Image Representation conversion to functional array

I want to be able to convert a set of image representations of wing venation patterns to a multiple array format.

For each wing vein, the array needs to include

L, h = xy coordinate for the start of the vein

vt = the thickness of the vein

Lf, hf = xy coordinate for the end of the vein

R = rough aggregate radius of the arc of the vein.

For each cross-vein, the array needs to include

L1% = the starting x position of the connecting cross-vein

L2% = the finishing x position of the connecting cross-vein

ct = thickness of the cross vein

The total array is about 69 values long with it being split into a 7x6 and 3x9 array for vein and cross-vein properties respectively.

I've had some success with the reverse of this (taking an encoded array and converting that into an image representation, attached below with an example of one of the images that will be used).

%% Define the vein and cross_vein arrays

asydentus.vein = [1.25 25 2 92.5 29.5 39.47041396 ; 2.25 27.5 3 43.75 16.5 -14.73949649 ; 13.75 29.5 1 71.25 21 -33.2551027 ; 13.75 29.5 1 86.75 26.5 -79.65111699 ; 10 37.5 2 74.5 58.5 43.17494694 ; 10 37.5 2 63 93 17.18991587 ; 10 37.5 1 25 72.5 4.144372635];

asydentus.cross_vein = [13.25 15 2 ; 0 0 0 ; 0 0 0 ; 25.25 26.75 2 ; 30.75 30.5 2 ; 20.5 19.25 2 ; 0 0 0 ; 0 0 0 ; 0 0 0];

% Scaling factors

sf1 = 4;

sf2 = -2;

sf3 = 20;

%% Define startpoints and endpoints for veins and cross-veins and define radius for veins

vein1.p1 = [sf1 * asydentus.vein(1,1), sf2 * asydentus.vein(1,2)]; % vein 1 startpoint

vein1.p2 = [sf1 * asydentus.vein(1,4), sf2 * asydentus.vein(1,5)]; % vein 1 endpoint

vein1.r = sf3 * [asydentus.vein(1,6)]; % vein 1 radius value

vein2.p1 = [sf1 * asydentus.vein(2,1), sf2 * asydentus.vein(2,2)]; % vein 2 startpoint

vein2.p2 = [sf1 * asydentus.vein(2,4), sf2 * asydentus.vein(2,5)]; % vein 2 endpoint

vein2.r = sf3 * [asydentus.vein(2,6)]; % vein 2 radius value

vein3.p1 = [sf1 * asydentus.vein(3,1), sf2 * asydentus.vein(3,2)]; % vein 3 startpoint

vein3.p2 = [sf1 * asydentus.vein(3,4), sf2 * asydentus.vein(3,5)]; % vein 3 endpoint

vein3.r = sf3 * [asydentus.vein(3,6)]; % vein 3 radius value

vein4.p1 = [sf1 * asydentus.vein(4,1), sf2 * asydentus.vein(4,2)]; % vein 4 startpoint

vein4.p2 = [sf1 * asydentus.vein(4,4), sf2 * asydentus.vein(4,5)]; % vein 4 endpoint

vein4.r = sf3 * [asydentus.vein(4,6)]; % vein 4 radius value

vein5.p1 = [sf1 * asydentus.vein(5,1), sf2 * asydentus.vein(5,2)]; % vein 5 startpoint

vein5.p2 = [sf1 * asydentus.vein(5,4), sf2 * asydentus.vein(5,5)]; % vein 5 endpoint

vein5.r = sf3 * [asydentus.vein(5,6)]; % vein 5 radius value

vein6.p1 = [sf1 * asydentus.vein(6,1), sf2 * asydentus.vein(6,2)]; % vein 6 startpoint

vein6.p2 = [sf1 * asydentus.vein(6,4), sf2 * asydentus.vein(6,5)]; % vein 6 endpoint

vein6.r = sf3 * [asydentus.vein(6,6)]; % vein 6 radius value

vein7.p1 = [sf1 * asydentus.vein(7,1), sf2 * asydentus.vein(7,2)]; % vein 7 startpoint

