Pattern Recognition

Alternate Font -vs- Standard Font

Doing comparisons against character @...
@ 5.10; a 3.16; b 4.69; c 5.83; d 4.47; e 7.87; f 8.94; g 4.24; h 6.32; i 10.77; j 8.25
k 5.29; l 9.38; m 10.10; n 5.83; o 4.00; p 6.00; q 3.46; r 4.47; s 3.74; t 11.49; u 5.48
v 4.24; w 10.95; x 4.00; y 4.69; z 7.07;
INCORRECT IDENTIFICATION

Doing comparisons against character a...
@ 8.00; a 5.66; b 7.75; c 9.06; d 8.49; e 11.31; f 12.49; g 6.78; h 8.12; i 11.40; j 9.70
k 9.06; l 12.73; m 11.83; n 7.35; o 6.00; p 10.30; q 5.10; r 8.25; s 6.32; t 12.08; u 7.21
v 6.16; w 11.58; x 5.48; y 7.07; z 8.37;
INCORRECT IDENTIFICATION

Doing comparisons against character b...
@ 7.48; a 6.48; b 6.48; c 7.87; d 7.62; e 9.38; f 11.05; g 6.48; h 8.94; i 10.39; j 9.90
k 7.62; l 11.83; m 12.25; n 7.87; o 6.16; p 9.06; q 6.00; r 6.78; s 5.48; t 11.31; u 7.87
v 6.93; w 12.25; x 5.29; y 6.93; z 7.21;
INCORRECT IDENTIFICATION

Doing comparisons against character c...
@ 6.00; a 6.32; b 6.78; c 2.00; d 5.48; e 6.32; f 6.78; g 5.10; h 8.60; i 9.49; j 7.87
k 4.90; l 6.16; m 11.49; n 9.38; o 5.83; p 6.00; q 5.83; r 6.32; s 3.46; t 10.30; u 6.93
v 5.66; w 11.49; x 4.24; y 5.29; z 5.66;
Correct Identification

Doing comparisons against character d...
@ 8.00; a 6.48; b 6.63; c 8.12; d 8.00; e 9.70; f 11.31; g 6.63; h 8.49; i 11.22; j 10.68
k 8.12; l 12.00; m 12.00; n 7.62; o 6.00; p 9.27; q 6.00; r 7.21; s 5.83; t 12.00; u 7.48
v 6.78; w 12.00; x 5.48; y 7.35; z 7.62;
INCORRECT IDENTIFICATION

Doing comparisons against character e...
@ 8.12; a 9.17; b 8.94; c 7.48; d 8.94; e 6.48; f 8.49; g 8.25; h 11.58; i 7.87; j 9.90
k 8.25; l 9.49; m 13.56; n 11.49; o 9.17; p 8.83; q 9.17; r 8.60; s 6.63; t 8.83; u 10.58
v 9.49; w 13.56; x 7.87; y 7.07; z 5.10;
INCORRECT IDENTIFICATION

Doing comparisons against character f...
@ 8.25; a 9.59; b 9.80; c 7.07; d 9.06; e 7.21; f 6.48; g 8.49; h 11.83; i 8.25; j 9.80
k 8.25; l 9.38; m 13.56; n 12.08; o 9.49; p 7.48; q 9.17; r 8.94; s 6.93; t 8.25; u 10.77
v 8.83; w 13.56; x 8.25; y 6.16; z 6.78;
INCORRECT IDENTIFICATION

Doing comparisons against character g...
@ 4.69; a 5.29; b 5.83; c 4.00; d 4.69; e 7.35; f 8.12; g 4.00; h 7.75; i 10.00; j 7.87
k 4.47; l 7.75; m 11.22; n 8.00; o 4.69; p 6.93; q 4.47; r 5.48; s 4.00; t 10.77; u 6.00
v 4.69; w 10.39; x 2.83; y 5.83; z 6.16;
INCORRECT IDENTIFICATION

Doing comparisons against character h...
@ 7.48; a 4.69; b 4.47; c 8.00; d 5.83; e 9.27; f 10.10; g 4.90; h 0.00; i 15.87; j 12.81
k 7.48; l 10.58; m 9.49; n 3.74; o 3.74; p 7.07; q 4.90; r 5.66; s 7.35; t 16.00; u 2.45
v 4.47; w 9.49; x 6.63; y 9.17; z 10.39;
Correct Identification

Doing comparisons against character i...
@ 9.90; a 11.58; b 11.75; c 10.20; d 11.05; e 9.27; f 11.05; g 11.14; h 14.56; i 4.00; j 7.75
k 10.20; l 11.83; m 15.49; n 13.93; o 12.08; p 11.75; q 11.31; r 11.05; s 9.27; t 4.47; u 13.49
v 11.83; w 15.49; x 9.80; y 7.75; z 5.29;
Correct Identification

Doing comparisons against character j...
@ 8.00; a 7.07; b 7.62; c 7.21; d 8.00; e 9.70; f 10.58; g 6.16; h 7.87; i 11.31; j 7.87
k 8.60; l 10.86; m 12.65; n 8.94; o 5.66; p 9.38; q 4.90; r 8.12; s 5.48; t 11.58; u 6.32
v 5.66; w 11.83; x 4.90; y 7.21; z 6.32;
INCORRECT IDENTIFICATION

