Gray

e5abe9b9-165a-4f36-bfdc-fbd87f1a6cf1 9 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

Gray

Gray 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mat :

Digitize image ... all modules Numeric

λ 0 :

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 Gray

Convert existing gray pixels to black N i 1 Gray rows range j 1 Gray cols range N i j el 0 Gray i j el λ ≤ 255 cases : for for N 21 line :

Gray Min Gray Max 21 mat 025521 mat

isolate N N :

Extract black pixels r N rows : c N cols : k 1 : i 1 c range j 1 r range N j i el 1 ≤ X k el i : Y k el r j - : k k 1 + : 31 line No pixel if for for 41 line

NOTES ... Hard to imagine someone dared publish that kind of crappy graph ! Once digitize, clean/smooth further, not offered

XY X Y augment :

Raw extraction to be cleaned

data StripX strip/nest repeated X u data 1 col : v data 2 col : k 0 : i 1 data rows 1 - (range u i 1 + el u i el - 0 ≠ R k k 1 + : el u i el v i el 12 mat : 11 line StripX done if 11 line for Un-nest R v R 1 el : j 2 R rows range v v R j el stack : for v 91 line :

stripped of repeated X xy XY StripX :

XY rows xy rows 21 mat 39319221 mat

XY 330329430429530529630629730729102 mat

Digitized ... cleaned

xy 2 1 sys

xy xy rows row 194212 mat

x f xy 1 col xy 2 col x cinterp :

x λ 10 x ≤ (x 194 ≤ (& cases :

x f x λ * ksmooth ... plotG

vx vy char size color plotG n vx length : plot vx 1 el vy 1 el char size color augment : i 2 n range plot plot vx i el vy i el char size color augment stack : for plot 41 line :

σ 0.3708158988058244 :

The Gaussian ksmooth

x K 12 π * sqrt σ * / x 2^2 σ 2^* / - exp * :

Smath recognises the silent 'bw', something
like the Mathcad "global definition". j X Y Ksmooth X i el X j el - bw / K Y i el * (i 1 X rows sum X i el X j el - bw / K (i 1 X rows sum / :

Gaussian Ksmooth Kernel

x K

X Y bw 13 mat

W W 0 : j 1 X rows range s j el j X Y Ksmooth eval : s Y rows el Y Y rows el : 21 line for s 31 line :

W 11 mat

raw

raw 32942952962972982992910291129122913291429152916291729182919292029212922292329242925292629272928292929302931293229332934293529362937293829392940294129422943294429452946294729482949295029512952295329542955295629572958295929602961296229632964296529662967296829692970287128722873287428752876287728782879288028812782278327842785278627872788278927902691269226932694269526962697259825992510025101251022510325104241052410624107241082410924110231112311223113231142311522116221172211822119221202112121122211232112421125201262012720128201291913019131191321913319134181351813618137181381713917140171411714216143161441614516146151471514815149141501415114152141531215412155121561215712158121591216012161111621116311164101651016610167101689169917091718172817381748175717671777178617961806181618251835184518541864187418841893190319131922193219421922 mat :

data n Decimate collect every 'n' pairs range 1 data rows n range : k 1 : i range u k el data i 1 el : v k el data i 2 el : k k 1 + : 31 line for u v augment 31 line 31 line :

XY raw 10 Decimate :

Prepare and code the Smath project

t0 1 time :

X XY 1 col : Y XY 2 col : 21 line

bw 20 : (bandwidth ≡ W W : (isolate W ≡ XW X W augment : 31 line

W 11 mat

XW 329122921293029392948 28.999 57 28.973 66 28.715 75 27.973 84 26.999 93 25.973 102 24.715 111 22.973 120 20.999 129 18.999 138 16.974 147 14.742 156 12.257 165 9.999 174 7.722 183 5.135 1922222 mat

Original XY : XW X W . 10 red plotG : raw X Y + 7 black plotG : 31 line

collect plot plot Original XW 21 sys :

===== Finish/collect the project =====

raw=>raw data, XW=>smoothed data

plot

1 time t0 - 3 s *