A bullet is 2.5 cm long, 1cm wide and its range of speed is . The bullet is flight is captured by a camera that exposes the scene for k sec and the bullet occupies 10% of the horizontal resolution of  frames. Find
i) Automatic segmentation of the bullet.

ii) Automatic determination of speed of the bullet.

 Perform histogram equalization for the following histogram.

 Apply the perception algorithm to the following pattern classes:
,

.
Let  and 
Also, Sketch the decision surface.

Suppose a low-pass spatial filter is formed by averaging the four immediate neighbours of a point (x, y) but excluding the point itself. Find the equivalent filter H(u,v) in the frequency domain.

 In image restoration, how are the noise parameters estimated?
b) Assume that the noise is estimated as exponential, with mean  Variance . How will you estimate the parameter 'a' of pdf of exponential Noise?

Explain in detail the adaptive mean and median filters.
b) Obtain mean and variance of the following noise pdfs:
i) 
ii) 
iii) 

Given an image with uniform histogram. Explain the effect of applying following compression techniques:
i) Huffman,

ii) Golomb,

iii) LZW,

iv) Prediction coding, and

v) Optimal Quantization

Explain the functioning of an adaptive, local noise reduction filter.

) Propose a gray level slicing algorithm capable of producing the 4-bit plane of an 8-bit monochrome image.

 Explain the Hough transform for edge linking with suitable example.

Show that Sobel masks can be implemented by one pass of differencing mask of the form [−1 0 1](or its vertical counterpart) followed by a smoothing mask of the form [1 2 1] (or its vertical counterpart).

 Verify Lagrange's mean value theorem for the function f defined by  over 

If , show that:

Hence find the value of .

Solve the equation:

given that its roots are in G.P.
b) Evaluate:

 If , then show that . Hence using Leibnitz's formula, find the value of (1 - x²)y_n+2 - (2n + 1)xy_n+1.
b) Find the largest subset of R on which the function  defined as:

is continuous.

Find the length of the cycloid  and show that the line  divides it in the ratio 1 : 3.
b) Find the condition for the curves,  and  intersecting orthogonally.

If the revenue function is given by , x being the input, find the maximum revenue. Also find the revenue function R, if the initial revenue is 0.
b) Trace the curve , clearly stating all the properties used for tracing it.

) Find the area between the curve  and its asymptote parallel to y-axis.

 Let f and g be two functions defined on R by:

and 
i) Find the value of  for which f is continuous at .

ii) Find all the roots of .

 For any two sets S and T, show that:

Depict this situation in the Venn diagram.