Two Image-Template Operations for Binary Image Processing. Hongchi Shi. Department of Computer Engineering and Computer Science

Size: px
Start display at page:

Download "Two Image-Template Operations for Binary Image Processing. Hongchi Shi. Department of Computer Engineering and Computer Science"

Transcription

1 Two Image-Template Operations for Binary Image Processing Hongchi Shi Department of Computer Engineering and Computer Science Engineering Building West, Room 331 University of Missouri - Columbia Columbia, MO Phone: (573) Fax: (573) shi@ece.missouri.edu 1

2 Two Image-Template Operations for Binary Image Processing HONGCHI SHI Department of Computer Engineering and Computer Science, University of Missouri - Columbia, Columbia, MO Abstract This paper presents two new image algebra image-template operations match and mismatch derived from the general image-template product. These image algebra operations extend the binary morphological erosion and dilation operations and can be used to express elegantly most of binary image processing algorithms in a more natural way than binary morphological operations from the image processing viewpoint. In addition, the match and mismatch operations are easy to implement eciently on SIMD bit-serial parallel computers. Keywords image algebra, mathematical morphology, binary image processing 1. Introduction Binary image processing involves manipulating binary images consisting of only 1-pixels and 0-pixels. Binary image processing techniques are employed by binary machine vision systems in the detection and recognition of objects or object defects [3]. Binary morphology is an algebraic system concerning with analysis of shapes. It plays an important role in machine vision, since shape is a prime carrier of information in machine vision [3]. Binary morphology can be used to enhance binary images by removing noise, decompose objects, extract object features, and identify objects in binary images [1, 10, 4]. Binary mathematical morphology is based on the set theory. The set of all the 1-pixels in a binary image gives a complete description of the binary image. The primary morphological operations are dilation and erosion. All other morphological operations such as opening, closing, and hit-and-miss operations are based on these two operations. Since binary mathematical morphology primarily deals with sets, one has to consider binary images as sets, perform operations on sets, and convert sets back to images, when applying mor- 2

3 phological operations on images. Although this process is not complicated, it involves three steps conceptually. Besides, it can not consider both 1-pixels and 0-pixels at the same time. For example, the hit-and-miss operation needs two structuring elements, one for the 1-pixels and the other for the 0-pixels of the object. Another mathematical theory concerning image processing and analysis, image algebra, denes images as its primary operands and deals with images directly [9, 6]. Image algebra extends mathematical morphology and it can manipulate image transformations between dierent domains and transformations between dierent value sets which are ignored in morphology-based image algebras. This paper introduces two image algebra operations and demonstrates how they are used to express binary image processing algorithms in a more natural way for binary image processing. 2. Match and Mismatch Operations Image algebra is a heterogeneous algebra concerned with image processing and analysis. In image algebra, basic objects in image processing such as images, point sets, and templates are formally dened as its operands. Most of image processing and analysis algorithms can be concisely expressed using image algebra [8]. A complete description of image algebra can be found in Ritter's book [7]. Images in image algebra are dened in terms of two other types of elementary operands: value sets and point sets. Given a point set X and a value set F, an F-valued image a on X is a function a : X! F, which is usually expressed in terms of the graph of a by a = f(x; a(x)) : x 2 Xg; where a(x) 2 F. An element (x; a(x)) of a is a pixel. The set of all F-valued images on X is denoted by F X. In image algebra, the denition of a template unies and generalizes the usual concepts of templates, masks, windows, structuring elements, and neighborhood functions into one general mathematical entity. Templates are special types of images. An F-valued template from Y to X is an element of (F X ) Y. If t 2 (F X ) Y, then for notational convenience we dene t y t(y) in order to denote the image t y for each y 2 Y. The pixel values t y (x) of the image t y = f(x; t y (x)) : x 2 Xg 3

4 are the weights of the template t at the target point y. Let X R n. A template t 2 (F X ) X is a translation invariant template if and only if for x; y 2 X with x + z; y + z 2 X, where z 2 R n, we have t y (x) = t y+z (x + z). Translation invariant templates can be dened pictorially. Figure 1 shows a translation invariant template. Image algebra denes many operations between images and between images and templates. In terms of image processing, image-template operations that combine images and templates are the most powerful tools of image algebra. They combine images and templates by using appropriate binary operations. They may be used for transformations between dierent domains and transformations between dierent value sets. Suppose that F 1, F 2, and F are value sets. The operation : F 1 F 2! F is a binary operation and the operation : F F! F is an associative and commutative binary operation on F. If a 2 F X 1 and t 2 (F X 2 )Y, then the generalized product of a with t is the binary operation : F X (F X 1 2 )Y! F Y dened by a t = f(y; b(y)) : b(y) =? x2xa(x) t y (x); y 2 Yg: We may derive dierent image-template operations by substituting appropriate operations for and in the denition of the generalized image-template product. Ritter has dened the most commonly used image-template operations in image processing such as +, _2, ^2, _, and ^ [7]. Here, we derive two image-template operations mismatch and match for binary image processing. First, we dene two logic operations ~+ and ~+ 0. The operation ~+ is dened as the exclusive-or operation, i.e., a ~+b = 1 if and only if a and b are dierent. The operation ~+ 0 is dened as the complement of the exclusive-or operation, i.e., a ~+ 0 b = a ~+b. The mismatch operation ~_2 is obtained by substituting the logic or _ and the operation ~+ for and. Specically, a ~_2 t = f(y; b(y)) : b(y) = _ x2x a(x) ~+t y (x); y 2 Yg: The match operation ~^2 is obtained by substituting the logic and ^ and the operation ~+ 0 for and. Specically, a ~^2 t = f(y; b(y)) : b(y) = ^ x2x a(x) ~+ 0 t y (x); y 2 Yg: 4

5 Most of binary image processing algorithms require only translation invariant templates. Thus, a template for binary image processing usually can be dened by a conguration of the neighborhood of each target pixel. For example, the template t in Figure 1 species the conguration of the 3 3 neighborhood of each target pixel. Figure 1 goes here. For the mismatch operation, each target pixel in the result image obtains 1 if and only if the conguration of its neighborhood does not match the conguration given by the template. For the match operation, each target pixel gets 1 if and only if the conguration of its neighborhood matches the conguration given by the template. The match and mismatch operations are bit-serial operations. They usually use information from a small neighborhood of each pixel to check if it matches/mismatches the conguration specied by the template. They are perfectly suited for implementation on bit-serial SIMD meshconnected computers such as Lockheed-Martin's CISP computer [11]. 3. Binary Image Processing Using Match and Mismatch Haralick and Shapiro present many applications of binary morphological operations such as erosion, dilation, and hit-and-miss to binary image processing [3]. The two basic binary morphological operations erosion and dilation can be expressed using match and mismatch, respectively. The operations given by match and mismatch are more natural to image processing researchers. The useful morphological operation hit-and-miss can be expressed using match with a single template specifying the foreground (1-pixels) and background (0-pixels) of the object to be matched Erosion and Dilation In morphology, the erosion of a set A E N by another set B E N, denoted by A B, is dened by A B = fy 2 E N : y + x B 2 A; 8x B 2 Bg: 5

