Btc-801(dip)qb.docx

SECTION-A

6 Marks Each

Module-1 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

Explain the importance of Image Processing in real world? Discuss the role of Segmentation in Digital Image Processing? How do you perform zooming and shrinking of digital images? Specify all the elements of DIP system with example? Differentiate between Photopic and Scotopic vision? How do you perform image sampling over an image? Explain the term image quantization in Image Processing? Define subjective brightness and brightness adaptation? How do you measure the distance between pixels? Differentiate Linear and Non-Linear Operations. Give an example of each. Module-2

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

Specify the objective of image enhancement technique? What do you understand by grey level slicing? Explain the two categories of image enhancement? Explain the concept of histogram and histogram equalization? How Smoothening filter is different from sharpening spatial filter? Write all the methods used for image enhancement technique? What are the possible ways for adding noise in images? Explain all the types of noise models? Write the application of sharpening filters? What is the purpose of image averaging? Module-3

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

Give the relation for Uniform Noise and Impulse Noise? Explain the role of harmonic mean filter? Explain image enhancement in frequency domain? How a degradation process is modeled? Explain the concept of image restoration in presence of noise? What is meant by least mean square filter or Wiener filter? Describe the role of geometric mean filter in DIP? Explain the concept of Inverse filtering? Give the difference between enhancement and restoration of an image? Why blur effect is to be removed from images? Module-4

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

Explain all the concepts of image compression models? What are the two main types of Data Compression? How do you calculate compression ratio for an image? What are the operations performed by error free compression? Define Image Segmentation. Write its applications? What are the two properties used for establishing similarity of edge pixels? What is meant by object point and background point? Write the differences between local threshold and global threshold in Image segmentation? What are the factors affecting the accuracy of region growing? Define region splitting and merging in DIP?

Module-5 1. 2.

Write the main uses of principal components for description of an image? What do you understand by the concept of Morphology? Give an example?

3. 4. 5.

Explain the fundamental steps used for analysis of an image? Write all the structural methods used for recognition of an image? How do you represent objects using external (boundary) and internal (regional) representation and description? 6. How do you perform scaling, rotation and translation over an image? Give a sketch diagram of each identity? 7. Define signature and how do you represent boundary segments over an image? 8. Define simple boundary (segment) descriptors and Fourier descriptors? 9. Explain the importance of pattern recognition with example? 10. Explain the importance of Principal component analysis in DIP?

SECTION- B

10 Marks Each

Module-1 1. 2. 3. 4. 5. 6. 7.

Explain the concept of color image processing fundamentals? Compare RGB and HIB color models. Discuss in detail. Explain all the properties of one-dimensional and two-dimensional Discrete Fourier Transform? Describe functions of elements of digital image processing system with a diagram? Describe image formation in the eye with brightness adaptation and discrimination? Find the DCT transform and its inverse for the given 2x2 image [ 3 6 ; 6 4 ]? Draw a block diagram and explain its various functional blocks of digital image processing system? Describe in detail. What is image transform and discuss how do you achieve perfect transform? Explain in detail the different separable transforms? Module-2

1. 2. 3. 4. 5. 6. 7.

1. 2. 3. 4. 5. 6. 7.

How do you perform image smoothening using image smoothening filter with its model in spatial domain? Why is it required? Write the salient features of image histogram. What do you infer? Explain any two techniques for image enhancement? Compare the differences between Geometric mean filter, Harmonic mean filter and Contra harmonic mean filter? Give a suitable example? Explain different types of noise models with noise function in image processing system with suitable examples? Explain the relationship between image sizes, intensity resolution and image quality with example? How linear operation is different from non-linear operation? Also prove operation MAX is nonlinear operation? Explain why the discrete histogram equalization technique does not, in general, yield a flat histogram? Module-3 Explain the process of performing image enhancement in frequency domain? How it is different form spatial domain filtering? How do you compare constrained and unconstrained restoration from the concept of Image restoration used in digital image processing system? Explain the types of grey level transformation used for enhancement of an image? What is meant by Image restoration and discuss in detail the use of Wiener filter or least mean square filter in image restoration? Explain all the schemes involved with the concept of grey level interpolation? Which is the most frequent method to overcome the difficulty to formulate the spatial relocation of pixels for an image? Describe constrained least square filtering for image restoration and derive its transfer function? Module-4

1.

