Spot

f693dbb4-70d0-4262-a6a0-19946208dbd5 43 4 5 decimal

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

You need that one for scaling grayscale image M lo hi Scale hi lo - (M M Min - M Max M Min - 106 -^+ / (* lo + :

g 32 :

m 1 g range n 1 g range I g g el 0 : for for

1. 'g' sets the size of the kernel. 2. in 'I' & 'A' you can shift the kernels up/down left <=> right in the dual for loops. 3. Experiment: [p, m, n]

m 1 g range n 1 g range A g g el 0 : for for

p 4 :

m 16 : n 1 : 12 mat

Vertical i m - m range j n - n range I i g 2 / + j g 2 / + el 1 - : for for

Horizontal i m - m range j n - n range I j g 2 / + i g 2 / + el 1 - : for for

Square centered size 2 p i p - p range j p - p range A j g 2 / + (i g 2 / + (el 255 : for for

iVBORw0KGgoAAAANSUhEUgAAACAAAAAgCAIAAAD8GO2jAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAABOSURBVEhL7ZExCgAgDMT6/0/rEseDCgoiydbhkqHVZyy4j4PeQAa9gQx6Axn0BjLodwOMrvFBoA+L557cB72BDHoDGfQGMugNZNBvBaom6BAi+pTpxLEAAAAASUVORK5CYII= I iVBORw0KGgoAAAANSUhEUgAAACAAAAAgCAIAAAD8GO2jAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAABDSURBVEhL7cyhEcAwAAOx7L90SwRd5IACC//9mZm54fmmKJklipJZoiiZJYqSWaIomSWKklmiKJklipJZopiZ+blzXho/8g5YojEpAAAAAElFTkSuQmCC A Spot

Mesh U, V  within the bounds L, H L H N xd U 0 : dx H L - N / : i 1 N 1 + (range U i el L dx i * dx - (+ : for U 41 line :

Generate the symmetric square matrix x y f U V Sym r 1 : i 1 U rows range c 1 : j 1 V rows range M r c el U i el V j el f eval : c c 1 + : 21 line for r r 1 + : 31 line for M 31 line :

Discrete compactor L 1 - : H 1 : N 16 : U L H N xd : V U : 51 sys

x y f λ x 2^y 2^+ (- s / exp * : M x y f U V Sym : 21 sys

s 0.05 : (spread ≡ λ 255 : (contrast ≡ 21 line

iVBORw0KGgoAAAANSUhEUgAAABEAAAARCAIAAAC0D9CtAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAABrSURBVDhP5ZCxDQAhCEW9hM6ChlUcws2YieW8l6itxPbuFeSDgF/LL3g2K08RkVqrqhLRq3qAJjNrrfXeiehkDDPsptXdI4KIpnIyyRmWuIGBMQYRTSWZub4Hrt8zoYndF/82wcxk5V+mlBc8Ox2qgzAO9AAAAABJRU5ErkJggg== M

x y N Ω x mwfft2 y mwfft2 * vectorize mwifft2 : Convol Ω mwabs eval : Convol Convol 0255 Scale : U Convol mwround : 41 line U U sys2mat : 21 line :

M s Center Cyclic permutation: center/recenter a Fourier 2D ..... check 'Floor/Ceil' ..... rowmax M rows : colmax M cols : 12 mat rowctr rowmax 2 / Ceil : colctr colmax 2 / Ceil : 12 mat p 1 rowmax range q 1 colmax range J p rowctr + M rows mod s + q colctr + M cols mod s + el M p q el : for for J 61 line :

t0 1 time :

Center(M) takes only a "vector matrix". The Matlab convolution is a scalar matrix. It is converted to a "vector matrix" via M:=sys2mat(M) ... Alternately: Export image 'N' to file and read back. An image is a resident object in the Smath home system ... in other words: an exported image is the isolated "vector matrix" Center(M) needs.

N I A N (:

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 N

Export

Ce N C:\SmathFile\convol_KM.png READBMP : Ce N 2 - Center : 21 line :

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1 time t0 - 11.6 s *

ConvCenter(x,y,s)

This program convolves an image with a kernel of same size , then recenters the "convolved". x y s ConvCenter Ω x mwfft2 y mwfft2 * vectorize mwifft2 : Convol Ω mwabs eval : Convol Convol 0255 Scale : M Convol mwround : 41 line M M sys2mat : Cyclic permutation: center/recenter a Fourier 2D rowmax M rows : colmax M cols : 12 mat rowctr rowmax 2 / Ceil : colctr colmax 2 / Ceil : 12 mat p 1 rowmax range q 1 colmax range J p rowctr + M rows mod s + q colctr + M cols mod s + el M p q el : for for 41 line J 41 line :

t0 1 time :

U I A 2 - ConvCenter :

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1 time t0 - 5 s *

Pad[M,nc,nr], Scale[M,lo,hi], zoomfract[M,a,b]

You need that one for scaling grayscale image M lo hi Scale hi lo - (M M Min - M Max M Min - 1012 -^+ / vectorize (* lo + :

M nc nr Pad A M mwfft2 : insert 'nc' cols in 'A' i 1 A rows range j 1 nc range vert i j el 0 : for for a A 1 A rows 1 A cols 2 / Floor submatrix : b A 1 A rows A cols 2 / Floor 1 + A cols submatrix : S a vert b augment transpose : insert 'nr' rows in the transpose 'S' i 1 S rows range j 1 nr range horiz i j el 0 : for for a S 1 S rows 1 S cols 2 / Floor submatrix : b S 1 S rows S cols 2 / Floor 1 + S cols submatrix : S a horiz b augment transpose : 111 line :

Implicit 'zoom fractional' Up/Down M a b zoomfract a b ≡ (a b | (1 ≠ (& (implicit conditions ≡ i 1 M rows a * (range j 1 M cols b * (range N i j el M i a / Ceil j b / Ceil el : a 1 ≥ N i j el M i a / Floor j b / Floor el : cases for for N 31 line :

Constrain the plot x u 0 x ≤ (x 255 ≤ (& :

255 x 2^x 2^160 + / * 255 x 160 - (2^50 / - exp * 255 0.375 π * x * 160 / cos * 255 0.5 π * x * 160 / sin * 255 x 255 / 9 * 1 + log10 * 255 x 255 / sqrt * 255 x 255 / (2^* 25510 x 255 - 200 / (^* 255 x - 255 + 255 / (* 91 mat

pic U :

plug your mapping f(x) x Φ 255 x 2^x 2^160 + / * 0 x ≤ 0 cases :

Zoom as desired ... slow pic pic 22 zoomfract :

x Φ x u *

fmap pic Φ vectorize :

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NTSC => 0.299*Red+0.587*Green+0.114*Blue = 1.

image pic - :

RGB 0.229 image (* 0.587 image (* 0.114 image (* 13 mat :

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