Representation and DescriptionREPRESENTATION AND DESCRIPTION 4/12/2013 IT-BMSP&I,2013 1 Representation and Description R. V.COLLEGE OF ENGINEERING PRESENTATION ON: REPRESENTATION AND DESCRIPTION PRESENTED BY: 1st Semester , Mtech. Students , BIOMEDICAL SIGNAL PROCESSING AND INSTUMENTATION DEPARTMENT ASUTOSH P.APARNA MADHUMITHA.V 4/12/2013 IT-BMSP&I,2013 2 Representation and Description Overview •Objective •Introduction •Representation •Boundary Descriptors •Regional Descriptors 4/12/2013 IT-BMSP&I,2013 3 Representation and Description Image Representation and Description? Objective: To represent and describe information embedded in an image in other forms that are more suitable than the image itself. Benefits: - Easier to understand - Require fewer memory, faster to be processed - More “ready to be used” What kind of information we can use? - Boundary, shape - Region - Texture - Relation between regions 4/12/2013 IT-BMSP&I,2013 4 Representation and Description Introduction • Representing region in 2 ways 1. in terms of its external characteristics (its boundary) focus on shape characteristics.g. e.2013 5 .. texture •sometimes. in terms of its internal characteristics (its region) focus on regional properties. 2. color. we may need to use both ways 4/12/2013 IT-BMSP&I. orientation of the straight line joining its extreme points. description length of the boundary.2013 6 . 4/12/2013 IT-BMSP&I. and the number of concavities in the boundary.Representation and Description Introduction •Description describes the region based on the chosen representation •example 1. representation boundary 2. Representation and Description Representation •Chain Codes •Polygon Approximation •Signature •Boundary Segment •Skeleton 4/12/2013 IT-BMSP&I.2013 7 . Representation and Description Shape Representation by Using Chain Codes Chain codes: represent an object boundary by a connected sequence of straight line segments of specified length and direction.2013 8 . 4-directional chain code 4/12/2013 8-directional chain code IT-BMSP&I. Representation and Description Shape Representation by Using Chain Codes 4/12/2013 IT-BMSP&I.2013 9 . the resulting chain of codes tends to be quite long 2.Representation and Description Shape Representation by Using Chain Codes •unacceptable because 1. resample the boundary by selecting a larger grid spacing 2. however. different grid can generate different chain codes •starting point is arbitrary 4/12/2013 IT-BMSP&I.2013 10 . any small disturbances along the boundary due to noise or imperfect segmentation cause changes in the code that may not be related to the shape of the boundary •Solve the problems by 1. The first difference = 3133030 . The first difference of a chain code: counting the number of direction change (in counterclockwise) between 2 adjacent elements of the code. Solution: treat a chain code as a circular sequence and redefine the starting point so that the resulting sequence of numbers forms an integer of minimum magnitude.Representation and Description The First Difference of a Chain Codes Problem of a chain code: A chain code sequence depends on a starting point.Treating a chain code as a circular sequence. 11 .2013 .a chain code: 10103322 . Example: Example: 1 2 0 3 4/12/2013 Chain code : The first difference 01 1 02 2 03 3 23 1 20 2 21 3 IT-BMSP&I. we get the first difference = 33133030 The first difference is rotational invariant. • The number of straight line segments used determines the accuracy of the approximation. and a closed path becomes a polygon.Representation and Description Polygon Approximation • Polygonal approximations: to represent a boundary by straight line segments. • A larger number of sides will only add noise to the model. • Only the minimum required number of sides necessary to preserve the needed shape information should be used (Minimum perimeter polygons).2013 12 . 4/12/2013 IT-BMSP&I. Find the line joining two extreme points 0. Find the farthest points from the line 3. Draw a polygon 4/12/2013 IT-BMSP&I. Object boundary 2.Representation and Description Polygon Approximation : Splitting Techniques 1.2013 13 . 4/12/2013 IT-BMSP&I.2013 14 .Representation and Description Shape Representation by Using Signature • The idea behind a signature is to convert a two dimensional boundary into a representative one dimensional function. Scale invariance can be achieved by either scaling the signature function to fixed amplitude or by dividing the function values by the standard deviation of the function. 4/12/2013 IT-BMSP&I.Representation and Description Shape Representation by Using Signature • Signatures are invariant to location.2013 15 . but will depend on rotation and scaling. 1. 2. Starting at the point farthest from the reference point or using the major axis of the region can be used to decrease dependence on rotation. 2013 16 .Representation and Description Shape Representation by Using Boundary Segment • Boundary segments: decompose a boundary into segments. 4/12/2013 IT-BMSP&I. • Use of the convex hull of the region enclosed by the boundary is a powerful tool for robust decomposition of the boundary. 2013 17 . 4/12/2013 IT-BMSP&I. like a stick figure of a human.Representation and Description Shape Representation by Using Skeletons • Skeletons: produce a one pixel wide graph that has the same basic shape of the region. It can be used to analyze the geometric structure of a region which has bumps and “arms”. . • Let N ( p1 ) p2 p3 .2013 18 ... p9 .1 transitions in the ordered sequence p2 . p8 . p3 . p2 4/12/2013 IT-BMSP&I....Representation and Description Shape Representation by Using Skeletons • Before a thinning algorithm: • A contour point is any pixel with value 1 and having at least one 8-neighbor valued 0. p8 p9 T ( p1 ) : the number of 0 . 