Pattern Recognition and Training Pattern set of values

Pattern Recognition and Training • Pattern -- set of values (known size) that describe things • The general problem • Approaches to the decision-making process. 1 Simple comparison. 2 Common property. 3 Clusters (using distance measurement |X 1 -u 1| + |X 2 -u 2| + … + |Xn-un( |. 4 Combination of 1, 2 and 3 10/20/2021 240 -373 Image Processing 1

Decision Functions • Decision function: • If the pattern vector is x = [x 1, x 2, x 3, …, xn, 1]T, then w = (w 1, w 2, w 3, …, wn( – The unknown pattern is in group B if w. Tx > 0 – The unknown pattern is in group A if w. Tx <= 0 – Example: (8, 4) is in group B because [1 , 4 , 8] [3. 5 - , 1. 0 - , 1. 5]T = 8 x 1. 5 -4 -3. 5 = 4. 5 and 4. 5 > 0 – How about (4, 4? ( 10/20/2021 240 -373 Image Processing 2

Decision Functions (Cont’d( • The number of groups can be more than 2 • Decision table Result of w 1 0> 0< • Result of w 2 0> 0> 0< 0< Implication no group A group C group B Decision function need not be a linear function 10/20/2021 240 -373 Image Processing 3

Cluster Means • If the cluster consists of [3, 4, 8, 2] [2, 9, 5, 1][5, 7, 7, 1], then the mean is [3. 33, 6. 67, 1. 33]. This represents the center of the four-dimensional cluster. • The Euclidean distance from the center to a new pattern can be calculated as follows: new vector [3, 5, 7, 0 , [ Euclidean distance = 4. 78 10/20/2021 (3 -3. 33)2 5 -6. 67)) +2 7 -6. 67)) +2 0 -1. 33)) +2 = 240 -373 Image Processing 4

Automatic Clustering Technique 1: K-means clustering USE: To automatically find the best groupings and means of K clusters. OPERATION: – The pattern vectors of K different items are given to the system – Classifying them as best it can (without knowing which vector belongs to which item( – Let the pattern vectors be X 1, …, Xn – Take the first K points as the initial estimation of the cluster means M 1 = X 1, M 2 = X 2, …, Mk = Xk * Allocate each pattern vector to the nearest group (minimum distance( – Calculate new cluster centers – If they are the same as the old centers, then STOP, other wise goto step* 10/20/2021 240 -373 Image Processing 5

K-means clustering example M 1 = (2, 5. 0) M 2 = (2, 5. 5( Allocating each pattern vector to the nearest center gives (2, 5. 0)1 (2, 5. 5)2 (6, 2. 5)3 (7, 2. 0)4 (7, 3. 0)5 (3, 4. 5)6 group 1 group 2 group 1 The group means now become group 1: M 1 = (5, 3. 4) group 2: M 2 = (2, 5. 5( 10/20/2021 240 -373 Image Processing 6

This gives new groupings as follows: (2, 5. 0)1 (2, 5. 5)2 (6, 2. 5)3 (7, 2. 0)4 (7, 3. 0)5 (3, 4. 5)6 group 2 group 1 group 2 And the group means become group 1: M 1 = (6. 67, 2. 5) group 2: M 2 = (2. 33, 5. 0( Groupings now stay the same and the processing stops. 10/20/2021 240 -373 Image Processing 7

Optical Character Recognition Technique: Isolation of a character in an OCR document USE: To create a window containing only one character onto an array containing a text image OPERATION: . 1 Assuming that the image is correctly oriented and the text is dark on a white background. 2 Calculate row sums of the pixel gray-level values. High row sums indicate a space between the rows. 3 Calculate column sums of the pixel gray-level values. High column sums indicate a space between the columns 10/20/2021 240 -373 Image Processing 8

Technique: Creating the pattern vector (feature extraction( USE: To create the pattern vector for a character so that it can be compared with the library OPERATION: . 1 Assuming that the character has been isolated. 2 Place a 4 x 4 grid over the image and count the number of “ink” pixels in each grid. . 3 These number are then divided by the total number of pixels in the grid. 4 Comparing resulting numbers with the library 10/20/2021 240 -373 Image Processing 9