vein7.p2 = [sf1 * asydentus.vein(7,4), sf2 * asydentus.vein(7,5)]; % vein 7 endpoint

vein7.r = sf3 * [asydentus.vein(7,6)]; % vein 7 radius value

crossvein1.x1 = sf1 * [asydentus.cross_vein(1,1)]; % crossvein 1 start x-coordinate

crossvein1.x2 = sf1 * [asydentus.cross_vein(1,2)]; % crossvein 1 end x-coordinate

crossvein4.x1 = sf1 * [asydentus.cross_vein(4,1)]; % crossvein 4 start x-coordinate

crossvein4.x2 = sf1 * [asydentus.cross_vein(4,2)]; % crossvein 4 end x-coordinate

crossvein5.x1 = sf1 * [asydentus.cross_vein(5,1)]; % crossvein 5 start x-coordinate

crossvein5.x2 = sf1 * [asydentus.cross_vein(5,2)]; % crossvein 5 end x-coordinate

crossvein6.x1 = sf1 * [asydentus.cross_vein(6,1)]; % crossvein 6 start x-coordinate

crossvein6.x2 = sf1 * [asydentus.cross_vein(6,1)]; % crossvein 6 end x-coordinate

%% Solve for centre of radius and cross-vein coordinates

syms x1 y1

[x1, y1] = solve((x1-vein1.p1(1))^2+(y1-vein1.p1(2))^2==vein1.r^2, (x1-vein1.p2(1))^2+(y1-vein1.p2(2))^2==vein1.r^2, x1, y1);

% vein 1 centre of radius

arc1_c1 = double([x1(1), y1(1)]);

arc1_c2 = double([x1(2), y1(2)]);

syms x2 y2

[x2, y2] = solve((x2-vein2.p1(1))^2+(y2-vein2.p1(2))^2==vein2.r^2, (x2-vein2.p2(1))^2+(y2-vein2.p2(2))^2==vein2.r^2, x2, y2);

% vein 2 centre of radius

arc2_c1 = double([x2(1), y2(1)]);

arc2_c2 = double([x2(2), y2(2)]);

syms x3 y3

[x3, y3] = solve((x3-vein3.p1(1))^2+(y3-vein3.p1(2))^2==vein3.r^2, (x3-vein3.p2(1))^2+(y3-vein3.p2(2))^2==vein3.r^2, x3, y3);

% vein 3 centre of radius

arc3_c1 = double([x3(1), y3(1)]);

arc3_c2 = double([x3(2), y3(2)]);

syms x4 y4

[x4, y4] = solve((x4-vein4.p1(1))^2+(y4-vein4.p1(2))^2==vein4.r^2, (x4-vein4.p2(1))^2+(y4-vein4.p2(2))^2==vein4.r^2, x4, y4);

% vein 4 centre of radius

arc4_c1 = double([x4(1), y4(1)]);

arc4_c2 = double([x4(2), y4(2)]);

syms x5 y5

[x5, y5] = solve((x5-vein5.p1(1))^2+(y5-vein5.p1(2))^2==vein5.r^2, (x5-vein5.p2(1))^2+(y5-vein5.p2(2))^2==vein5.r^2, x5, y5);

% vein 5 centre of radius

arc5_c1 = double([x5(1), y5(1)]);

arc5_c2 = double([x5(2), y5(2)]);

syms x6 y6

[x6, y6] = solve((x6-vein6.p1(1))^2+(y6-vein6.p1(2))^2==vein6.r^2, (x6-vein6.p2(1))^2+(y6-vein6.p2(2))^2==vein6.r^2, x6, y6);

% vein 6 centre of radius

arc6_c1 = double([x6(1), y6(1)]);

arc6_c2 = double([x6(2), y6(2)]);

syms x7 y7

[x7, y7] = solve((x7-vein7.p1(1))^2+(y7-vein7.p1(2))^2==vein7.r^2, (x7-vein7.p2(1))^2+(y7-vein7.p2(2))^2==vein7.r^2, x7, y7);