Explain the concept of region growing in Image segmentation? State the problems found in region splitting and merging based on image segmentation?

2. 3. 4. 5. 6. 7.

Discuss about region based image segmentation techniques. How it is different from threshold region based techniques. Give an explanation for the concept of thresholding and explain the various methods of thresholding in detail? Define Huffman coding used for compression of an image. Write the need for compression and also discuss its advantages and limitations. State and explain the block diagram of transform coding system used in image compression? Explain the functionality of each identity block from the system? Explain the schematics of image compression standard JPEG. Write the performance metrics for image compression? Given the following Huffman codes, encode the string ‘goat’ Huffman Code Character 00 a 01 o 10 t 110 d 1110 g 1111 c

Module-5 1. 2. 3. 4. 5. 6. 7.

Explain how to choose or design representations and descriptors for an image, take suitable example to justify your views? Explain the role of face recognition and how do you perform face recognition using PCA? Discuss its importance and reliability in real world? Explain all the features of pattern recognition and also discuss its applications in real world? How do you perform training and testing over data to identify the patterns associated with objects? Sketch a block diagram to show the classification. Write all the advantages and disadvantages of Pattern recognition. Give an example to support your answer. Discuss the importance of feature extraction for the classification of images. How pattern recognition help in identifying images? List the applications used with pattern recognition in real world?

SECTION –C

20 Marks Each

Module-1 1. 2. 3. 4. 5.

Explain the convolution property in 2D discrete fourier transform? How do you obtain 2D DFT for a digital image? Discuss about the time complexities in image processing system? Explain all the different transforms used in digital image processing and also discuss the most advantageous one in detail along with their equations or symbolic representation? Define Optical Illusion and state the problems encountered when viewing such images constantly for longer period of time? Why KL transform is called optimal transform and also discuss how Fast Fourier Transform (FFT) is different from KL transform with the help of symbolic notations of image transforms? Obtain forward KL transform for the given vectors.X1 = [ 1 0 0 ] ; X2 = [ 1 0 1 ] ; X3 = [ 1 1 0 ] (Transpose these vectors) and analyse how the principal components are used for remote sensing applications?

Module-2 1.

Describe how homomorphic filtering is used to separate illumination and reflectance components with a suitable example?

2.

3. 4. 5.

Explain the following concepts along with its application and a suitable example of each. a. Image Negatives b. Contrast Stretching c. Bit-plane Slicing d. Histogram processing Compare spatial and frequency domain methods used for performing image enhancement in spatial and frequency domain in DIP? What is the requirement of image sampling and quantization? Explain the significant of spatial resolution with an example? Describe histogram equalization. Obtain histogram equalization for the following image segment of size 5 X 5. Write the interference on the image segment before and after equalization. 20 20 20 18 16 15 15 16 18 15 15 15 19 15 17 16 17 19 18 16 Module-3

1.

2. 3. 4. 5.

1.

Explain why noise probability density functions are important? Give the properties and relations of each of the following noisesa. Gaussian Noise b. Gamma noise c. Exponential noise d. Rayleigh Noise e. Uniform noise Enumerate the differences between image enhancement and image restoration along with suitable example? Explain about restoration filters used when the image degradation is due to noise only. Justify your answer using various mean filters? What are the two approaches used for blind image restoration? How do you differentiate indirect estimation from direct measurement in degradation process? Geometric spatial transformation is somehow different from spatial transformation. Justify your answer with suitable example? Module-4 What is meant by optimal thresholding? How do you obtain the threshold for image processing tasks? Write morphological concepts applicable for image processing.

