 5.5 approximate to 5 and the operation is performed in the second row.

Column Wise Zooming

When an image is zoomed column-wise, then columns are added (5+7) = 12 and then it is divided by 2. We will get 6, and this operation is performed in all the columns.

As we can see that the original image was having 2 rows and 2 columns but after zooming, the image it is converted into 3 rows and 3 columns.

It is very simple and it does not create a blurry picture.

Disadvantage

It works on the power of 2.

Reasons behind Twice Zooming

As we have seen in the above example, we have an image of 2 rows and 2 columns. If we want to zoom in an image 7 or 9 times then it cannot be done.

It can only zoom in the power of 2 i.e 2, 4, 8, 16, 32, etc.

K-Times zooming

K-Times Zooming is the perfect zooming algorithm. In this algorithm, k stands for the zooming factor.

Following are the steps to get a zoomed image which are used in both row and column:

1. Two adjacent pixels are taken.
2. Greater pixel is subtracted by a smaller pixel and the result is called OP.
3. Now, OP is divided by the zooming factor (k).
4. Now, the result is added in smaller pixel, and then it is placed in between those pixels.

For example:

We have 2 rows and 3 columns of an image. And we have to zoom in the image thrice.

In this case, the zooming factor (k) is 3. So, the number of values to be inserted is k-1 = 3-1 = 2.

Row Wise Zooming

Let's take 1st two adjacent pixels. i.e. 2 and 3.

Now, subtract 3 from 2.
3-2=1.
Divide 1 by k
1/3=0.3
Let 0.3 be OP.
Add OP with the lower number
0.3+2=2.3 (approx 2)
And again add OP with a higher number
0.3+3=3.3

Note: We have calculated two values because we have to insert k-1 values.

Now, repeat the above steps for the next two pixels.

Column Wise Zooming

In column wise zooming, the same steps are performed as done in row-wise zooming.

As, we can see that the original image was having 2 rows and 3 columns but after zooming, the image it is converted into 4 rows and 7 columns.

Advantages

It can be zoomed to any factor, thrice or four times or even more.

Disadvantages

Cost of computation is increased due to the additional step in the end.