6 This can also be expressed as follows: A B = fy 2 E N : B y Ag; where B y is the set of elements of B translated by y. The dilation of a set A E N by another set B E N, denoted by A B, is dened by A B = fz 2 E N : y = x A + x B ; 9x A 2 A and 9x B 2 Bg: This can also be represented as follows: A B = fy 2 E N : x A 2 By ; 9x A 2 Ag; where B = fx :?x 2 Bg. For binary image processing, the set A corresponds to a source binary image a with a(x) = 1 if and only if x 2 A, while the set B corresponds to a template t. To achieve the erosion eect, the template is dened by t y (x) = 1 if x 2 B y. To achieve the dilation eect, the template t is dened by t y (x) = 0 if x 2 B y. For example, if the structuring element B is as shown in Figure 2(a), the corresponding erosion template is t 1 shown in Figure 2(b) and the dilation template is t 2 shown in Figure 2(c). Figure 2 goes here. The match operation implements exactly the morphological erosion operation. Let c = a ~^2 t. By the denition of the match operation, c(y) = V x2by a(x) ~+ 0 t y (x), which means c(y) = 1 if and only if all the elements in B y are in A. The mismatch operation implements exactly the morphological dilation operation. Let c = a ~_2 t. By the denition of the mismatch operation, c(y) = W x2 By a(x) ~+t y (x), which means c(y) = 1 if and only if some element of A is in B y. When we use the match and mismatch operations for binary image processing, we work on images directly and design templates specifying what kind of conguration of the neighborhood to match or to avoid, which is more natural. 6

7 3.2. Hit-and-Miss The structuring elements in morphological operations can only specify one kind of pixels either 1-pixels or 0-pixels. The match and mismatch operations extend the morphological erosion and dilation operations by allowing the neighborhood to contain 1-pixels and 0-pixels, making some image processing algorithms more natural and concise. The hit-and-miss transformation is a useful operation for selecting pixels that satisfy certain geometric properties [3]. It is represented in morphology using two structuring elements, one for the object to be hit and the other for the object to be missed. Let J and K be two structuring elements that satisfy T J K = ;. The hit-and-miss transformation of set A by (J; K), denoted by A (J; K), is dened by \ A (J; K) = (A J) (A c K); where A c is the complement of A. When applied to binary image processing, the hit-and-miss operation gives a pixel value 1 if and only if the pixel's neighborhood of 1's specied by J matches J and its neighborhood of 0's specied by K matches K. Let a be the binary image corresponding to set A. Dene a template t by t y (x) = 1 if x 2 J y and t y (x) = 0 if x 2 K y. The match operation a ~^2 t performs the hit-and-miss operation with one template specifying the conguration of the neighborhood to be matched. We give three examples to show the match operation gives more natural expression of some binary image processing algorithms. Finding 8-isolated pixels An 8-isolated pixel is a 1-pixel with its eight 8-neighbors all 0 as shown in Figure 3. Figure 3 goes here. To identify all 8-isolated pixels of an image using the hit-and-miss transform, we need to design two structuring elements J = f(0; 0)g shown in Figure 4(a) and K = f(0; 1); (0;?1); (1; 0); (?1; 0)g shown in Figure 4(b). Using the match operation, we just need to dene a template as shown in Figure 4(c). The conguration given by the template directly reects the denition of 8-isolated 7

8 pixels. Figure 4 goes here. Identifying upper right-hand corner pixels An upper right-hand corner pixel can be dened as a 1-pixel whose south and west neighbors are 1-pixels and whose north, northeast, and east neighbors are 0-pixels as shown in Figure 5. Figure 5 goes here. To identify upper right-hand corner pixels using hit-and-miss, we have to dene two structuring elements J and K as shown in Figure 6. The structuring element J species the object to be hit and K species the object that has to be missed. Using the match operation, we need to derive only one template directly from the denition of upper right-hand corner pixels. The template is dened as shown in Figure 6(c). Figure 6 goes here. Pattern matching In binary image processing, a pattern to be matched in a binary image can be dened as a smaller binary image. Figure 7 gives a pattern of a diamond with side length 3. A pixel at x in the source image is said to match the pattern exactly if the pattern image translated by x matches the subimage at x in the source image. 8

9 Figure 7 goes here. Using the morphological hit-and-miss operation for pattern matching, we have to design two structuring elements J and K, one for the 1-pixels and the other for the 0-pixels of the pattern. To perform pattern matching using the match operation, we only need a template t which can be derived directly from the pattern to be matched. The structuring elements and the template for matching the pattern dened in Figure 7 are shown in Figure 8. Figure 8 goes here. Pattern matching with tolerance can be done by leaving some 1's out in the template conguration. For example, to match diamond-like patterns with side lengths from 2 to 3 using the match operation, we can dene a template as shown in Figure 9. Figure 9 goes here Computing Binary Image Topological Properties We further demonstrate the applicability of the match and mismatch operations by describing two more binary image processing algorithms using these operations. The algorithms given here compute some topological properties of binary images. We only consider 8-connected components. That is, we use 8-connectivity for 1-pixels and 4-connectivity for 0-pixels. Shrinking and Counting Components Levialdi gives an algorithm that counts the components in a binary image by shrinking the components into isolated pixels [5]. The basic idea is to shrink each component to an isolated pixel 9

10 at one corner of its bounding rectangle and then count the isolated pixels. The bounding rectangle of a component is the smallest upright rectangle containing all the 1-pixels of the component. The shrinking process preserves the component connectivity. Let a 2 f0; 1g X denote the source image, where X is an n n point set. The shrink operator ' that shrinks components toward the upper left corners of their bounding rectangles can be dened in terms of the congurations of the 2 2 neighborhood as shown in Figure 10. Figure 10 goes here. The operator ' assigns a value to each pixel as follows: If the pixel's neighborhood has the conguration shown in Figure 11(a), it is assigned 0; If its neighborhood has the conguration shown in Figure 11(b), it is assigned 1; Otherwise, it keeps its old value. Figure 11 goes here. Dening two templates t 1 and t 2 shown in Figure 12, the operator ' can be expressed using the match and mismatch operations as follows. Let a = '(a), the image resulted from applying ' to a. Then, a = a ^ (a ~_2 t 1 ) _ (a ~^2 t 2 ): To count components in a binary image, we apply the shrink operator repeatedly. After each iteration, we use a match operation with the template t dened in Figure 4. Let a 0 be the source binary image and c 0 = P a 0 ~^2 t, the number of isolated pixels in the source image. Dene a k+1 = a k ^ (a k ~_2 t 1 ) _ (a k ~^2 t 2 ) 10