Optimal thresholding is a technique that approximates the histogram using a weighted sum of distribution functions, and then sets a threshold in such a way that the number of in- correctly segmented pixels (as predicted from the approximation) is minimum. 2. Why is edge detection useful in image processing? Discuss various gradient operators used in detecting the edge points? Edge detection is a process that detects the presence and location of edges constituted by sharp changes in intensity of an image. Edges define the boundaries between regions in an image, which helps with segmentation and object recognition. Edge detection of an image significantly reduces the amount of data and filters out useless information, while preserving the important structural properties in an image. The general method of edge detection is to study the changes of a single image pixel in an area, use the variation of the edge neighboring first order or second-order to detect the edge. In this paper after a brief introduction, overview of different edge detection techniques like differential operator method such as sobel operator,prewitt’s technique,Canny technique and morphological edge detection technique are given. various gradient operators used in detecting the edge points Prewitt Operator-Prewitt operator is used for detecting edges horizontally and vertically. Sobel Operator-The sobel operator is very similar to Prewitt operator. It is also a derivate mask and is used for edge detection. It also calculates edges in both horizontal and vertical direction. Robinson Compass Masks-This operator is also known as direction mask. In this operator we take one mask and rotate it in all the 8 compass major directions to calculate edges of each direction. Kirsch Compass Masks-Kirsch Compass Mask is also a derivative mask which is used for finding edges. Kirsch mask is also used for calculating edges in all the directions. Laplacian Operator-Laplacian Operator is also a derivative operator which is used to find edges in an image. Laplacian is a second order derivative mask. It can be further divided into positive laplacian and negative laplacian.

All these masks find edges. Some find horizontally and vertically, some find in one direction only and some find in all the directions.

3.

Differentiate between parametric and non-parametric decision making. Explain two nonparametric decision making methods?

two non-parametric decision making methods= 1KNN algorithm- K-Nearest Neighbors is one of the most basic yet essential classification algorithms in Machine Learning. It belongs to the supervised learning domain and finds intense application in pattern recognition, data mining and intrusion detection. It is widely disposable in real-life scenarios since it is non-parametric, meaning, it does not make any underlying assumptions about the distribution of data K-Nearest Neighbors is one of the most basic yet essential classification algorithms in Machine Learning. It belongs to the supervised learning domain and finds intense application in pattern recognition, data mining and intrusion detection. It is widely disposable in real-life scenarios since it is non-parametric, meaning, it does not make any underlying assumptions about the distribution of data

2 Decision tree- Decision tree is the most powerful and popular tool for classification and prediction. A Decision tree is a flowchart like tree structure, where each internal node denotes a test on an attribute, each branch represents an outcome of the test, and each leaf node (terminal node) holds a class label. Decision trees classify instances by sorting them down the tree from the root to some leaf node, which provides the classification of the instance. An instance is classified by starting at the root node of the tree,testing the attribute specified by this node,then moving down the tree branch corresponding to the value of the attribute as shown in the above figure.This process is then repeated for the subtree rooted at the new node.  Decision trees are able to generate understandable rules.  Decision trees perform classification without requiring much computation.  Decision trees are able to handle both continuous and categorical variables.  Decision trees provide a clear indication of which fields are most important for prediction or classification.

1. 



   

How MPEG standard is different from JPEG also draw and explain the block diagram of MPEG encoder? How the quality can be achieved using both the standards? JPEG is mainly used for image compression.JPEG stands for Joint Photographic Expert Group.The file name for a JPEG image is .jpg or .jpeg.JPEG is the most commonly used format for photographs. It is specifically good for color photographs or for images with many blends or gradients. However, it is not the best with sharp edges and might lead to a little blurring.JPEG is a method of lossy compression for digital photography.An advantage to using the JPEG format is that due to compression, a JPEG image will take up a few MB of data.Due to the popularity of JPG, it is also accepted in most if not in all programs. It is quite popular for web hosting of images, for amateur and average photographers, digital cameras, etc. MPEG, stands for the Moving Picture Experts Group. It is a working group of experts that was formed in 1988 by ISO and IEC.The aim of MPEG was to set standards for audio and video compression and transmission.The standards as set by MPEG consist of different Parts. Each part covers a certain aspect of the whole specification. MPEG has standardized the following compression formats and ancillary standards:

