Introduction to Convolution Neural Networks（CNN）and systems

Find clm, n) ∑∑hm(-m+j,-n+k)×(j,k) J=-0k=-00 Shift flipped h to m=l, n= K K 253 multiply overlapped elements and add( see next slide hence,C(m=1,n=0)=-2+5=3, ch9. CNN. V9b3 16

Find C(m,n) •             j j k k flip h m j n k I j k C m n ( , ) ( , ) ( , ) ( ) ch9. CNN. V9b3 16 Shift Flipped h to m=1,n=0 K J hence, C(m  1,n  0)  2  5  3, 1 4 1 2 5 3 I        J K multiply overlapped elements and add (see next slide)

C(m,n) Find clm, n) ∑ hm(-m+j,-n+k)×/(j,k) Shift flipped h to m=l, n= K I n 53 multiply overlapped elements and add C(m=1,n=0)=(2×-1)+(5×1)=3, ch9. CNN. V9b3 17

Find C(m,n) •             j j k k flip h m j n k I j k C m n ( , ) ( , ) ( , ) ( ) ch9. CNN. V9b3 17 Shift Flipped h to m=1,n=0 K J C(m  1,n  0)  (2  1)  (51)  3, 1 4 1 2 5 3 I        J K multiply overlapped elements and add m n C(m,n)

Steps to find c(m, n) °step1: 141 Step 3 (00) 53 C(20) =1X2=2 1*5+1*3 Step 2: C(10) 14 Step 4 141 1*2+1*5=3 C(30) 1*3 11 3 c(0,0) c(1,0) C(2,0) c(3,0) C(m, n)= C(0,0) C(1,0) C(2,0) C(3,0) C(0,0)=2c(10)=3C(2,0)=2c(3,0)=3 ch9. CNN. V9b3 18

Steps to find C(m,n) • Step1: • C(0,0) • =1x2=2 • Step 2: • C(1,0) • = -1*2+1*5=3 • Step 3: • C(2,0) • = -1*5+1*3 • =-2 • Step 4: • C(3,0) • = -1*3 • =-3 1 4 1 2 5 3 -1 1 1 1 1 4 1 2 5 3 -1 1 1 1 1 4 1 2 5 3 -1 1 1 1 1 4 1 2 5 3 -1 1 1 1 C(m,n)= C(0,0) C(1,0) C(2,0) C(3,0) C(0,0) C(1,0) C(2,0) C(3,0) C(0,0)=2 C(1,0)=3 C(2,0)=-2 C(3,0)=-3 ch9. CNN. V9b3 18

Steps continue Step 5: Step 7 C(0,1) C(2,1) 25 1 1x1+1*2 1*4+1*1+1米5+1*3 5 1 Step 8 Step 6 3 C(3,1 1*1+1*3 1*1+1*4+1*2+1米5 2 =10 c(0,2)c(1,2) C(2,2) c(3,2) c(m, n C(0,1)=3c(1,1)=10C(2,1)=5c(3,1)=2 C(0,0)=2c(10)=3C(2,0)=2c(3,0)=3 ch9. CNN. V9b3 19

Steps continue • Step 5: • C(0,1) • =1x1+1*2 • =3 • Step 6: • C(1,1) • = -1*1+1*4+1*2+1*5 • =10 • Step 7: • C(2,1) • = -1*4+1*1+1*5+1*3 • =5 • Step 8: • C(3,1) • = -1*1+1*3 • =2 1 4 1 2 5 3 -1 1 1 1 1 4 1 2 5 3 -1 1 1 1 1 4 1 2 5 3 -1 1 1 1 1 4 1 2 5 3 -1 1 1 1 C(m,n)= C(0,2) C(1,2) C(2,2) C(3,2) C(0,1)=3 C(1,1)=10 C(2,1)=5 C(3,1)=2 C(0,0)=2 C(1,0)=3 C(2,0)=-2 C(3,0)=-3 ch9. CNN. V9b3 19

Find all elements in C for all possible m, n c(m=0,n=0)=2, c(m=1,n=0)=-2+5=3, n c(m=1,n=1)=10, etc *h=C]=31052 23-2-3 ch9. CNN. V9b3

Find all elements in C for all possible m,n ( 0, 0) 2, ( 1, 0) 2 5 3, ( 1, 1) 10, ,...., . 1 5 5 1 * [] 3 10 5 2 2 3 2 3 c m n c m n c m n etc I h c                       ch9. CNN. V9b3 20 m n m n C(m,n)