11 and c k+1 = c k + X a k+1 ~^2 t: The number of components in a 0 is given by c K, where K is the smallest integer for which a K = 0. Figure 12 goes here. Computing Binary Image Euler Number Euler number is a topological descriptor for binary images. It is useful in image processing because the topological counts in an image are of intrinsic interest in characterizing and recognizing the image. The Euler number of a binary image is dened to be the number of connected components minus the number of holes inside the connected components. Gray studied computation of Euler numbers using local information [2]. Given a direction, let X denote a -facing convexity and V denote a -facing concavity as shown in Figure 13. Gray proved that E = #(X ) + #(V ); where #(X ) is the number of -facing convexities and #(V ) is the number of -facing concavities. Choosing to point to the northwest direction, we have an X only if we have the conguration shown in Figure 14(a). A V can only arise from the conguration shown in Figure 14(b). Figure 13 goes here. Figure 14 goes here. 11

12 Thus, we can design two templates t 1 and t 2 as shown in Figure 15 and compute the Euler number of a binary image a as follows: E = X a ~^2 t 1? X a ~^2 t 2 : Figure 15 goes here. 4. Conclusion We have derived two image algebra image-template operations match and mismatch. They extend the binary morphological erosion and dilation operations. We have demonstrated how to design templates directly from binary image processing problems. When applied to binary image processing, the match and mismatch operations give more natural algorithms. Acknowledgements The author wishes to thank Dr. Gerhard Ritter and Dr. Joseph Wilson for their advice on this work. The author also wishes to thank Dr. Patrick Coeld of Wright Laboratory, Eglin AFB, for his continued support of this research. References [1] T. R. Crimmins and W. R. Brown. Image algebra and automatic shape recognition. IEEE Transactions on Aerospace and Electronic Systems, 21:60{69, [2] S. B. Gray. Local properties of binary images in two dimensions. IEEE Transactions on Computers, 20(5):551{561, May

13 [3] R. M. Haralick and L. G. Shapiro. Computer and Robot Vision, volume 1. Addison-Wesley, Reading, MA, [4] R. M. Haralick, S. R. Sternberg, and X. Zhuang. Image analysis using mathematical morphology. IEEE Transactions on Pattern Analysis and Machine Intelligence, 9:523{550, [5] S. Levialdi. On shrinking binary picture patterns. Communications of the ACM, 15:7{10, [6] G. X. Ritter. Recent developments in image algebra. In P. Hawkes, editor, Advances in Electronics and Electron Physics, 80, pages 243{308. Academic Press, New York, NY, [7] G. X. Ritter. Image algebra, in preparation. [8] G. X. Ritter and J. N. Wilson. Handbook of Computer Vision Algorithms in Image Algebra. CRC Press, [9] G. X. Ritter, J. N. Wilson, and J. L. Davidson. Image algebra: An overview. Computer Vision, Graphics, and Image Processing, 49(3):297{331, March [10] J. Serra. An introduction to mathematical morphology. Computer Vision, Graphics, and Image Processing, 35:283{305, [11] M. S. Tomassi and R. D. Jackson. An evolving SIMD architecture approach for a changing image processing environment. DSP & Multimedia Technology, pages 1{7, October

14 t = Figure 1: Template t specifying a 3 3 neighborhood conguration 14

15 t = t 2 = (a) (b) (c) Figure 2: A structuring element and its corresponding templates 15

16 Figure 3: An 8-isolated pixel in the center 16

17 J K t = (a) (b) (c) Figure 4: Structuring elements and template for nding 8-isolated pixels 17

18 Figure 5: An upper right-hand corner pixel in the center 18

19 J K 0 0 t = (a) (b) (c) Figure 6: Structuring elements and template for identifying upper right-hand corner pixels 19

20 Figure 7: A pattern image 20

21 J K (a) (b) t = (c) Figure 8: Structuring elements and template for pattern matching 21

22 t = Figure 9: Template for pattern matching with tolerance 22

23 Figure 10: Neighborhood for the Levialdi shrinking operator ' 23

24 (a) (b) Figure 11: Neighborhood congurations for the Levialdi shrinking operator ' 24

25 t 1 = 0 t 2 = Figure 12: Templates for the Levialdi shrinking operator ' 25

26 V θ X V θ θ V θ X θ X θ θ Figure 13: -facing convexities and concavities 26

27 (a) * (b) Figure 14: Congurations for convexity and concavity, where is 0 or 1 27

28 t 1 = 1 0 t 2 = Figure 15: Templates derived from the congurations for convexity and concavity 28

Document Image Restoration Using Binary Morphological Filters. Jisheng Liang, Robert M. Haralick. Seattle, Washington Ihsin T.

Document Image Restoration Using Binary Morphological Filters. Jisheng Liang, Robert M. Haralick. Seattle, Washington Ihsin T. Document Image Restoration Using Binary Morphological Filters Jisheng Liang, Robert M. Haralick University of Washington, Department of Electrical Engineering Seattle, Washington 98195 Ihsin T. Phillips

More information

morphology on binary images

morphology on binary images morphology on binary images Ole-Johan Skrede 10.05.2017 INF2310 - Digital Image Processing Department of Informatics The Faculty of Mathematics and Natural Sciences University of Oslo After original slides

More information

Morphological Image Processing

Morphological Image Processing Morphological Image Processing Ranga Rodrigo October 9, 29 Outline Contents Preliminaries 2 Dilation and Erosion 3 2. Dilation.............................................. 3 2.2 Erosion..............................................

More information

Introduction. Computer Vision & Digital Image Processing. Preview. Basic Concepts from Set Theory

Introduction. Computer Vision & Digital Image Processing. Preview. Basic Concepts from Set Theory Introduction Computer Vision & Digital Image Processing Morphological Image Processing I Morphology a branch of biology concerned with the form and structure of plants and animals Mathematical morphology

More information

Mathematical morphology... M.1 Introduction... M.1 Dilation... M.3 Erosion... M.3 Closing... M.4 Opening... M.5 Summary... M.6

Mathematical morphology... M.1 Introduction... M.1 Dilation... M.3 Erosion... M.3 Closing... M.4 Opening... M.5 Summary... M.6 Chapter M Misc. Contents Mathematical morphology.............................................. M.1 Introduction................................................... M.1 Dilation.....................................................