MPEG-1 : Coding of moving pictures and associated audio for digital storage media MPEG-2 : Generic coding of moving pictures and associated audio information (ISO/IEC 13818). MPEG-3: dealt with standardizing scalable and multi-resolution compression and was intended for HDTV compression but was found to be redundant and was merged with MPEG-2. MPEG-4 : Coding of audio-visual objects. It includes the MPEG-4 Part 14 (MP4) Encoder mpeg

2.

The table below shows different symbols with their corresponding occurring probabilities. Symbol a b c d e f g

Probability 0.05 0.2 0.1 0.05 0.3 0.2 0.1

Create a Huffman tree and Huffman table for the above table. The table should show the code word for each symbol and the corresponding code-word length.

Module-5 1.

How do you classify objects while performing object recognition? State and prove Baye’s theorem as applied to pattern recognition? Discuss in detail. Object recognition is a computer vision technique for identifying objects in images or videos. Object recognition is a key output of deep learning and machine learning algorithms. When humans look at a photograph or watch a video, we can readily spot people, objects, scenes, and visual details.

The Bayes theorem describes the probability of an event based on the prior knowledge of the conditions that

might be related to the event. If we know the conditional probability

find out the reverse probabilities

.

How can we do that?

The above statement is the general representation of the Bayes rule. We can generalize the formula further. If multiple events Ai form an exhaustive set with another event B. We can write the equation as

, we can use the bayes rule to

2. Explain the following concepts with an example of each – Feature Vector - A vector is a series of numbers. It is like a matrix with only one row but multiple columns (or only one column but multiple rows). An example is: [1,2,3,5,6,3,2,0]. A feature vector is just a vector that contains information describing an object's important characteristics. In image processing, features can take many forms. A simple feature representation of an image is the raw intensity value of each pixel. However, more complicated feature representations are also possible. For facial expression analysis, mostly SIFT descriptor features (scale invariant feature transform). These features capture the prevalence of different line orientations.

example of color image, color of an object is also represented as one the feature. then it can be represented as f=[r,g,b] where r, g, b are corresponding values of pixel in three different planes which represents the color feature of the particular pixel. Likewise collection of other features that may be related with texture, object etc considered as feature vector. Random variables A random variable, usually written X, is a variable whose possible values are numerical outcomes of a random phenomenon. There are two types of random variables, discrete and continuous. A discrete random variable is one which may take on only a countable number of distinct values such as 0,1,2,3,4,........ Discrete random variables are usually (but not necessarily) counts. If a random variable can take only a finite number of distinct values, then it must be discrete. Examples of discrete random variables include the number of children in a family, the Friday night attendance at a cinema, the number of patients in a doctor's surgery, the number of defective light bulbs in a box of ten. A continuous random variable is one which takes an infinite number of possible values. Continuous random variables are usually measurements. Examples include height, weight, the amount of sugar in an orange, the time required to run a mile. Conditional probability - The conditional probability of an event B is the probability that the event will occur given the knowledge that an event A has already occurred. This probability is written P(B|A), notation for the probability of B given A. In the case where events A and B are independent (where event A has no effect on the probability of event B), the conditional probability of event B given event A is simply the probability of event B, that is P(B)If events A and B are not independent, then the probability of the intersection of A and B (the probability that both events occur) is defined by P(A and B) = P(A)P(B|A). the conditional probability P(B|A) is easily obtained by dividing by P(A):

