MCA0086 Assignment

7/28/2019 MCA0086 Assignment

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All recording devices, both analogue and digital, have traits which make themsusceptible to noise. Noise can be random or white noise with no coherence, orcoherent noise introduced by the device's mechanism or processing algorithms.

In electronic recording devices, a major form of noise is hiss caused by randomelectrons that, heavily influenced by heat, stray from their designated path.These stray electrons influence the voltage of the output signal and thus createdetectable noise.

In the case of photographic film and magnetic tape, noise (both visible andaudible) is introduced due to the grain structure of the medium. In photographicfilm, the size of the grains in the film determines the film's sensitivity, moresensitive film having larger sized grains. In magnetic tape, the larger the grainsof the magnetic particles (usually ferric oxide or magnetite), the more prone themedium is to noise.

To compensate for this, larger areas of film or magnetic tape may be used tolower the noise to an acceptable level.

Linear smoothing filters:

One method to remove noise is by convolving the original image with a maskthat represents a low-pass filter or smoothing operation. For example, theGaussian mask comprises elements determined by a Gaussian function. Thisconvolution brings the value of each pixel into closer harmony with the values ofits neighbours. In general, a smoothing filter sets each pixel to the averagevalue, or a weighted average, of itself and its nearby neighbours; the Gaussianfilter is just one possible set of weights.

Smoothing filters tend to blur an image, because pixel intensity values that aresignificantly higher or lower than the surrounding neighborhood would "smear"across the area. Because of this blurring, linear filters are seldom used inpractice for noise reduction; they are, however, often used as the basis fornonlinear noise reduction filters.

Anisotropic diffusion :

Another method for removing noise is to evolve the image under a smoothingpartial differential equation similar to the heat equation which is calledanisotropic diffusion. With a spatially constant diffusion coefficient, this isequivalent to the heat equation or linear Gaussian filtering, but with a diffusion

coefficient designed to detect edges, the noise can be removed without blurringthe edges of the image.


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Question 3 - Which are the two quantitative approaches used for theevaluation of image features? Explain.

Ans: The theory of histogram modification of continuous real-valued pictures isdeveloped. It is shown that the transformation of gray levels taking a picture'shistogram to a desired histogram is unique under the constraint that thetransformation is monotonic increasing. Algorithms for implementing thissolution on digital pictures are discussed. A gray-level transformation is useful

for increasing visual contrast, but may destroy some of the information content.It is shown that solutions to the problem of minimizing the sum of theinformation loss and the histogram discrepancy are solutions to certaindifferential equations, which can be solved numerically.

Question 4 - Explain with diagram Digital image restoration model.

Ans:

Digital image restoration - in which a noisy, blurred image is restored on thebasis of a mathematical model of the blurring process - is a well-known exampleof a 2-D deconvolution problem. A recent survey of this topic, including adiscussion of many practical aspects, can be found in [1].


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edge is deemed present. The gradient along the line normal to the edge slope

can be computed in terms of the derivatives along orthogonal axes according to

the following

For computational efficiency, the gradient amplitude is sometimes approximated

by the magnitude combinationThe orientation of the spatial gradient with respect to the row axis isThe remaining issue for discrete domain orthogonal gradient generation is to

choose a good discrete approximation to the continuous differentials of Eq. 8.3a.The simplest method of discrete gradient generation is to form the runningdifference of pixels along rows and columns of the image. The row gradient isdefined asand the column gradient isDiagonal edge gradients can be obtained by forming running differences ofdiagonal pairs of pixels. This is the basis of the Roberts cross-differenceoperator, which is defined in magnitude form asand in square-root form as

Prewitt has introduced a pixel edge gradient operator described by the pixel

numbering The Prewitt operator square root edge gradient is defined asWith

where K= 1. In this formulation, the row and column gradients are normalized

to provide unit-gain positive and negative weighted averages about a separated

edge position.

The Sobel operator edge detector differs from the Prewitt edge detector in that

the values of the north, south, east and west pixels are doubled (i.e., K = 2).

The motivation for this weighting is to give equal importance to each pixel in

terms of its contribution to the spatial gradient.

Question 6- Explain about the Region Splitting and merging with

example.

Ans: The basic idea of region splitting is to break the image into a set of disjoint

regions which are coherent within themselves:

Initially take the image as a whole to be the area of interest. Look at the area of interest and decide if all pixels contained in theregion satisfy some similarity constraint. IfTRUE then the area of interest corresponds to a region in theimage. IfFALSE split the area of interest (usually into four equal sub-areas) and consider each of the sub-areas as the area of interest in turn.

This process continues until no further splitting occurs. In the worstcase this happens when the areas are just one pixel in size. This is a divide and conqueror top down method.


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If only a splitting schedule is used then the final segmentation would probablycontain many neighbouring regions that have identical or similar properties.

Thus, a merging process is used after each split which compares adjacentregions and merges them if necessary. Algorithms of this nature are calledsplitand merge algorithms.

To illustrate the basic principle of these methods let us consider an imaginary

image.

Let denote the whole image shown in Fig (a). Not all the pixels in are similar so the region is split as in Fig (b). Assume that all pixels within regions , and respectively aresimilar but those in are not.

Therefore is split next as in Fig (c). Now assume that all pixels within each region are similar withrespect to that region, and that after comparing the split regions,

regions and are found to be identical. These are thus merged together as inFig 35(d).

Fig. Example of region splitting andmerging

We can describe the splitting of the image usinga tree structure, using a modified quadtree.

Each non-terminal node in the tree has at mostfour descendants, although it may have less dueto merging. See Fig. 36.

Fig. Region splitting and merging tree
http://www.cs.cf.ac.uk/Dave/Vision_lecture/node34.html#figureregion_splithttp://www.cs.cf.ac.uk/Dave/Vision_lecture/node34.html#figuresplit_treehttp://www.cs.cf.ac.uk/Dave/Vision_lecture/node34.html#figuresplit_treehttp://www.cs.cf.ac.uk/Dave/Vision_lecture/node34.html#figureregion_split

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MCA0086 Assignment