Digital Image Processing

Let H be a degraded/degradation function which follows the additivity,homogeneity and position invariant property. Show that in the spatial domain, degraded image g(x,y), can be modelled as convolution of the degraded/degradation function with an image followed by the addition of noise.

Let us assume the following patterns and classes. Apply the Bayesian classifier to predict the pattern (2, 2). 

Determine the Erosion between two vector sets as given below:

A = {(0, 1) (1, 1) (2, 1) (2, 2) (3, 0)}

B = {(0, 0) (0, 1)}

Also show that the erosion between two sets in the intersection of negative translations.

Explain the Linear discriminant analysis. Let us assume that mean vectors of two classes i and j respectively are m₁ = (3.2,1.2) and m2 = (3.0, 1.0). What is the decision boundary? 

Determine the dilation between two vector sets as given below:

A={(0, 1) (1, 1) (2, 1) (3, 1)}

B={(0,0 ) (0, 2)}

Also show that the dilation between two sets is the union of positive translations.

Explain the spatial based image segmentation techniques. 

Find G₄(7) and G₄ (9) by using Golomb coding.

Explain region splitting and merging techniques for image segmentation with suitable examples.

Perform the Arithmetic encoding for the sequence 'abab' according to the following distribution.

The image gets blurred due to the uniform acceleration in the x-direction. If the image is at rest at time t=0 and accelerate with a uniform acceleration  for a time T. Find the blurring function H(u, v).

Let f(x,y) = F(u, v), then show the following: (denotes Fourier Transform)

(i) f(x,y)= F(0,0), where f(x,y) is the mean of (x,y).

(ii) F(u, v) of f(x, y)= A sin (u₀x + v₀y)

Define contrast stretching and intensity-level slicing transformation with proper illustrations. 

Consider a 3x3 spatial mask that average the four closest neighbors of a point (x,y), but exclude 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 low pass filter. 

Apply Sobel operator for the following 4X4 image with the replication on the boundary pixels and show the resultant image. 

Consider the following intensity distribution tables of two images:

Explain the Unsharp masking and High-boost filtering along with one-dimensional illustrations.

he histogram of a 4 X4 image segment (2-bit image) is given as

It is given that the mean and variance of the above image segment are 2 and 1, respectively. Find the value of a, b and c.

Explain the Run-length coding.

Explain Hit-or-Miss transformation in binary image morphology.

Show that Laplacian is an isotropic operator in 2-D space.

Write all the steps of the filtering process in frequency domain with proper expressions.

Define mixed adjacency between two pixels in a gray-scale image. Write the conditions under which a D₄ distance between two pixels p and q is equal to the shortest 4-path between them. Give proper illustrations if needed.