Image Analysis- Image analysis is a technique often used to obtain quantitative data from tissue samples using analysis software that segments pixels in a digital image based on features such as color (i.e., RGB), density, or texture. A limitation of image analysis is that it often requires assumptions to be made and only provides measurements of relative changes to the object(s) of interest in tissues. Even with its recognized limitations, image analysis is a powerful tool when used correctly to obtain quantitative data. image analysis is a major research and development task. Without model-based techniques that make the segmentation as robust, reproducible, and efficient as possible, the interactive visualization described in the following would not be possible in routine clinical practice. Voice Analysis- Voice Analysis is a voice biometrics program used for law enforcement and criminal identification. It analyzes audio evidence accurately by applying voice biometrics technology in a way that makes it easier to work with audio evidence. It assists forensics experts and security organizations complete voice treatment and speaker identification processes accurately. With the straightforward identification it

provides, Forensic Voice Analysis contributes to criminal investigation and prosecution of suspects. It involves the following-Gender detection, format verification,speaker identification , speech silence detection and likelihood ratio calculation. Pattern Classes- a pattern is an arrangement of descriptors(or features). A pattern class is a family of patterns that share some common properties . pattern classes are denoted w1,w2,…..wn where n is the number of classes . pattern recognition by machine involves techniques for assigning patterns to their respective classes automatically and with as littlehuman intervention possible . pattern recognition consists of two steps1. Feature selection (extraction) 2. Matching(classification) 3. Explain all the real world applications of pattern recognition and also write how one can identify facial expressions using image analysis approaches? Applications –  Image processing, segmentation and analysis Pattern recognition is used to give human recognition intelligence to machine which is required in image processing.  Computer vision Pattern recognition is used to extract meaningful features from given image/video samples and is used in computer vision for various applications like biological and biomedical imaging.  Seismic analysis Pattern recognition approach is used for the discovery, imaging and interpretation of temporal patterns in seismic array recordings. Statistical pattern recognition is implemented and used in different types of seismic analysis models.  Radar signal classification/analysis Pattern recognition and Signal processing methods are used in various applications of radar signal classifications like AP mine detection and identification.  Speech recognition The greatest success in speech recognition has been obtained using pattern recognition paradigms. It is used in various algorithms of speech recognition which tries to avoid the problems of using a phoneme level of description and treats larger units such as words as pattern  Finger print identification The fingerprint recognition technique is a dominant technology in the biometric market. A number of recognition methods have been used to perform fingerprint matching out of which pattern recognition approaches is widely used. facial expressions using image analysis approaches1.convert vedio into frames. 2.read the input vedio frame image . 3.convert the image into gray scale image 4.enhance the input image with median , wiener and gaussian filters. 5.Find the best filter based PSNR, RMSE values . 6.Apply viola -jones algorithm to detect the face region . 7.Use bounding box method and crop the face region . 8.Use threshold value to extract nnon skin regions 9.Apply morphological operations to extract continuous boundaries of non skin region . 10.Mask the boundary from the original image 11.Extract the mouth region 12.Area is calculated from mouth region 13.Recognize facial emotions based on the value of area .

4.

“Suppose you have recorded voices of 10 peoples. Now your job is to identify the voice of a particular person among those individuals”. Write all the steps you would perform for identifying those voice samples?



The first stage of the speech recognition process is preprocessing. In order for any speech recognition system to operate at a reasonable speed, the amount of data used as input must be kept to a minimum. The inherent challenge in this is to remove the "bad" data, such as noise, without losing or distorting the critical data needed to identify what has been said. Two of the more common ways of reducing this data are sampling, where "snapshots" of the data are taken at regular time intervals, and filtering, where only data in a certain frequency range is kept. These analog samples are then converted to digital form. Most approaches group the samples into small time intervals called frames. The preprocessor then extracts acoustic patterns from each frame, as well as the changes that occur between frames. This process is called spectral analysis because it focuses on individual frequency elements (Markowitz). Once preprocessing is completed, the input data moves to the recognition stage, where the primary work involved in speech recognition is accomplished. There are two main approaches to attacking the speech recognition problem: a knowledge-based approach and a data-based approach. In the knowledge-based approach, the goal is to express what people know about speech in terms of specific rules (whether they are phonetic, syntactic, or some other type) that can then be used to analyze the input. The two main problems with this approach are the depth of linguistic knowledge and the large amount of manual labor needed to establish a fast, accurate system. As a result, the data-based approaches are the dominant technique used in commercial speech recognition products on the market today Data-based approaches become more accurate as they encounter more data; that is, the data encountered gradually improves the models used to analyze the data .Hidden Markov Models are an example of a data-based approach to speech recognition. For the speech recognition equipment, although it cannot determine with certainty what words occurred earlier in the input signal it received, it can use its feature information to determine which words had the greatest probability of occurring. The final stage in the speech recognition process is the communication stage. In this stage, the software system acts upon the voice input it has received and translated. Applications of speech recognition systems are usually grouped into four categories: Command-and-Control, Data Entry, Data Access/Information Retrieval, and Dictation