More information

Morphological Image Processing

Morphological Image Processing Morphological Image Processing Morphology Identification, analysis, and description of the structure of the smallest unit of words Theory and technique for the analysis and processing of geometric structures

More information

Morphological Image Processing

Morphological Image Processing Morphological Image Processing Binary image processing In binary images, we conventionally take background as black (0) and foreground objects as white (1 or 255) Morphology Figure 4.1 objects on a conveyor

More information

APPLICATION OF FLOYD-WARSHALL LABELLING TECHNIQUE: IDENTIFICATION OF CONNECTED PIXEL COMPONENTS IN BINARY IMAGE. Hyunkyung Shin and Joong Sang Shin

APPLICATION OF FLOYD-WARSHALL LABELLING TECHNIQUE: IDENTIFICATION OF CONNECTED PIXEL COMPONENTS IN BINARY IMAGE. Hyunkyung Shin and Joong Sang Shin Kangweon-Kyungki Math. Jour. 14 (2006), No. 1, pp. 47 55 APPLICATION OF FLOYD-WARSHALL LABELLING TECHNIQUE: IDENTIFICATION OF CONNECTED PIXEL COMPONENTS IN BINARY IMAGE Hyunkyung Shin and Joong Sang Shin

More information

Biomedical Image Analysis. Mathematical Morphology

Biomedical Image Analysis. Mathematical Morphology Biomedical Image Analysis Mathematical Morphology Contents: Foundation of Mathematical Morphology Structuring Elements Applications BMIA 15 V. Roth & P. Cattin 265 Foundations of Mathematical Morphology

More information

EECS490: Digital Image Processing. Lecture #17

EECS490: Digital Image Processing. Lecture #17 Lecture #17 Morphology & set operations on images Structuring elements Erosion and dilation Opening and closing Morphological image processing, boundary extraction, region filling Connectivity: convex

More information

Digital image processing

Digital image processing Digital image processing Morphological image analysis. Binary morphology operations Introduction The morphological transformations extract or modify the structure of the particles in an image. Such transformations

More information

EE 584 MACHINE VISION

EE 584 MACHINE VISION EE 584 MACHINE VISION Binary Images Analysis Geometrical & Topological Properties Connectedness Binary Algorithms Morphology Binary Images Binary (two-valued; black/white) images gives better efficiency

More information

COMPUTER AND ROBOT VISION

COMPUTER AND ROBOT VISION VOLUME COMPUTER AND ROBOT VISION Robert M. Haralick University of Washington Linda G. Shapiro University of Washington A^ ADDISON-WESLEY PUBLISHING COMPANY Reading, Massachusetts Menlo Park, California

More information

Mathematical Morphology and Distance Transforms. Robin Strand

Mathematical Morphology and Distance Transforms. Robin Strand Mathematical Morphology and Distance Transforms Robin Strand robin.strand@it.uu.se Morphology Form and structure Mathematical framework used for: Pre-processing Noise filtering, shape simplification,...

More information

CS443: Digital Imaging and Multimedia Binary Image Analysis. Spring 2008 Ahmed Elgammal Dept. of Computer Science Rutgers University

CS443: Digital Imaging and Multimedia Binary Image Analysis. Spring 2008 Ahmed Elgammal Dept. of Computer Science Rutgers University CS443: Digital Imaging and Multimedia Binary Image Analysis Spring 2008 Ahmed Elgammal Dept. of Computer Science Rutgers University Outlines A Simple Machine Vision System Image segmentation by thresholding

More information

Practical Image and Video Processing Using MATLAB

Practical Image and Video Processing Using MATLAB Practical Image and Video Processing Using MATLAB Chapter 18 Feature extraction and representation What will we learn? What is feature extraction and why is it a critical step in most computer vision and

More information

Renyan Ge and David A. Clausi

Renyan Ge and David A. Clausi MORPHOLOGICAL SKELETON ALGORITHM FOR PDP PRODUCTION LINE INSPECTION Renyan Ge and David A. Clausi Systems Design Engineering University of Waterloo, 200 University Avenue West Waterloo, Ontario, Canada

More information

Morphological Image Processing

Morphological Image Processing Morphological Image Processing Binary dilation and erosion" Set-theoretic interpretation" Opening, closing, morphological edge detectors" Hit-miss filter" Morphological filters for gray-level images" Cascading

More information

Topic 6 Representation and Description

Topic 6 Representation and Description Topic 6 Representation and Description Background Segmentation divides the image into regions Each region should be represented and described in a form suitable for further processing/decision-making Representation

More information

Albert M. Vossepoel. Center for Image Processing

Albert M. Vossepoel.   Center for Image Processing Albert M. Vossepoel www.ph.tn.tudelft.nl/~albert scene image formation sensor pre-processing image enhancement image restoration texture filtering segmentation user analysis classification CBP course:

More information

CS534 Introduction to Computer Vision Binary Image Analysis. Ahmed Elgammal Dept. of Computer Science Rutgers University

CS534 Introduction to Computer Vision Binary Image Analysis. Ahmed Elgammal Dept. of Computer Science Rutgers University CS534 Introduction to Computer Vision Binary Image Analysis Ahmed Elgammal Dept. of Computer Science Rutgers University Outlines A Simple Machine Vision System Image segmentation by thresholding Digital

More information

Boundary descriptors. Representation REPRESENTATION & DESCRIPTION. Descriptors. Moore boundary tracking

Boundary descriptors. Representation REPRESENTATION & DESCRIPTION. Descriptors. Moore boundary tracking Representation REPRESENTATION & DESCRIPTION After image segmentation the resulting collection of regions is usually represented and described in a form suitable for higher level processing. Most important

More information

Processing of binary images

Processing of binary images Binary Image Processing Tuesday, 14/02/2017 ntonis rgyros e-mail: argyros@csd.uoc.gr 1 Today From gray level to binary images Processing of binary images Mathematical morphology 2 Computer Vision, Spring

More information

Fuzzy Soft Mathematical Morphology

Fuzzy Soft Mathematical Morphology Fuzzy Soft Mathematical Morphology. Gasteratos, I. ndreadis and Ph. Tsalides Laboratory of Electronics Section of Electronics and Information Systems Technology Department of Electrical and Computer Engineering

More information

Computer and Machine Vision

Computer and Machine Vision Computer and Machine Vision Lecture Week 10 Part-2 Skeletal Models and Face Detection March 21, 2014 Sam Siewert Outline of Week 10 Lab #4 Overview Lab #5 and #6 Extended Lab Overview SIFT and SURF High

More information

Extension and VLSI Implementation of the Majority-Gate Algorithm for Gray-Scale Morphological Operations

Extension and VLSI Implementation of the Majority-Gate Algorithm for Gray-Scale Morphological Operations Extension and VLSI Implementation of the Majority-Gate Algorithm for Gray-Scale Morphological Operations A Gasteratos, I Andreadis and Ph Tsalides Laboratory of Electronics Section of Electronics and Information

More information

RESEARCH ON OPTIMIZATION OF IMAGE USING SKELETONIZATION TECHNIQUE WITH ADVANCED ALGORITHM

RESEARCH ON OPTIMIZATION OF IMAGE USING SKELETONIZATION TECHNIQUE WITH ADVANCED ALGORITHM 881 RESEARCH ON OPTIMIZATION OF IMAGE USING SKELETONIZATION TECHNIQUE WITH ADVANCED ALGORITHM Sarita Jain 1 Sumit Rana 2 Department of CSE 1 Department of CSE 2 Geeta Engineering College 1, Panipat, India