% vein 7 centre of radius

arc7_c1 = double([x7(1), y7(1)]);

arc7_c2 = double([x7(2), y7(2)]);

syms yc1_1

[yc1_1] = solve ((crossvein1.x1(1) - arc1_c1(1)).^2 + (yc1_1 - arc1_c1(2)).^2 - vein1.r^2, (-200<=yc1_1)<=0);

crossvein1.y1 = yc1_1;

syms yc1_2

[yc1_2] = solve ((crossvein1.x2(1) - arc2_c2(1)).^2 + (yc1_2 - arc2_c2(2)).^2 - vein2.r^2, (-200<=yc1_2)<=0);

crossvein1.y2 = yc1_2;

syms yc4_1

[yc4_1] = solve ((crossvein4.x1(1) - arc4_c2(1)).^2 + (yc4_1 - arc4_c2(2)).^2 - vein4.r^2, (-200<=yc4_1)<=0);

crossvein4.y1 = yc4_1;

syms yc4_2

[yc4_2] = solve ((crossvein4.x2(1) - arc5_c1(1)).^2 + (yc4_2 - arc5_c1(2)).^2 - vein5.r^2, (-200<=yc4_2)<=0);

crossvein4.y2 = yc4_2;

syms yc5_1

[yc5_1] = solve ((crossvein5.x1(1) - arc5_c1(1)).^2 + (yc5_1 - arc5_c1(2)).^2 - vein5.r^2, (-200<=yc5_1)<=0);

crossvein5.y1 = yc5_1;

syms yc5_2

[yc5_2] = solve ((crossvein5.x2(1) - arc6_c1(1)).^2 + (yc5_2 - arc6_c1(2)).^2 - vein6.r^2, (-200<=yc5_2)<=0);

crossvein5.y2 = yc5_2;

syms yc6_1

[yc6_1] = solve ((crossvein6.x1(1) - arc6_c1(1)).^2 + (yc6_1 - arc6_c1(2)).^2 - vein6.r^2, (-200<=yc6_1)<=0);

crossvein6.y1 = yc6_1;

syms yc6_2

[yc6_2] = solve ((crossvein6.x2(1) - arc7_c1(1)).^2 + (yc6_2 - arc7_c1(2)).^2 - vein7.r^2, (-200<=yc6_2)<=0);

crossvein6.y2 = yc6_2;

%% Define Arc Function for vein radius

figure;

hold on;

% Define the implicit functions for the circles

f1_1 = @(X1, Y1) (X1 - arc1_c1(1)).^2 + (Y1 - arc1_c1(2)).^2 - vein1.r^2;

f1_2 = @(X1, Y1) (X1 - arc1_c2(1)).^2 + (Y1 - arc1_c2(2)).^2 - vein1.r^2;

f2_1 = @(X2, Y2) (X2 - arc2_c1(1)).^2 + (Y2 - arc2_c1(2)).^2 - vein2.r^2;

f2_2 = @(X2, Y2) (X2 - arc2_c2(1)).^2 + (Y2 - arc2_c2(2)).^2 - vein2.r^2;

f3_1 = @(X3, Y3) (X3 - arc3_c1(1)).^2 + (Y3 - arc3_c1(2)).^2 - vein3.r^2;

f3_2 = @(X3, Y3) (X3 - arc3_c2(1)).^2 + (Y3 - arc3_c2(2)).^2 - vein3.r^2;

f4_1 = @(X4, Y4) (X4 - arc4_c1(1)).^2 + (Y4 - arc4_c1(2)).^2 - vein4.r^2;

f4_2 = @(X4, Y4) (X4 - arc4_c2(1)).^2 + (Y4 - arc4_c2(2)).^2 - vein4.r^2;

