Rebol R3 skeleton

Using erode and dilate is similar to OpenCV morphologyEx (not supported by Rebol 3) 

#!/usr/local/bin/r3
Rebol [
]
;--all images are binary with 1 channel
;--using erode and dilate is similar to OpenCV morphologyEx (not supported by Rebol 3)
cv: import opencv
with cv [
    img: imread/with "../images/char.png" IMREAD_GRAYSCALE ;--source image as GS
    threshold :img :img 127 255 THRESH_BINARY ;--binary thresholding
    namedWindow win1: "Source"
    moveWindow win1 0x0
    imshow/name img "Source"
    skel: Matrix [:img/size CV_8UC1] ;--1 channel matrix (8-bit)
    element: getStructuringElement MORPH_CROSS 3x3 -1x-1 ;--structuring element for the kernel
    until [
    eroded: erode :img none element -1x-1 1 ;--erode
    temp: dilate :eroded none element -1x-1 1 ;--then dilate
    subtract :img :temp :temp ;--img source - eroded image
    bitwise-or :skel :temp :skel ;--just OR operator
    img: :eroded ;--update source image
    maxi: second minMaxLoc img ;--get maxi value
    maxi = 0 ;--repeat until maxi = 0
    ]
    namedWindow win2: "Skeleton"
    moveWindow win2 250x0
    imshow/name skel win2
    waitKey 0
    destroyAllWindows
]

Heat diffusion

From https://en.wikipedia.org/wiki/Heat_equation

"In mathematics and physics (more specifically thermodynamics), the heat equation is a parabolic partial differential equation. The theory of the heat equation was first developed by Joseph Fourier in 1822 for the purpose of modeling how a quantity such as heat diffuses through a given region. Since then, the heat equation and its variants have been found to be fundamental in many parts of both pure and applied mathematics". 

The idea is to see how Rebol or Red can solve this problem. Let’s imagine a coin heated at its center at T0.0 and calculate the temperature distribution toward the edges of the coin. We get a nice Gaussian curve.

Now, let’s look at how the phenomenon changes over time (from 0.0 to 0.10). We still see nice Gaussian curves whose mean decreases over time. We can also model the cooling of the metal part. 

Due to vector datatype  (https://github.com/Oldes/Rebol3) these equations are very easy to solve.

#!/usr/local/bin/r3

REBOL [

]

b2d: import 'blend2d ;--use blend2d (draw module)

cv2: import 'opencv ;--use OpenCV for visualisation

;--Global Physical Parameters

k: 0.5 ;--Diffusion coefficient (Thermal diffusivity coefficient of material)

l: 1.0     ;--Domain size

itime: 0.1   ;--Integration time

;--Global Numerical Parameters

nx: 100     ;--Number of grid points

nt: 1000   ;--Number of time steps

dx: l / (nx - 1)   ;--Grid step (Spatial step size: 0.0101010101010101)

dt: itime / nt   ;--Grid step (Time step size :0.0001)

;--Based on Oldes's code

linSpace: func [

    "Generates n linearly spaced numbers from a to b (inclusive)."

    a [number!]  "Start"

    b [number!]  "End"

    n [integer!] "Number of samples"

    /no-end      "Don't include end value in the result"

    /local vec div step i ;--local values

][

    vec: make vector! [f64! :n]

    div: either no-end [n][n - 1]

    step: (b - a) / div

    repeat i n [vec/:i: a + (step * (i - 1))]

    vec

]

;--Initialisation (using global variables)

init: does [

x: linSpace 0.0 1.0 nx ;--linear spacing between 0.0 and 1.0

t: (x * 2.0 * pi) ;--t is a vector

repeat i nx [t/:i: sin t/:i] ;--in radians

;--use blend2d commands in plot block

plot: compose [

font %/System/Library/Fonts/Geneva.ttf

fill black

text 0x10  10 "+1.0"

text 0x204 10 "0"

text 0x390 10 "-1.0"

pen black

line 5x200 410x200 

]

]

;--Heat diffusion equation (using global variables)

diffusion: does [

vect: make vector! [f64! :nx]

posy: 0

n: 0

while [n <= nt] [

j: 2

while [j < nx] [

vect/:j: dt * k * (t/(j - 1) - (2.0 * t/:j) + t/(j + 1)) / (dx ** 2)

++ j

]

repeat j nx [t/:j: t/:j + vect/:j]

;--Plot every 100 time steps

if zero? n % 100 [ 

acolor: random white

posy: posy + 15

either n = 0 [tt: 0.0] [tt: round/to n % (n * dt) 0.001]

tt: ajoin ["time: " tt]  

pos: as-pair 340 posy

append plot reduce ['fill (acolor) 'text (pos) 12 (tt) 'pen (acolor) 'line]

xx: 2

foreach val t [

append plot as-pair xx * 4 200 - (val * 195) 

++ xx 

]

]

++ n

]

]

;************************ Main Program ************************

init 

diffusion

img: b2d/draw 410x400 :plot

img: cv2/resize img 150% 

cv2/imshow/name :img "Heat Diffusion"

print "Any key to close"

cv2/waitKey 0

Using Filter2D with Rebol-OpenCV

 Rebol-OpenCV (https://github.com/Oldes/Rebol-OpenCV) Filter2D is really fantastic for creating various filters on image.

filter2D: [
"Convolves an image with the kernel."
src    [handle!] "cvMat"
dst    [handle! none!] "cvMat"
ddepth [integer!] "desired depth of the destination image"
kernel [handle!] "convolution kernel (or rather a correlation kernel), a single-channel floating point matrix"
anchor [pair! integer!] "position of the anchor within the element"
delta  [number!] "value added to the filtered pixels before storing them in dst"
/border "border mode used to extrapolate pixels outside of the image"
type [integer!] "one of: [0 1 2 4 5 16]"
]

This is an example of creating a Kuwahara_filter

#!/usr/local/bin/r3
Rebol [
]
;--https://en.wikipedia.org/wiki/Kuwahara_filter
cv: import opencv
with cv [
    src: imread/with "../images/mandrill.jpg" -1 ;--(IMREAD_UNCHANGED)
    dst: Matrix :src ;--create a matrix
    ;--using Rebol vector type for a 3x3 kernel
    vec: #(f32! [-0.5 1.5 -0.5 1.5 -3.0 1.5 -0.5 1.5 -0.5]) ;--sum = 1
    filter: Matrix [CV_32FC1 3x3 :vec] ;--a 3x3 kernel
    filter2D :src :dst -1 :filter -1x1 0 ;-1 same image depth
    ;--show result
    imshow/name src "Source"
    imshow/name dst "Kuwahara"
    moveWindow "Source"  0x0
    moveWindow "Kuwahara" 260x0
    waitKey 0
    destroyAllWindows
]

The trick is to use vector datatype implemented by Oldes to create the kernel used by the filter2D function.

The result for the Kuwahara_filter:

You can find here https://github.com/ldci/R3_OpenCV_Samples/tree/main/image_filtering a lot of examples for generating filters on image.