2013 19 .Representation and Description Shape Representation by Using Skeletons • Step 1: Flag a contour point p1 for deletion if the following conditions are satisfied (a ) 2 N ( p1 ) 6 (b) T ( p1 ) 1 4/12/2013 ( c ) p 2 p 4 p6 0 (d ) p4 p6 p8 0 IT-BMSP&I. but conditions (c) and (d) are changed to (d' ) p2 p6 p8 0 (c' ) p2 p4 p8 0 4/12/2013 IT-BMSP&I.2013 20 . conditions (a) and (b) remain the same.Representation and Description Shape Representation by Using Skeletons • Step 2: Flag a contour point p1 for deletion again. However. 4/12/2013 IT-BMSP&I.2013 21 .Representation and Description Shape Representation by Using Skeletons • A thinning algorithm: (1) applying step 1 to flag border points for deletion (2) deleting the flagged points (3) applying step 2 to flag the remaining border points for deletion (4) deleting the flagged points • This procedure is applied iteratively until no further points are deleted. 4/12/2013 IT-BMSP&I.Representation and Description Shape Representation by Using Skeletons • One application of skeletonization is for character recognition. • A letter or character is determined by the center-line of its strokes. and is unrelated to the width of the stroke lines.2013 22 . 2013 23 . Fourier descriptor 4.Length of the boundary . Statistical moments 4/12/2013 IT-BMSP&I.Representation and Description Boundary Descriptors 1. Simple boundary descriptors: we can use . Shape number 3.The size of smallest circle or box that can totally enclosing the object 2. 2013 1 2 0 3 24 .Representation and Description Shape Number Shape number of the boundary definition: the first difference of smallest magnitude The order n of the shape number: the number of digits in the sequence 4/12/2013 IT-BMSP&I. Representation and Description Shape Number (cont. 6 and 8 4/12/2013 IT-BMSP&I.2013 25 .) Shape numbers of order 4. 2013 Shape No. Create grid 4/12/2013 4. Find the nearest Grid. Original boundary Chain code: 000030032232221211 First difference: 300031033013003130 3. 000310330130031303 26 . IT-BMSP&I. Find the smallest rectangle that fits the shape 1.Representation and Description Example: Shape Number 2. Let s(k) be a coordinate of a boundary point k : Fourier descriptor : s(k ) x ( k ) jy (k ) 1 a (u ) K K 1 2uk / K s ( k ) e k 0 Reconstruction formula 1 s(k ) K K 1 2uk / K a ( u ) e k 0 Boundary points 4/12/2013 IT-BMSP&I.y) as a complex number (x = real part and y = imaginary part) then apply the Fourier transform to a sequence of boundary points.Representation and Description Fourier Descriptor Fourier descriptor: view a coordinate (x.2013 27 . 2013 28 .Representation and Description Example: Fourier Descriptor Examples of reconstruction from Fourier descriptors 1 sˆ(k ) K P 1 2uk / K a ( u ) e k 0 P is the number of Fourier coefficients used to reconstruct the boundary 4/12/2013 IT-BMSP&I. 2013 29 .Representation and Description Fourier Descriptor Properties Some properties of Fourier descriptors 4/12/2013 IT-BMSP&I. 2013 30 .Representation and Description Statistical Moments Definition: the nth moment K 1 n ( r ) ( ri m)n g ( ri ) Example of moment: The first moment = mean The second moment = variance i 0 K 1 where m ri g ( ri ) Boundary segment 1. 3. 2. i 0 1D graph Convert a boundary segment into 1D graph View a 1D graph as a PDF function Compute the nth order moment of the graph 4/12/2013 IT-BMSP&I. • Applications and Advancements . • Example using MATLAB. • Topological Descriptor. • Regional Descriptors -Area and Perimeter Descriptor.2013 31 . 4/12/2013 IT-BMSP&I. • Texture Descriptor.Representation and Description Regional Descriptors • What is Representation and Description ? • Types of Representation and Description . • Texture Descriptors.perimeter and compactness. . 4/12/2013 IT-BMSP&I.Representation and Description Types of Representation and Description • Area.2013 32 . • Topological Descriptors . 2013 33 .Representation and Description Regional Descriptors 4/12/2013 IT-BMSP&I. Representation and Description Example for Area and Perimeter Descriptor 4/12/2013 IT-BMSP&I.2013 34 . Representation and Description Example for Area and Perimeter Descriptor 4/12/2013 IT-BMSP&I.2013 35 . 2013 36 .Representation and Description Example for Area and Perimeter Descriptor 4/12/2013 IT-BMSP&I. 2013 37 .Representation and Description Example for Area and Perimeter Descriptor 4/12/2013 IT-BMSP&I. 2013 38 .Representation and Description Topological Descriptors • Topological property 1: the number of holes (H) • Topological property 2: the number of connected components (C) 4/12/2013 IT-BMSP&I. Representation and Description Texture Descriptors 4/12/2013 IT-BMSP&I.2013 39 . Representation and Description Texture Descriptors Statistical approach • Statistical Moments . L 1 n ( z ) ( zi m) n p ( zi ) k 0 L 1 where m zi p ( zi ) i 0 1 R 1 1 2 ( z) 4/12/2013 IT-BMSP&I.2013 40 . for example. For instance. whenever a player approaches the goal area. • Possibility of an automatic connection to a TV channel broadcasting a soccer match. 4/12/2013 IT-BMSP&I. etc.2013 41 . • Personalized electronic news service. • Digital library : visual descriptors allow a very detailed and concrete search of any video or image by means of different search parameters. the search of films where a known actor appears.Representation and Description Descriptor Applications • Multimedia documents search engines and classifiers. the search of videos containing the Everest mountain. Representation and Description Latest Development 4/12/2013 IT-BMSP&I.2013 42 . Representation and Description Latest Development 4/12/2013 IT-BMSP&I.2013 43 . 2013 44 .Representation and Description THANK YOU 4/12/2013 IT-BMSP&I.