1. Derive the intensity transformation function, s=T(r) such that the input image with pdf, p(r)=1er is transformed to an output image with, pdf, p(s)=I/L1; where r is the intensity variable of input image and s is the intensity variable of the transformed image and L=28. [10] 2. Write a function, histe) to compute the histogram of an image variable, x (in python, x is a two dimensional byte array ) [10] 3. Present a piece-wise linear transformation of image intensity from r to s; where r is the intensity of the input image and s is the intensity of the output image. The piece-wise transformation f:rs 0>0;r1s1;r2s2;255>255 4. Write a program to transform input image intensities as given in Q3 [10] 5. Given four spatially adjacent points in an image be (x1,y1),(x1,y2),(x2,y1), and (x2,y2) and the corresponding intensities g1,g2,g3, and g4; find the intensity, g at point (x,y) which is inside the square formed by the four locations given above using bi-linear interpolation. [10] 6. Derive 33 Laplacian operators for sharpening images. [10] 7. Write a program to smoothen a given image using an averaging operator in 33 window [10] 10. a) What is homomorphic filtering used for in images? b) Describe homomorphic filtering applied to image function f(x,y) given its intensity function is i(x,y) and reflection is r(x,y) [8]