Doing comparisons against character k...
@ 3.74; a 5.66; b 4.47; c 4.24; d 2.00; e 5.48; f 6.32; g 4.69; h 7.48; i 11.14; j 9.49
k 0.00; l 6.93; m 10.00; n 7.07; o 5.29; p 4.69; q 5.66; r 3.16; s 5.66; t 11.49; u 6.32
v 5.29; w 10.00; x 4.47; y 6.32; z 7.21;
Correct Identification

Doing comparisons against character l...
@ 9.06; a 9.90; b 11.05; c 7.21; d 9.90; e 8.37; f 9.06; g 9.49; h 12.96; i 7.75; j 10.00
k 8.83; l 8.00; m 14.07; n 13.19; o 10.30; p 9.90; q 10.20; r 10.49; s 7.62; t 9.38; u 11.58
v 10.20; w 13.93; x 8.49; y 7.75; z 7.21;
INCORRECT IDENTIFICATION

Doing comparisons against character m...
@ 7.48; a 4.90; b 5.83; c 8.00; d 6.00; e 9.90; f 10.58; g 6.32; h 3.74; i 15.43; j 12.57
k 7.21; l 9.90; m 8.83; n 4.47; o 4.47; p 7.62; q 5.29; r 6.63; s 8.00; t 15.68; u 3.46
v 4.69; w 9.49; x 6.16; y 8.83; z 10.49;
INCORRECT IDENTIFICATION

Doing comparisons against character n...
@ 7.07; a 4.24; b 4.00; c 8.72; d 5.48; e 9.90; f 11.05; g 5.29; h 3.46; i 15.23; j 12.65
k 6.93; l 11.83; m 9.17; n 1.41; o 4.24; p 7.87; q 4.90; r 4.90; s 7.62; t 15.36; u 4.24
v 4.90; w 9.17; x 6.32; y 8.94; z 10.58;
Correct Identification

Doing comparisons against character o...
@ 5.29; a 3.46; b 3.16; c 5.48; d 4.00; e 8.00; f 8.94; g 2.83; h 3.74; i 13.04; j 10.00
k 5.29; l 9.27; m 9.80; n 4.47; o 0.00; p 6.00; q 2.00; r 4.00; s 4.47; t 13.49; u 2.00
v 2.45; w 9.80; x 3.16; y 6.78; z 7.87;
Correct Identification

Doing comparisons against character p...
@ 5.29; a 6.16; b 5.10; c 4.90; d 4.24; e 4.90; f 4.69; g 5.29; h 7.07; i 11.92; j 10.68
k 4.24; l 7.07; m 10.10; n 7.48; o 5.83; p 1.41; q 6.32; r 4.24; s 5.83; t 11.92; u 6.48
v 5.48; w 11.05; x 6.16; y 5.83; z 7.62;
Correct Identification

Doing comparisons against character q...
@ 5.83; a 3.46; b 3.16; c 5.66; d 4.24; e 8.25; f 9.27; g 3.16; h 4.24; i 12.88; j 10.10
k 5.29; l 9.70; m 9.90; n 4.47; o 1.41; p 6.48; q 2.45; r 4.00; s 4.47; t 13.34; u 2.83
v 2.83; w 9.70; x 3.16; y 6.93; z 8.00;
INCORRECT IDENTIFICATION

Doing comparisons against character r...
@ 5.10; a 4.24; b 1.41; c 6.00; d 2.83; e 7.21; f 8.25; g 3.16; h 4.00; i 13.49; j 10.49
k 4.47; l 9.38; m 9.90; n 4.24; o 2.83; p 5.10; q 3.74; r 2.00; s 5.48; t 13.71; u 3.46
v 3.74; w 9.90; x 4.69; y 7.35; z 8.37;
Correct Identification

Doing comparisons against character s...
@ 6.63; a 5.29; b 6.78; c 5.29; d 6.63; e 8.25; f 9.17; g 4.90; h 8.49; i 8.72; j 6.63
k 6.78; l 9.38; m 12.25; n 8.83; o 5.66; p 7.48; q 4.90; r 6.63; s 2.00; t 9.80; u 7.21
v 5.66; w 12.25; x 4.47; y 4.47; z 5.66;
Correct Identification

Doing comparisons against character t...
@ 11.14; a 12.88; b 13.56; c 11.31; d 12.41; e 11.22; f 11.22; g 12.49; h 16.00; i 3.46; j 7.75
k 11.49; l 13.27; m 16.55; n 15.43; o 13.49; p 12.25; q 12.33; r 12.49; s 10.49; t 0.00; u 14.90
v 12.49; w 16.55; x 11.14; y 7.75; z 7.75;
Correct Identification

Doing comparisons against character u...
@ 6.48; a 4.47; b 4.00; c 6.32; d 4.90; e 8.60; f 9.38; g 4.00; h 2.45; i 14.63; j 11.40
k 6.32; l 9.49; m 9.59; n 4.47; o 2.00; p 6.48; q 3.46; r 5.10; s 6.00; t 14.90; u 0.00
v 3.16; w 9.59; x 4.69; y 8.12; z 9.06;
Correct Identification

