MAJOR
20th November 1999
Maximum Marks 50 ................................2 hours
* Solve the following problems:
- Suppose that you form a lowpass spatial filter that averages the 4-neighbors off a point (x,y), but excludes the point (x,y) instead.
- Find the equivalent filter H(u,v) in the frequency domain.
- Is the filter low-pass, high-pass or bandpass in nature? Justify.
(6)
- The basic approach to compute the digital gradient involves taking differences of the form f(x,y)-f(x+1,y).
- Obtain the filter transfer function, H(u,v) for performing the equivalent process in the frequency domain
- Is the filter low-pass, high-pass or bandpass in nature? Justify.
(6)
- Start with Eq. (5.7-12) and derive Eq. (5.7-14).
(5)
- Define operators for doing the following (Give the simplest solutions you can think of): (a) Filling small black holes in objects (b) filling small holes of arbitrary gray levels in objects (c) detecting small gaps in line segments of a gradient image.
(4)
- The ballistics of a 2.5 cm long x 1.5 cm wide object moving at a speed of 750+250 m/s in the horizontal direction is studied in a series of 256 x 256 digital images in which the object occupies 10% of the horizontal resolution. What is the minimum duration T of the flash which exposes the object, so that the blur due to motion is less than or equal to 1 pixel? What is the minimum frame rate, so that at least 2 complete images of the object are obtained? Propose a segmentation procedure for automatically extracting the bullet from a sequence of frames. Devise and completely describe a method for automatically determining the exact speed of the object.
(5)
- Assume that two clusters in feature space are described by Gaussian distributions in two dimensions. Cluster 1 has mean at (x,y)= (2,2) and cluster 2 has its mean at (x,y)=(2,4). If the standard deviation of each distribution is 1.0, what is the equation of the boundary separating the two classes assuming that the probability of belonging to each class is equal?
(3)
- Is it possible to restore the original image by running the erosion operation over an image that has been dilated? Justify.
(3)
- Write a program in C to implement region filling. [Remember you are not being graded for your knowledge of C programming].
(5)
- A binary image is corrupted by nonoverlapping noise spikes that can be modelled as small, circular artifacts of radii Rmin =< r =< R max. Develop a morphological filtering approach for cleaning up the image.
(5)
- The signal-to-noise for an edge detector is given by
where, S is the response of the edge detector to a unit-strength edge passing through the center of the kernel. N is the standard deviation of the output noise (noise filtered by the detector). Compare the performance of Sobel and Prewitt's operator in terms of their SNR. An example of unit-strength edge is given below.
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