More information

University of Groningen. Morphological design of Discrete-Time Cellular Neural Networks Brugge, Mark Harm ter

University of Groningen. Morphological design of Discrete-Time Cellular Neural Networks Brugge, Mark Harm ter University of Groningen Morphological design of Discrete-Time Cellular Neural Networks Brugge, Mark Harm ter IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you

More information

Machine vision. Summary # 5: Morphological operations

Machine vision. Summary # 5: Morphological operations 1 Machine vision Summary # 5: Mphological operations MORPHOLOGICAL OPERATIONS A real image has continuous intensity. It is quantized to obtain a digital image with a given number of gray levels. Different

More information

transformation must be reversed if vector is the final data type required. Unfortunately, precision and information are lost during the two transforma

transformation must be reversed if vector is the final data type required. Unfortunately, precision and information are lost during the two transforma Vector-based Mathematical Morphology Huayi Wu, Wenxiu Gao State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, 129 Luoyu Road, Wuhan, 430079, China

More information

v : erosion h : erosion H : dilation V : dilation s : erosion r : erosion R : dilation S : dilation

v : erosion h : erosion H : dilation V : dilation s : erosion r : erosion R : dilation S : dilation AUTOMATIC GENERATION OF DIRECTIONAL EROSION AND DILATION SEQUENCE BY GENETIC ALGORITHMS Ikushi Yoda Image Understanding Section Machine Understanding Division Electrotechnical Laboratory 1-1-4 Umezono,

More information

Binary Shape Characterization using Morphological Boundary Class Distribution Functions

Binary Shape Characterization using Morphological Boundary Class Distribution Functions Binary Shape Characterization using Morphological Boundary Class Distribution Functions Marcin Iwanowski Institute of Control and Industrial Electronics, Warsaw University of Technology, ul.koszykowa 75,

More information

Filters. Advanced and Special Topics: Filters. Filters

Filters. Advanced and Special Topics: Filters. Filters Filters Advanced and Special Topics: Filters Dr. Edmund Lam Department of Electrical and Electronic Engineering The University of Hong Kong ELEC4245: Digital Image Processing (Second Semester, 2016 17)

More information

Skeletonization Algorithm for Numeral Patterns

Skeletonization Algorithm for Numeral Patterns International Journal of Signal Processing, Image Processing and Pattern Recognition 63 Skeletonization Algorithm for Numeral Patterns Gupta Rakesh and Kaur Rajpreet Department. of CSE, SDDIET Barwala,

More information

However, m pq is just an approximation of M pq. As it was pointed out by Lin [2], more precise approximation can be obtained by exact integration of t

However, m pq is just an approximation of M pq. As it was pointed out by Lin [2], more precise approximation can be obtained by exact integration of t FAST CALCULATION OF GEOMETRIC MOMENTS OF BINARY IMAGES Jan Flusser Institute of Information Theory and Automation Academy of Sciences of the Czech Republic Pod vodarenskou vez 4, 82 08 Prague 8, Czech

More information

11/10/2011 small set, B, to probe the image under study for each SE, define origo & pixels in SE

11/10/2011 small set, B, to probe the image under study for each SE, define origo & pixels in SE Mathematical Morphology Sonka 13.1-13.6 Ida-Maria Sintorn ida@cb.uu.se Today s lecture SE, morphological transformations inary MM Gray-level MM Applications Geodesic transformations Morphology-form and

More information

09/11/2017. Morphological image processing. Morphological image processing. Morphological image processing. Morphological image processing (binary)

09/11/2017. Morphological image processing. Morphological image processing. Morphological image processing. Morphological image processing (binary) Towards image analysis Goal: Describe the contents of an image, distinguishing meaningful information from irrelevant one. Perform suitable transformations of images so as to make explicit particular shape

More information

2 ATTILA FAZEKAS The tracking model of the robot car The schematic picture of the robot car can be seen on Fig.1. Figure 1. The main controlling task

2 ATTILA FAZEKAS The tracking model of the robot car The schematic picture of the robot car can be seen on Fig.1. Figure 1. The main controlling task NEW OPTICAL TRACKING METHODS FOR ROBOT CARS Attila Fazekas Debrecen Abstract. In this paper new methods are proposed for intelligent optical tracking of robot cars the important tools of CIM (Computer

More information

Image Enhancement Using Fuzzy Morphology

Image Enhancement Using Fuzzy Morphology Image Enhancement Using Fuzzy Morphology Dillip Ranjan Nayak, Assistant Professor, Department of CSE, GCEK Bhwanipatna, Odissa, India Ashutosh Bhoi, Lecturer, Department of CSE, GCEK Bhawanipatna, Odissa,

More information

DEVELOPMENT OF A MATHEMATICAL MORPHOLOGY TOOL FOR EDUCATION PURPOSE

DEVELOPMENT OF A MATHEMATICAL MORPHOLOGY TOOL FOR EDUCATION PURPOSE 12 TH INTERNATIONAL CONFERENCE ON GEOMETRY AND GRAPHICS 2006 ISGG 6-10 AUGUST, 2006, SALVADOR, BRAZIL DEVELOPMENT OF A MATHEMATICAL MORPHOLOGY TOOL FOR EDUCATION PURPOSE César C. NUÑEZ and Aura CONCI Federal

More information

EECS490: Digital Image Processing. Lecture #23

EECS490: Digital Image Processing. Lecture #23 Lecture #23 Motion segmentation & motion tracking Boundary tracking Chain codes Minimum perimeter polygons Signatures Motion Segmentation P k Accumulative Difference Image Positive ADI Negative ADI (ADI)

More information

EE795: Computer Vision and Intelligent Systems

EE795: Computer Vision and Intelligent Systems EE795: Computer Vision and Intelligent Systems Spring 2012 TTh 17:30-18:45 WRI C225 Lecture 04 130131 http://www.ee.unlv.edu/~b1morris/ecg795/ 2 Outline Review Histogram Equalization Image Filtering Linear

More information

Morphological Image Processing

Morphological Image Processing Morphological Image Processing Introduction Morphology: a branch of biology that deals with the form and structure of animals and plants Morphological image processing is used to extract image components

More information

CLASSIFICATION OF BOUNDARY AND REGION SHAPES USING HU-MOMENT INVARIANTS

CLASSIFICATION OF BOUNDARY AND REGION SHAPES USING HU-MOMENT INVARIANTS CLASSIFICATION OF BOUNDARY AND REGION SHAPES USING HU-MOMENT INVARIANTS B.Vanajakshi Department of Electronics & Communications Engg. Assoc.prof. Sri Viveka Institute of Technology Vijayawada, India E-mail:

More information

Heap-on-Top Priority Queues. March Abstract. We introduce the heap-on-top (hot) priority queue data structure that combines the