Doing comparisons against character v...
@ 5.29; a 3.74; b 4.47; c 5.48; d 4.24; e 8.25; f 8.12; g 3.46; h 4.47; i 12.49; j 9.49
k 5.29; l 9.38; m 9.59; n 5.10; o 2.45; p 5.29; q 2.00; r 4.47; s 4.69; t 12.49; u 3.16
v 0.00; w 9.59; x 3.46; y 5.66; z 8.00;
Correct Identification

Doing comparisons against character w...
@ 7.21; a 5.66; b 5.83; c 8.00; d 6.00; e 9.90; f 9.80; g 5.66; h 3.74; i 15.43; j 12.41
k 7.21; l 10.68; m 9.49; n 4.90; o 4.47; p 7.35; q 4.90; r 6.32; s 8.00; t 15.17; u 3.46
v 3.74; w 8.83; x 6.16; y 8.83; z 10.49;
INCORRECT IDENTIFICATION

Doing comparisons against character x...
@ 4.69; a 4.69; b 4.69; c 4.47; d 4.24; e 7.62; f 8.60; g 4.00; h 6.63; i 10.58; j 8.00
k 4.47; l 8.72; m 10.39; n 6.48; o 3.16; p 6.48; q 2.83; r 4.69; s 3.74; t 11.14; u 4.69
v 3.46; w 10.39; x 0.00; y 5.29; z 6.00;
Correct Identification

Doing comparisons against character y...
@ 5.66; a 6.16; b 7.48; c 6.16; d 6.48; e 7.75; f 7.62; g 6.32; h 9.17; i 7.75; j 6.78
k 6.32; l 9.38; m 11.31; n 8.83; o 6.78; p 6.00; q 5.66; r 6.63; s 4.69; t 7.75; u 8.12
v 5.66; w 12.17; x 5.29; y 0.00; z 5.66;
Correct Identification

Doing comparisons against character z...
@ 6.48; a 6.48; b 6.16; c 7.07; d 6.78; e 5.66; f 8.12; g 5.66; h 8.25; i 9.59; j 8.60
k 7.21; l 9.38; m 12.08; n 8.60; o 6.78; p 7.21; q 6.63; r 6.16; s 5.10; t 10.00; u 7.87
v 7.21; w 12.08; x 6.63; y 6.00; z 4.47;
Correct Identification

Font Comparison Results

For comarisons of one font against another, the results were fairly poor.

15 correct out of 27
8 correct only because the bitmaps were coincidentally identical in the two fonts
Mistakes not rational from human perspective;
- places where mistakes would have been expected (i.e. "Z" verses "Z") it worked correctly;
- places where mistakes were made had odd results, such as confusing "L" with "C" or "D" with "S".

For comarisons of different characters in the same font, the results were fairly good.

The distance between different characters tended to be large
The algorithm is tolerant to small amounts of noise

Character Horizontal / Vertical Projection Construction

(runs on a C64 or C128 in C64 mode)

2000 rem construct the horizontal / vertical data from c64 rom
2001 print "Constructing horizontal / vertical matrixes..."
2002 for t=. to 26: printchr$(t+64)" ";
2005 n(t,8)=.: n(t,9)=.: n(t,10)=.: n(t,11)=.
2006 n(t,12)=.: n(t,13)=.: n(t,14)=.: n(t,15)=.:
     for tt=. to 7: n(t,tt)=.
2020 if m(t,tt) and 128 then n(t,tt)=1: n(t,8)=n(t,8)+1
2021 if m(t,tt) and 64 then n(t,tt)=n(t,tt)+1: n(t,9)=n(t,9)+1
2022 if m(t,tt) and 32 then n(t,tt)=n(t,tt)+1: n(t,10)=n(t,10)+1
2023 if m(t,tt) and 16 then n(t,tt)=n(t,tt)+1: n(t,11)=n(t,11)+1
2024 if m(t,tt) and 8 then n(t,tt)=n(t,tt)+1: n(t,12)=n(t,12)+1
2025 if m(t,tt) and 4 then n(t,tt)=n(t,tt)+1: n(t,13)=n(t,13)+1
2026 if m(t,tt) and 2 then n(t,tt)=n(t,tt)+1: n(t,14)=n(t,14)+1
2027 if m(t,tt) and 1 then n(t,tt)=n(t,tt)+1: n(t,15)=n(t,15)+1
2040 next
2080 next: print
2090 return

Fourier Representations

The normal Discrete Fourier Transform:

Fourier Transform formula

The version used by Bourbakis & Gumahad (obtained by using the trapezoidal rule on the Continuous Fourier Transform):

B&G's Fourier Transform formula

This is probably supposed to represent:

Another Fourier Transform formula

Which should in theory reduce to:

Reduced Fourier Transform formula

Pattern Recognition

	Copyright © 1992 E. W. Brown, feneric@ccs.neu.edu, NU Note that Feneric is now more apt to be found through either Saugus.net or BU