  

5.

Explain the concept of morphology and discuss all the morphological algorithms used in digital image processing, take suitable example to justify your answer?

Morphology -Identification, analysis, and description of the structure of the smallest unit of words .it is Theory and technique for the analysis and processing of geometric structures – Based on set theory, lattice theory, topology, and random functions – Extract image components useful in the representation and description of region shape such as boundaries, skeletons, and convex hull – Input in the form of images, output in the form of attributes extracted from those images – Attempt to extract the meaning of the images 1. Erosion and dilation∗ Erosion shrinks or thins objects in a binary image .Morphological filter in which image details smaller than the se are filtered/removed from the image Dilation –Grows or thickens objects in a binary image. Bridging gaps in broken characters. Lowpass filtering produces a grayscale image; morphological operation produces a binary image 2.

Opening and closing -- Opening smoothes the contours of an object, breaks narrow isthmuses, and eliminates thin protrusions --Closing smoothes sections of contours, fusing narrow breaks and long thin gulfs, eliminates small holes, and fills gaps in the contour (B)z ⊆ A} – Union of all translates of B that fit into A 3. Hit -or- mis transformation - Basic tool for shape detection in a binary image – Uses the morphological erosion operator and a pair of disjoint set – First set fits in the foreground of input image; second set misses it completely – The pair of two set is called composite structuring element

the morphological algorithms used in digital image processing, 1 Boundary extraction – extracting the boundary of an object is often useful . Boundary of a set A –∗ Denoted by β(A) ∗ Extracted by eroding A by a suitable set B and computing set difference between A and its erosion β(A) = A − (A B) Using a larger set will yield a thicker boundary 2 Hole filling –  Hole -Background region surrounded by a connected border of foreground pixels.  Algorithm based on set dilation, complementation, and intersection  Let A be a set whose elements are 8-connected boundaries, each boundary enclosing a background (hole)  Given a point in each hole, we want to fill all holes  Start by forming an array X0 of 0s of the same size as A - The locations in X0 corresponding to the given point in each hole are set to 1 

let B be a symmetric se with 4-connected neighbors to the origin 01 0 111 010  Compute Xk = (Xk−1 ⊕ B) ∩ Ac k = 1, 2, 3, . . .  Algorithm terminates at iteration step k if Xk = Xk−1  Xk contains all the filled holes – Xk ∪ A contains all the filled holes and their boundaries  The intersection with Ac at each step limits the result to inside the roi ∗ Also called conditioned dilation 3 Extraction of connected components – Let A be a set containing one or more connected components – Form an array X0 of the same size as A .All elements of X0 are 0 except for one point in each connected component set to 1 – Select a suitable se B, possibly an 8-connected neighborhood as 111 111

111 – Start with X0 and find all connected components using the iterative procedure Xk = (Xk−1 ⊕ B) ∩ A k = 1, 2, 3, . . . – Procedure terminates when Xk = Xk−1; Xk contains all the connected components in the input image – The only difference from the hole-filling algorithm is the intersection with A instead of Ac . This is because here, we are searching for foreground points while in hole filling, we looked for background points (holes)