Heap-on-Top Priority Queues. March Abstract. We introduce the heap-on-top (hot) priority queue data structure that combines the Heap-on-Top Priority Queues Boris V. Cherkassky Central Economics and Mathematics Institute Krasikova St. 32 117418, Moscow, Russia cher@cemi.msk.su Andrew V. Goldberg NEC Research Institute 4 Independence

More information

Testing a Set of Image Processing Operations for Completeness

Testing a Set of Image Processing Operations for Completeness Testing a Set of Image Processing Operations for Completeness Leonard Brown Le Gruenwald The University of Oklahoma School of Computer Science Norman, OK, 73019 lbrown@cs.ou.edu, gruenwal@cs.ou.edu Greg

More information

ELEN E4830 Digital Image Processing. Homework 6 Solution

ELEN E4830 Digital Image Processing. Homework 6 Solution ELEN E4830 Digital Image Processing Homework 6 Solution Chuxiang Li cxli@ee.columbia.edu Department of Electrical Engineering, Columbia University April 10, 2006 1 Edge Detection 1.1 Sobel Operator The

More information

MA651 Topology. Lecture 4. Topological spaces 2

MA651 Topology. Lecture 4. Topological spaces 2 MA651 Topology. Lecture 4. Topological spaces 2 This text is based on the following books: Linear Algebra and Analysis by Marc Zamansky Topology by James Dugundgji Fundamental concepts of topology by Peter

More information

What will we learn? What is mathematical morphology? What is mathematical morphology? Fundamental concepts and operations

What will we learn? What is mathematical morphology? What is mathematical morphology? Fundamental concepts and operations What will we learn? What is mathematical morphology and how is it used in image processing? Lecture Slides ME 4060 Machine Vision and Vision-based Control Chapter 13 Morphological image processing By Dr.

More information

ECEN 447 Digital Image Processing

ECEN 447 Digital Image Processing ECEN 447 Digital Image Processing Lecture 7: Mathematical Morphology Ulisses Braga-Neto ECE Department Texas A&M University Basics of Mathematical Morphology Mathematical Morphology (MM) is a discipline

More information

Topology Correction for Brain Atlas Segmentation using a Multiscale Algorithm

Topology Correction for Brain Atlas Segmentation using a Multiscale Algorithm Topology Correction for Brain Atlas Segmentation using a Multiscale Algorithm Lin Chen and Gudrun Wagenknecht Central Institute for Electronics, Research Center Jülich, Jülich, Germany Email: l.chen@fz-juelich.de

More information

Digital Image Processing Fundamentals

Digital Image Processing Fundamentals Ioannis Pitas Digital Image Processing Fundamentals Chapter 7 Shape Description Answers to the Chapter Questions Thessaloniki 1998 Chapter 7: Shape description 7.1 Introduction 1. Why is invariance to

More information

A Vertex Chain Code Approach for Image Recognition

A Vertex Chain Code Approach for Image Recognition A Vertex Chain Code Approach for Image Recognition Abdel-Badeeh M. Salem, Adel A. Sewisy, Usama A. Elyan Faculty of Computer and Information Sciences, Assiut University, Assiut, Egypt, usama471@yahoo.com,

More information

MORPHOLOGICAL BOUNDARY BASED SHAPE REPRESENTATION SCHEMES ON MOMENT INVARIANTS FOR CLASSIFICATION OF TEXTURES

MORPHOLOGICAL BOUNDARY BASED SHAPE REPRESENTATION SCHEMES ON MOMENT INVARIANTS FOR CLASSIFICATION OF TEXTURES International Journal of Computer Science and Communication Vol. 3, No. 1, January-June 2012, pp. 125-130 MORPHOLOGICAL BOUNDARY BASED SHAPE REPRESENTATION SCHEMES ON MOMENT INVARIANTS FOR CLASSIFICATION

More information

Tilings of the Euclidean plane

Tilings of the Euclidean plane Tilings of the Euclidean plane Yan Der, Robin, Cécile January 9, 2017 Abstract This document gives a quick overview of a eld of mathematics which lies in the intersection of geometry and algebra : tilings.

More information

Babu Madhav Institute of Information Technology Years Integrated M.Sc.(IT)(Semester - 7)

Babu Madhav Institute of Information Technology Years Integrated M.Sc.(IT)(Semester - 7) 5 Years Integrated M.Sc.(IT)(Semester - 7) 060010707 Digital Image Processing UNIT 1 Introduction to Image Processing Q: 1 Answer in short. 1. What is digital image? 1. Define pixel or picture element?

More information

(i,j,k) North. Back (0,0,0) West (0,0,0) 01. East. Z Front. South. (a) (b)

(i,j,k) North. Back (0,0,0) West (0,0,0) 01. East. Z Front. South. (a) (b) A Simple Fault-Tolerant Adaptive and Minimal Routing Approach in 3-D Meshes y Jie Wu Department of Computer Science and Engineering Florida Atlantic University Boca Raton, FL 33431 Abstract In this paper

More information

IE 5531: Engineering Optimization I

IE 5531: Engineering Optimization I IE 5531: Engineering Optimization I Lecture 3: Linear Programming, Continued Prof. John Gunnar Carlsson September 15, 2010 Prof. John Gunnar Carlsson IE 5531: Engineering Optimization I September 15, 2010

More information

Power Functions and Their Use In Selecting Distance Functions for. Document Degradation Model Validation. 600 Mountain Avenue, Room 2C-322

Power Functions and Their Use In Selecting Distance Functions for. Document Degradation Model Validation. 600 Mountain Avenue, Room 2C-322 Power Functions and Their Use In Selecting Distance Functions for Document Degradation Model Validation Tapas Kanungo y ; Robert M. Haralick y and Henry S. Baird z y Department of Electrical Engineering,

More information

Symbol Detection Using Region Adjacency Graphs and Integer Linear Programming

Symbol Detection Using Region Adjacency Graphs and Integer Linear Programming 2009 10th International Conference on Document Analysis and Recognition Symbol Detection Using Region Adjacency Graphs and Integer Linear Programming Pierre Le Bodic LRI UMR 8623 Using Université Paris-Sud

More information

Formal Model. Figure 1: The target concept T is a subset of the concept S = [0, 1]. The search agent needs to search S for a point in T.

