Apply Prewitt operators and Sobel operators for the image given below:
To apply Prewitt and Sobel operators numerically, we use their standard convolution kernels for edge detection. These operators compute gradients in the \( x \)-direction (\( G_x \)) and \( y \)-direction (\( G_y \)). ### 1. Prewitt Operator The Prewitt operator uses the following convolution kernels: \[ G_x = \begin{bmatrix} -1 & 0 & 1 \\ -1 & 0 & 1 \\ -1 & 0 & 1 \end{bmatrix} \] \[ G_y = \begin{bmatrix} -1 & -1 & -1 \\ 0 & 0 & 0 \\ 1 & 1 & 1 \end{bmatrix} \] ### 2. Sobel Operator The Sobel operator is similar ________ ____ ______ _______ ______ ___ _________ ______.
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Consider an 8-pixel line of intensity data, (108,139,135,244,172,173,56,99). If it is uniformly quantized with 4-bit accuracy, compute the rms error and rms signal-to- noise ratios for the quantized data.
Two images, f (x,y) and g (x,y), have histograms he and hg. Give the condition under which you can determine the histograms of
i) f(x,y)+g(x, y)
ii) f(x,y)-g(x,y)
iii) f(x, y)xg(x, y)
iv) f(x,y)+g(x,y)
Consider a 3x3 spatial mask that averages the four closet neighbours of a point
(x, y), but excludes the point itself from the average.
i) Find the equivalent filter, H (u, v), in the frequency domain.
ii) Show that your result is a lowpass filter.
Suppose that an image f(x, y) is convolved with a mask of size n x n (with cofficients 1/n²) to produce a smoothed image .
i) Derive an expression for edge strength (edge magnitude) of the smoothed image as a function of mask size. Assume for simplicity that n is odd and that edges are obtained using the partial derivatives
ii) Show that the ratio of the maximum edge strength of the smoothed image to the maximum edge strength of the orginal is 1/n. In other words, edge strength is inversely proportional to the size of the smoothing mask.
What do you understand by the term "Entropy" in context of any digital image? Calculate the entropy for the symbols, where probability distribution is given below:
| Symbol | Probability |
| 1 | 0.4 |
| 2 | 0.3 |
| 3 | 0.1 |
| 4 | 0.1 |
| 5 | 0.1 |
Write an expression for 2-D continuous convolution.
Consider a linear, position-invariant image degradation system with impulse response
Supose that the input to the system is an image cosnsiting of a line of infinitesimal width located at x = a, and modeled by f(x, y) = 8(x-a), where 8 is an impulse. Assuming no noise, what is the output image g(x, y)?