II IMAGE ENHANCEMENT PART A. 1. Give the PDF of uniform noise and sketch it.(april/may 2015)(Nov./Dec.2013)

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1 UNIT II IMAGE ENANCEMENT PART A 1. Gie the PD of niform noise and sketch it.april/may 015No./Dec.013 The probability density fnction of the continos niform distribtion is:. Define and gie the transfer fnction of Mean and Geometric Mean filter. April/May 015 Mean filtering is a simple intitie and easy to implement method of smoothing images i.e. redcing the amont of intensity ariation between one pixel and the next. It is often sed to redce noise in images The geometric mean filter is member of a set of nonlinear mean filters which are better at remoing Gassian type noise and presering edge featres than the arithmetic mean filter. The geometric mean filter is ery ssceptible to negatie otliers. The definition of geometric mean filter is fˆ x y s t S g s t xy 1 mn

2 where the coordinate x y is defined oer the image f and the coordinate st is defined oer the sb image g. 3. State the principle of directional smoothing.no./dec. 011 Directional smoothing is the process sed to protect the edges from distortion in the form of blrring while smoothing the images. 4. What are the types of Image enhancement aailable? No./Dec.01 The types of Image enhancement are: reqency domain methods. Spatial domain methods 5. Mention the procedre in Marker selection..no./dec.01 'Major genes' that are responsible for economically important characteristics are freqent in the plant kingdom. Sch characteristics inclde disease resistance male sterility [7] self-incompatibility and others related to shape color and architectre of whole plants and are often of mono- or oligogenic in natre. The marker loci that are tightly linked to major genes can be sed for selection and are sometimes more efficient than direct selection for the target gene. 6. Define and gie the transfer fnction of contraharmonic filters. April/May 013 The contraharmonic mean of a set of positie nmbers is defined as the arithmetic mean of the sqares of the nmbers diided by the arithmetic mean of the nmbers: 7. What is meant by bit plane slicing? No./Dec.016 Separating a digital image into its bit planes and analyzing the relatie importance played by each bit of the image implying it determines the adeqacy of nmbers of bits sed to qantize each pixel sefl for image compression. 8. What is nsharp masking? No./Dec.016

3 Unsharp masking USM is an image sharpening techniqe often aailable in digital image processing software. The "nsharp" of the name deries from the fact that the techniqe ses a blrred or "nsharp" negatie image to create a mask of the original image. 9. List ot the categories of image enhancement. No./Dec.01 The categories of image enhancement are: Spatial domain enhancement reqency domain enhancement. Spatial domain refers to image plane itself & approaches in this category are based on direct maniplation of pictre image.reqency domain methods based on modifying the image by orier transform. 10. What is a mltimodal histogram? May/Jne 01 A mltimodal histogram is the histogram which has two or more dominant modes i.e probability distribtion with two or more modes. 11. State the principle of directional smoothing. No./Dec. 011 Directional smoothing is the process sed to protect the edges from distortion in the form of blrring while smoothing the images. 1. Define istogram No./Dec.009 No./Dec.01 The histogram of a digital image with gray leels in the range [0 L-1] is a discrete fnction hrk = nk where rk is the kth gray leel and nk is the nmber of pixels in the image haing gray leel rk. PART B 1. What is istogram eqalization?discss in detail procedre inoled in histogram eqalization.no./dec.01no./dec.016april/may015.may/jne014no./dec.014 istogram eqalization is sed to enhance contrast. It is not necessary that contrast will always be increase in this. There may be some cases were histogram eqalization can be worse. In that cases the contrast is decreased. Consider for a moment continos fnctions and let the ariable r represent the gray leels of the image to be enhanced. We assme that r has been normalized to the interal [0 1] with r=0 representing black and r=1 representing white. Later we consider a discrete formlation and allow pixel ales to be in