4Convex hull – Convex set A - Straight line segment joining any two points in A lies entirely within A – Convex hull H of an arbitrary set of points S is the smallest convex set containing S – Set difference H − S is called the convex deficiency of S – Convex hull and convex deficiency are useful to describe objects – Algorithm to compute convex hull C(A) of a set A . Let Bi , i = 1, 2, 3, 4 represent the four structuring elements in the figure · Bi is a clockwise rotation of Bi−1 by 90◦ . Implement the equation Xi k = (Xk−1 ~ B i ) ∪ A i = 1, 2, 3, 4 and k = 1, 2, 3, . . . with Xi 0 = A . Apply hit-or-miss with B1 till Xk == Xk−1, then, with B2 over original A, B3 , and B4 . Procedure converges when Xi k = Xi k−1 and we let Di = Xi k . Convex hull of A is given by C(A) = [ 4 i=1 Di Convex hull can grow beyond the minimum dimensions required to guarantee convexity. May be fixed by limiting growth to not extend past the bounding box for the original set of points . 5 Thinning – Transformation of a digital image into a simple topologically equivalent image .Remove selected foreground pixels from binary images . Used to tidy up the output of edge detectors by reducing all lines to single pixel thickness – Thinning of a set A by se B is denoted by A ⊗ B – Defined in terms of hit-or-miss transform as A ⊗ B = A − (A ~ B) = A ∩ (A ~ B) c – Only need to do pattern matching with set; no background operation required in hit-or-miss transform – A more useful expression for thinning A symmetrically based on a sequence of set {B} = {B 1 , B2 , . . . , Bn } where Bi is a rotated version of Bi−1 – Define thinning by a sequence of set as A ⊗ {B} = ((. . .((A ⊗ B 1 ) ⊗ B 2 ). . .) ⊗ B n ) – Iterate over the procedure till convergence 6Thickening – Morphological dual of thinning defined by A B = A ∪ (A ~ B) – set complements of those used for thinning – Thickening can also be defined as a sequentialoperation A{B}=((...((AB1)B2)...) B n ) Usual practice to thin the background and take the complement .May result in disconnected points . Post-process to remove the disconnected points 7 Skeletons – Skeleton S(A) of a set A .Deductions 1. If z is a point of S(A) and (D)z is the largest disk centered at z and contained in A, one cannot find a larger disk (not necessarily centered at z) containing (D)z and included in A; (D)z is called a maximum disk 2. Disk (D)z touches the boundary of A at two or more different places – Skeleton can be expressed in terms of erosions and openings S(A) = [ K k=0 Sk(A) where Sk(A) = (A kB) −(A kB) ◦ B _--8A kB indicates k successive erosions of A (A kB) = ((. . .((A B) B) . . .) B) . K is the last iterative step before A erodes to an empty set K = max{k | (A kB) 6= ∅} . S(A) can be obtained as the union of skeleton subsets Sk(A) . A can be reconstructed from the subsets using the equation [ K k=0 (Sk(A) ⊕ kB) where (Sk(A) ⊕ kB) denotes k successive dilations of Sk(A) (Sk(A) ⊕ kB) = ((. . .((Sk(A) ⊕ B) ⊕ B) ⊕ . . .) ⊕ B) 8Pruning – Complement to thinning and sketonizing algorithms to remove unwanted parasitic components – Automatic recognition of hand-printed characters .Analyze the shape of the skeleton of each character . Skeletons characterized by “spurs” or parasitic components . Spurs caused during erosion by non-uniformities in the strokes .Assume that the length of a spur does not exceed a specific number of pixels – Skeleton of hand-printed “a” .Suppress a parasitic branch by successively eliminating its end point ∗ Assumption: Any branch with ≤ 3 pixels will be removed .Achieved with thinning of an input set A with a sequence of ses designed to detect only end points X1 = A ⊗ {B}

– Result of applying the above thinning three times . Restore the character to its original form with the parasitic branches removed . Form a set X2 containing all end points in X1 X2 = [ 8 k=1 (X1 ~ B k ).Dilate end points three times using set A as delimiter X3 = (X2 ⊕ H) ∩ A where H is a 3 × 3 se of 1s and intersection with A is applied after each step .The final result comes from X4 = X1 ∪ X3