Formal Model. Figure 1: The target concept T is a subset of the concept S = [0, 1]. The search agent needs to search S for a point in T. Although this paper analyzes shaping with respect to its benefits on search problems, the reader should recognize that shaping is often intimately related to reinforcement learning. The objective in reinforcement

More information

Partition definition. Partition coding. Texture coding

Partition definition. Partition coding. Texture coding IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 5, NO. 6, JUNE 1996 881 Morphological Operators for Image and Video Compression Philippe Salembier, Patrick Brigger, Josep R. Casas and Montse Pardas Abstract

More information

Chapter 11 Representation & Description

Chapter 11 Representation & Description Chain Codes Chain codes are used to represent a boundary by a connected sequence of straight-line segments of specified length and direction. The direction of each segment is coded by using a numbering

More information

Localization in Graphs. Richardson, TX Azriel Rosenfeld. Center for Automation Research. College Park, MD

Localization in Graphs. Richardson, TX Azriel Rosenfeld. Center for Automation Research. College Park, MD CAR-TR-728 CS-TR-3326 UMIACS-TR-94-92 Samir Khuller Department of Computer Science Institute for Advanced Computer Studies University of Maryland College Park, MD 20742-3255 Localization in Graphs Azriel

More information

The. Handbook ijthbdition. John C. Russ. North Carolina State University Materials Science and Engineering Department Raleigh, North Carolina

The. Handbook ijthbdition. John C. Russ. North Carolina State University Materials Science and Engineering Department Raleigh, North Carolina The IMAGE PROCESSING Handbook ijthbdition John C. Russ North Carolina State University Materials Science and Engineering Department Raleigh, North Carolina (cp ) Taylor &. Francis \V J Taylor SiFrancis

More information

Blood Vessel Segmentation in Angiograms using Fuzzy Inference System and Mathematical Morphology

Blood Vessel Segmentation in Angiograms using Fuzzy Inference System and Mathematical Morphology Blood Vessel Segmentation in Angiograms using Fuzzy Inference System and Mathematical Morphology 1 K.Hari Babu, Assistant Professor, Department of Electronics and Communication Engineering, MLRIT, Hyderabad,

More information

An automatic correction of Ma s thinning algorithm based on P-simple points

An automatic correction of Ma s thinning algorithm based on P-simple points Author manuscript, published in "Journal of Mathematical Imaging and Vision 36, 1 (2010) 54-62" DOI : 10.1007/s10851-009-0170-1 An automatic correction of Ma s thinning algorithm based on P-simple points

More information

Chapter 9 Morphological Image Processing

Chapter 9 Morphological Image Processing Morphological Image Processing Question What is Mathematical Morphology? An (imprecise) Mathematical Answer A mathematical tool for investigating geometric structure in binary and grayscale images. Shape

More information

A Real Time System for Detecting and Tracking People. Ismail Haritaoglu, David Harwood and Larry S. Davis. University of Maryland

A Real Time System for Detecting and Tracking People. Ismail Haritaoglu, David Harwood and Larry S. Davis. University of Maryland W 4 : Who? When? Where? What? A Real Time System for Detecting and Tracking People Ismail Haritaoglu, David Harwood and Larry S. Davis Computer Vision Laboratory University of Maryland College Park, MD

More information

Fast Distance Transform Computation using Dual Scan Line Propagation

Fast Distance Transform Computation using Dual Scan Line Propagation Fast Distance Transform Computation using Dual Scan Line Propagation Fatih Porikli Tekin Kocak Mitsubishi Electric Research Laboratories, Cambridge, USA ABSTRACT We present two fast algorithms that approximate

More information

Morphological Image Processing

Morphological Image Processing Morphological Image Processing Megha Goyal Dept. of ECE, Doaba Institute of Engineering and Technology, Kharar, Mohali, Punjab, India Abstract The purpose of this paper is to provide readers with an in-depth

More information

Mathematical morphology (1)

Mathematical morphology (1) Chapter 9 Mathematical morphology () 9. Introduction Morphology, or morphology for short, is a branch of image processing which is particularly useful for analyzing shapes in images. We shall develop basic

More information

A Bintree Representation of Generalized Binary. Digital Images

A Bintree Representation of Generalized Binary. Digital Images A intree Representation of Generalized inary Digital mages Hanspeter ieri gor Metz 1 inary Digital mages and Hyperimages A d-dimensional binary digital image can most easily be modelled by a d-dimensional

More information

sizes. Section 5 briey introduces some of the possible applications of the algorithm. Finally, we draw some conclusions in Section 6. 2 MasPar Archite

sizes. Section 5 briey introduces some of the possible applications of the algorithm. Finally, we draw some conclusions in Section 6. 2 MasPar Archite Parallelization of 3-D Range Image Segmentation on a SIMD Multiprocessor Vipin Chaudhary and Sumit Roy Bikash Sabata Parallel and Distributed Computing Laboratory SRI International Wayne State University

More information

Digital Image Processing COSC 6380/4393

Digital Image Processing COSC 6380/4393 Digital Image Processing COSC 6380/4393 Lecture 6 Sept 6 th, 2017 Pranav Mantini Slides from Dr. Shishir K Shah and Frank (Qingzhong) Liu Today Review Logical Operations on Binary Images Blob Coloring

More information

Research Article Image Segmentation Using Gray-Scale Morphology and Marker-Controlled Watershed Transformation

Research Article Image Segmentation Using Gray-Scale Morphology and Marker-Controlled Watershed Transformation Discrete Dynamics in Nature and Society Volume 2008, Article ID 384346, 8 pages doi:10.1155/2008/384346 Research Article Image Segmentation Using Gray-Scale Morphology and Marker-Controlled Watershed Transformation

More information

EE795: Computer Vision and Intelligent Systems

EE795: Computer Vision and Intelligent Systems EE795: Computer Vision and Intelligent Systems Spring 2012 TTh 17:30-18:45 WRI C225 Lecture 02 130124 http://www.ee.unlv.edu/~b1morris/ecg795/ 2 Outline Basics Image Formation Image Processing 3 Intelligent

More information

Lecture 2 - Graph Theory Fundamentals - Reachability and Exploration 1

Lecture 2 - Graph Theory Fundamentals - Reachability and Exploration 1 CME 305: Discrete Mathematics and Algorithms Instructor: Professor Aaron Sidford (sidford@stanford.edu) January 11, 2018 Lecture 2 - Graph Theory Fundamentals - Reachability and Exploration 1 In this lecture

More information

Unconstrained Optimization

Unconstrained Optimization Unconstrained Optimization Joshua Wilde, revised by Isabel Tecu, Takeshi Suzuki and María José Boccardi August 13, 2013 1 Denitions Economics is a science of optima We maximize utility functions, minimize

More information

Finger Print Analysis and Matching Daniel Novák

Finger Print Analysis and Matching Daniel Novák Finger Print Analysis and Matching Daniel Novák 1.11, 2016, Prague Acknowledgments: Chris Miles,Tamer Uz, Andrzej Drygajlo Handbook of Fingerprint Recognition, Chapter III Sections 1-6 Outline - Introduction

More information

Table 1. Different types of Defects on Tiles

Table 1. Different types of Defects on Tiles DETECTION OF SURFACE DEFECTS ON CERAMIC TILES BASED ON MORPHOLOGICAL TECHNIQUES ABSTRACT Grasha Jacob 1, R. Shenbagavalli 2, S. Karthika 3 1 Associate Professor, 2 Assistant Professor, 3 Research Scholar

More information

Figure 1: An Area Voronoi Diagram of a typical GIS Scene generated from the ISPRS Working group III/3 Avenches data set. 2 ARRANGEMENTS 2.1 Voronoi Di