4 the interal [0 L-1]. or any r satisfying the aforementioned conditions we focs attention on transformations of the form that prodce a leel s for eery pixel ale r in the original image. or reasons that will become obios shortly we assme that the transformation fnction Tr satisfies the following conditions: a Tr is single-aled and monotonically increasing in the interal 0 r 1; and b b 0 Tr 1 for 0 r 1. The reqirement in a that Tr be single aled is needed to garantee that the inerse transformation will exist and the monotonicity condition preseres the increasing order from black to white in the otpt image.a transformation fnction that is not monotonically increasing cold reslt in at least a section of the intensity range being inerted ths prodcing some inerted gray leels in the otpt image. inally condition b garantees that the otpt gray leels will be in the same range as the inpt leels..the inerse transformation from s a back to r is denoted b It can be shown by example that een if Tr satisfies conditions a and b it is possible that the a corresponding inerse T-1 s may fail to be single aled. A gray-leel transformation fnction that is both single aled and monotonically increasing. The gray leels in an image may be iewed as random ariables in the interal [0 1].One of the most fndamental descriptors of a random ariable is its probability density fnction PD. Let prr and pss denote the probability density fnctions of random ariables r and srespectielywhere the sbscripts on p are sed to denote that pr and ps are different fnctions.a basic reslt from an elementary probability theory is that if prr and Tr are known and T-1 s satisfies condition a then the probability density fnction pss of the transformed ariable s can be obtained sing a rather simple formla:

5 Ths the probability density fnction of the transformed ariable s is determined by the grayleel PD of the inpt image and by the chosen transformation fnction. A transformation fnction of particlar importance in image processing has the form Gien transformation fnction Trwe find pss by applying Eq. We know from basic calcls Leibniz s rle that the deriatie of a definite integral with respect to its pper limit is simply the integrand ealated at that limit. In other words Sbstitting this reslt for dr/ds and keeping in mind that all probability ales are positieyields The probability of occrrence of gray leel r in an image is approximated by where as noted at the beginning of this section n is the total nmber of pixels in the image nk is the nmber of pixels that hae gray leel rk and L is the total nmber of possible gray leels in the image.the discrete ersion of the transformation fnction gien in Eq. is Ths a processed otpt image is obtained by mapping each pixel with leel rk in the inpt image into a corresponding pixel with leel sk in the otpt image. As indicated earlier a plot of pr rk erss rk is called a histogram. The transformation mapping is called histogram eqalization or histogram linearization. It is not difficlt to show that the transformation in Eq.satisfies conditions a and b stated preiosly. Unlike its continos conterpart it cannot be proed in general that this discrete transformation will prodce the discrete eqialent of a niform probability density fnction which wold be a niform histogram

6 a Images b Reslts of histogram eqalization. c Corresponding histograms.. Specify the expression for No./Dec.01May/Jne Mean filter.armonic filter 3. Contra harmonic filter Mean filter This is the simplest of the mean filters. Let Sx represent the set of coordinates in a rectanglar sbimage window of size m X n centered at point x y.the arithmetic mean filtering process comptes the aerage ale of the corrpted image gx y in the area defined by Sxy.The ale of the restored

7 image at any point x y is simply the arithmetic mean compted sing the pixels in the region defined by S. In other words. armonic filter The harmonic mean filtering operation is gien by the expression Contraharmonic filter The contraharmonic mean filtering operation yields a restored image based on the expression 3. Write notes on omomorphic filtering. No./Dec.01April/May 015 omomorphic filtering is a generalized techniqe for signal and image processing inoling a nonlinear mapping to a different domain in which linear filter techniqes are applied followed by mapping back to the original domain. omomorphic iltering can be sed for improing the appearance of a grayscale image by simltaneos intensity range compression illstration and contrast enhancement reflection. Where m = image i = illmination r = reflectance We hae to transform the eqation into freqency domain in order to apply high pass filter. oweer it's ery difficlt to do calclation after applying orier transformation to this eqation becase it's not a prodct eqation anymore. Therefore we se 'log' to help soling this problem. Then applying orier transformation

