Given a 4 ×4 image, decompose it into 4 bit planes and...

Given a $4 \times 4$ image, decompose it into 4 bit planes and represent each of them by run-length coding. Use both the methods. (i) $$ \left[\begin{array}{rrrr} 6 & 6 & 15 & 14 \\ 8 & 8 & 4 & 11 \\ 9 & 9 & 10 & 12 \\ 10 & 14 & 13 & 1 \end{array}\right] $$ (ii) $$ \left[\begin{array}{rrrr} 11 & 9 & 15 & 14 \\ 13 & 7 & 6 & 7 \\ 6 & 5 & 5 & 5 \\ 11 & 4 & 4 & 2 \end{array}\right] $$ (iii) $$ \left[\begin{array}{rrrr} 13 & 9 & 12 & 10 \\ 13 & 13 & 12 & 9 \\ 13 & 13 & 12 & 9 \\ 11 & 13 & 12 & 10 \end{array}\right] $$

Given a $4 \times 4$ image, decompose it into 4 bit planes and represent each of them by run-length coding. Use both the methods.
(i)
$$
\left[\begin{array}{rrrr}
6 & 6 & 15 & 14 \\
8 & 8 & 4 & 11 \\
9 & 9 & 10 & 12 \\
10 & 14 & 13 & 1
\end{array}\right]
$$
(ii)
$$
\left[\begin{array}{rrrr}
11 & 9 & 15 & 14 \\
13 & 7 & 6 & 7 \\
6 & 5 & 5 & 5 \\
11 & 4 & 4 & 2
\end{array}\right]
$$
(iii)
$$
\left[\begin{array}{rrrr}
13 & 9 & 12 & 10 \\
13 & 13 & 12 & 9 \\
13 & 13 & 12 & 9 \\
11 & 13 & 12 & 10
\end{array}\right]
$$

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Key Concepts

Bit-Plane Decomposition

Bit-plane decomposition is the process of separating an image into a set of binary images, each corresponding to one of the bits in the binary representation of the image's pixel values. This technique allows for the analysis or manipulation of the image at different levels of significance by isolating the contribution of each bit, and is particularly useful in image processing tasks such as compression, enhancement, and watermarking.

Run-Length Coding

Run-length coding is a simple form of lossless data compression in which sequences of the same data value (runs) are stored as a single data value and count. In the context of image processing, it is applied to binary images (like bit planes) to efficiently encode long runs of identical pixels, thereby reducing the amount of data needed to represent the image.

Transcript

00:01 So we have these four points, g, 0 .0, h4, 4, 4, i, 4, negative, and j, 8 ,0.

00:10 And we're being asked to translate these 3 units to the left and 5 units up.

00:18 So how we're going to do this is we're going to be using matrix addition.

00:24 So first, let's just graph this to see what we're dealing with.

00:27 So we have g 0 .0, right here at the origin, h 4 .4, we have i, 4 comma, negative 4, and we have j8 .0.

00:48 So as you can see, this is like sort of a square or a diamond, and it's going to be translated 3 units to the left and 5 units up.

01:00 So how we're going to set this up is we're first going to have a matrix for the original points.

01:06 And we're going to set the top row as x and the bottom row as y.

01:11 This is going to be g, h, i, and j.

01:16 So four columns.

01:19 So we have g is 0, 0, h is 4, 4, i is 4, negative 4, and j is 8 ,0.

01:32 So that's our first matrix.

01:36 And we're going to be adding another matrix that represents this transformation over here.

01:42 So if we're moving three units to the left, that means we're going to be moving the x coordinate to the left by three.

01:49 So we're subtracting three for each point.

01:55 For the y coordinate, we're moving five units up...

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