Figure 1: An Area Voronoi Diagram of a typical GIS Scene generated from the ISPRS Working group III/3 Avenches data set. 2 ARRANGEMENTS 2.1 Voronoi Di Qualitative Spatial Relations using Arrangements for Complex Images M. Burge and W. Burger Johannes Kepler University, Department of Systems Science Computer Vision Laboratory, A-4040 Linz, Austria burge@cast.uni-linz.ac.at

More information

Detection of Edges Using Mathematical Morphological Operators

Detection of Edges Using Mathematical Morphological Operators OPEN TRANSACTIONS ON INFORMATION PROCESSING Volume 1, Number 1, MAY 2014 OPEN TRANSACTIONS ON INFORMATION PROCESSING Detection of Edges Using Mathematical Morphological Operators Suman Rani*, Deepti Bansal,

More information

Machine vision. Summary # 6: Shape descriptors

Machine vision. Summary # 6: Shape descriptors Machine vision Summary # : Shape descriptors SHAPE DESCRIPTORS Objects in an image are a collection of pixels. In order to describe an object or distinguish between objects, we need to understand the properties

More information

Lecture 7: Morphological Image Processing

Lecture 7: Morphological Image Processing I2200: Digital Image processing Lecture 7: Morphological Image Processing Prof. YingLi Tian Oct. 25, 2017 Department of Electrical Engineering The City College of New York The City University of New York

More information

Research in Computational Differential Geomet

Research in Computational Differential Geomet Research in Computational Differential Geometry November 5, 2014 Approximations Often we have a series of approximations which we think are getting close to looking like some shape. Approximations Often

More information

Ray shooting from convex ranges

Ray shooting from convex ranges Discrete Applied Mathematics 108 (2001) 259 267 Ray shooting from convex ranges Evangelos Kranakis a, Danny Krizanc b, Anil Maheshwari a;, Jorg-Rudiger Sack a, Jorge Urrutia c a School of Computer Science,

More information

A.1 Numbers, Sets and Arithmetic

A.1 Numbers, Sets and Arithmetic 522 APPENDIX A. MATHEMATICS FOUNDATIONS A.1 Numbers, Sets and Arithmetic Numbers started as a conceptual way to quantify count objects. Later, numbers were used to measure quantities that were extensive,

More information

Machine Learning And Adaptive Morphological Operators

Machine Learning And Adaptive Morphological Operators Machine Learning And Adaptive Morphological Operators Magno P. de Almeida Filho Dept. of Electrical Engineering Federal University of Ceará, UFC Fortaleza, Brazil magnoprudencio@gmail.com Francisco de

More information

Chapter 3. Image Processing Methods. (c) 2008 Prof. Dr. Michael M. Richter, Universität Kaiserslautern

Chapter 3. Image Processing Methods. (c) 2008 Prof. Dr. Michael M. Richter, Universität Kaiserslautern Chapter 3 Image Processing Methods The Role of Image Processing Methods (1) An image is an nxn matrix of gray or color values An image processing method is algorithm transforming such matrices or assigning

More information

Digital Image Processing

Digital Image Processing Digital Image Processing Third Edition Rafael C. Gonzalez University of Tennessee Richard E. Woods MedData Interactive PEARSON Prentice Hall Pearson Education International Contents Preface xv Acknowledgments

More information

. Introduction Image moments and various types of moment-based invariants play very important role in object recognition and shape analysis [], [2], [

. Introduction Image moments and various types of moment-based invariants play very important role in object recognition and shape analysis [], [2], [ On the Calculation of Image Moments Jan Flusser and Tomas Suk Institute of Information Theory and Automation Academy of Sciences of the Czech Republic Pod vodarenskou vez 4, 82 08 Prague 8, Czech Republic

More information

Object Modeling from Multiple Images Using Genetic Algorithms. Hideo SAITO and Masayuki MORI. Department of Electrical Engineering, Keio University

Object Modeling from Multiple Images Using Genetic Algorithms. Hideo SAITO and Masayuki MORI. Department of Electrical Engineering, Keio University Object Modeling from Multiple Images Using Genetic Algorithms Hideo SAITO and Masayuki MORI Department of Electrical Engineering, Keio University E-mail: saito@ozawa.elec.keio.ac.jp Abstract This paper

More information

Cellular Automata. Nicholas Geis. January 22, 2015

Cellular Automata. Nicholas Geis. January 22, 2015 Cellular Automata Nicholas Geis January 22, 2015 In Stephen Wolfram s book, A New Kind of Science, he postulates that the world as we know it and all its complexities is just a simple Sequential Dynamical

More information

Let v be a vertex primed by v i (s). Then the number f(v) of neighbours of v which have

Let v be a vertex primed by v i (s). Then the number f(v) of neighbours of v which have Let v be a vertex primed by v i (s). Then the number f(v) of neighbours of v which have been red in the sequence up to and including v i (s) is deg(v)? s(v), and by the induction hypothesis this sequence

More information

Topological Invariance under Line Graph Transformations

Topological Invariance under Line Graph Transformations Symmetry 2012, 4, 329-335; doi:103390/sym4020329 Article OPEN ACCESS symmetry ISSN 2073-8994 wwwmdpicom/journal/symmetry Topological Invariance under Line Graph Transformations Allen D Parks Electromagnetic

More information

Topology Preserving Tetrahedral Decomposition of Trilinear Cell

Topology Preserving Tetrahedral Decomposition of Trilinear Cell Topology Preserving Tetrahedral Decomposition of Trilinear Cell Bong-Soo Sohn Department of Computer Engineering, Kyungpook National University Daegu 702-701, South Korea bongbong@knu.ac.kr http://bh.knu.ac.kr/

More information

Asynchronous Cellular Operations on Gray Images Extracting Topographic Shape Features and Their Relations

Asynchronous Cellular Operations on Gray Images Extracting Topographic Shape Features and Their Relations Asynchronous Cellular Operations on Gray Images Extracting Topographic Shape Features and Their Relations Igor Polkovnikov Yes San Francisco LLC, ipolk@virtuar.com, www.virtuar.com/ia/ March 19, 2013 Abstract

More information

ECE 172A: Introduction to Intelligent Systems: Machine Vision, Fall Midterm Examination

ECE 172A: Introduction to Intelligent Systems: Machine Vision, Fall Midterm Examination ECE 172A: Introduction to Intelligent Systems: Machine Vision, Fall 2008 October 29, 2008 Notes: Midterm Examination This is a closed book and closed notes examination. Please be precise and to the point.

More information

Binary Image Analysis. Binary Image Analysis. What kinds of operations? Results of analysis. Useful Operations. Example: red blood cell image

Binary Image Analysis. Binary Image Analysis. What kinds of operations? Results of analysis. Useful Operations. Example: red blood cell image inary Image Analysis inary Image Analysis inary image analysis consists of a set of image analysis operations that are used to produce or process binary images, usually images of s and s. represents the

More information