8 Or Next applying high-pass filter to the image. To make the illmination of an image more een the highfreqency components are increased and low-freqency components are decrease. Where = any high-pass filter N = filtered image in freqency domain Afterward retrning freqency domain back to the spatial domain by sing inerse orier transform. inally sing exponential fnction to eliminate the log we sed at the beginning to get the enhanced image 4. Explain in detail the method for smoothening the image in freqency domain.no./dec.016 May/Jne 013 In inerse filtering - there is no clear proision for handling noise. Wiener filtering - incorporates both degradation fnction and random noise factor. The objectie of this method is the difference between an estimate and ncorrpted image f is minimized. The difference is known as error and is gien by e E f f Where E represents the mean ale The assmptions are: The noise and image are ncorrelated. Either noise or image has zero mean ale Gray leels in the estimate are a linear fnction of the leels in the degraded image. Based on these assmptions the minimm of the error fnction in freqency domain S f G S f S G S / S f

9 where is the transform of the degraded fnction G is the transform of the degraded image. is complex conjgate of is power spectrm of the noise is power spectrm of ndegraded image. This reslt is known as Wiener filter. The filter which consists of the terms inside the bracket is referred as minimm mean sqare error filter or the least sqare error filter. Wiener filter oercome the problem as inerse filter with zeros in the degradation fnction. Note that if the noise is zero then the noise power spectrm anishes and the Wiener filter redces to the inerse filter. If the noise is white noise then we know that the spectrm of white noise is constant. Now the estimate expression becomes Inerse filtering The inerse filtering is one of the restoration techniqes of images degraded by a degradation fnction. Also inerse filtering is simplest method. Already we know that the objectie of image restoration is to estimate the original image from the degrade image. In this inerse filtering techniqe an estimate of the transform of the original image simply by diiding the transform of the degraded image G by the degradation fnction. G. 1 we know that. sbstitte in Eq.1 we get N. / 1 G S S f N S S f 1 G K N G

10 rom Eq. we obsered that een we known abot the degradation fnction we cannot recoer the original image. Becase noise is a random fnction whose orier transform is not known. Also if the degraded fnction ale is zero or small ale then the second term dominate the estimation. 5. Explain Gradient operators for Image Enhancement.May/Jne 013 The gradient of the pictre fnction can be estimated by applying the masks to the 8- neighborhood N8[x; y] of pixel [x; y] as gien in Eqations. These masks dene the Prewitt operator credited to Dr Jdith Prewitt who sed them in detecting bondaries in biomedical images. The operation M 0 N is defined formally in the next section: operationally mask M is oerlaid on image neighborhood N so that each intensity Nij can be mltiplied by weight Mij ; finally all these prodcts are smmed. the two analogos Sobel masks; their deriation and interpretation is the same as for the Prewitt masks except that the assmption is that the center estimate shold be weighted twice as mch as the estimate to either side. The Roberts masks are only x; hence they are both more efficient to se and more locally applied. Often referred to as the Roberts cross operator these masks actally compte a gradient estimate at the center of a 4-neighborhood and not at a center pixel. Moreoer the actal coordinate system in which the operator is defined is rotated 45degree off the standard row direction. It is common to aoid compting a sqare root in order to compte gradient magnitde; alternaties are j j @y =. With these estimates one mst be carefl when trying to interpret the actal gradient or gradient direction.

11 6. ow Mean filters are sed for image enhancement? May/Jne 013 Mean filtering is a simple intitie and easy to implement method of smoothing images i.e. redcing the amont of intensity ariation between one pixel and the next. It is often sed to redce noise in images. The idea of mean filtering is simply to replace each pixel ale in an image with the mean `aerage' ale of its neighbors inclding itself. This has the effect of eliminating pixel ales which are nrepresentatie of their srrondings. Mean filtering is sally thoght of as a conoltion filter. Like other conoltions it is based arond a kernel which represents the shape and size of the neighborhood to be sampled when calclating the mean. Often a 3 3 sqare kernel is sed as shown in igre 1 althogh larger kernels e.g. 5 5 sqares can be sed for more seere smoothing. Note that a small kernel can be applied more than once in order to prodce a similar bt not identical effect as a single pass with a large kernel. Compting the straightforward conoltion of an image with this kernel carries ot the mean filtering process.