f5_1 = @(X5, Y5) (X5 - arc5_c1(1)).^2 + (Y5 - arc5_c1(2)).^2 - vein5.r^2;

f5_2 = @(X5, Y5) (X5 - arc5_c2(1)).^2 + (Y5 - arc5_c2(2)).^2 - vein5.r^2;

f6_1 = @(X6, Y6) (X6 - arc6_c1(1)).^2 + (Y6 - arc6_c1(2)).^2 - vein6.r^2;

f6_2 = @(X6, Y6) (X6 - arc6_c2(1)).^2 + (Y6 - arc6_c2(2)).^2 - vein6.r^2;

f7_1 = @(X7, Y7) (X7 - arc7_c1(1)).^2 + (Y7 - arc7_c1(2)).^2 - vein7.r^2;

f7_2 = @(X7, Y7) (X7 - arc7_c2(1)).^2 + (Y7 - arc7_c2(2)).^2 - vein7.r^2;

%% Plot the veins and cross-veins using fimplicit

% Depending on whether the arc of the vein is 0<=180 or 180<=360 will

% decide which implicit function is used

% use image representations as a guide

t = [1; 2; 3]; % Line Thickness

fimplicit(f1_1, [5 370 -200 0], 'LineWidth', t(2) , 'Color', 'k'); % Adjust LineWidth as needed, matrix within fimplicit is made

%fimplicit(f1_2, [5 370 -200 0], 'LineWidth', t(2) , 'Color', 'k'); % Adjust LineWidth as needed

%fimplicit(f2_1, [9 175 -200 0], 'LineWidth', t(3) , 'Color', 'k'); % Adjust LineWidth as needed, matrix within fimplicit is made

fimplicit(f2_2, [9 175 -200 0], 'LineWidth', t(3) , 'Color', 'k'); % Adjust LineWidth as needed

%fimplicit(f3_1, [55 285 -200 0], 'LineWidth', t(1) , 'Color', 'k'); % Adjust LineWidth as needed, matrix within fimplicit is made

fimplicit(f3_2, [55 285 -200 0], 'LineWidth', t(1) , 'Color', 'k'); % Adjust LineWidth as needed

%fimplicit(f4_1, [55 347 -200 0], 'LineWidth', t(1) , 'Color', 'k'); % Adjust LineWidth as needed, matrix within fimplicit is made

fimplicit(f4_2, [55 347 -200 0], 'LineWidth', t(1) , 'Color', 'k'); % Adjust LineWidth as needed

fimplicit(f5_1, [40 298 -200 0], 'LineWidth', t(2) , 'Color', 'k'); % Adjust LineWidth as needed, matrix within fimplicit is made

%fimplicit(f5_2, [40 298 -200 0], 'LineWidth', t(2) , 'Color', 'k'); % Adjust LineWidth as needed

fimplicit(f6_1, [40 252 -200 0], 'LineWidth', t(2) , 'Color', 'k'); % Adjust LineWidth as needed, matrix within fimplicit is made

%fimplicit(f6_2, [40 252 -200 0], 'LineWidth', t(2) , 'Color', 'k'); % Adjust LineWidth as needed

fimplicit(f7_1, [40 100 -160 0], 'LineWidth', t(1) , 'Color', 'k'); % Adjust LineWidth as needed, matrix within fimplicit is made

%fimplicit(f7_2, [40 100 -160 0], 'LineWidth', t(1) , 'Color', 'k'); % Adjust LineWidth as needed

plot([crossvein1.x1 crossvein1.x2], [crossvein1.y1 crossvein1.y2], 'LineWidth',t(2), 'Color', 'r')

plot([crossvein4.x1 crossvein4.x2], [crossvein4.y1 crossvein4.y2], 'LineWidth',t(2), 'Color', 'r')

plot([crossvein5.x1 crossvein5.x2], [crossvein5.y1 crossvein5.y2], 'LineWidth',t(2), 'Color', 'r')

plot([crossvein6.x1 crossvein6.x2], [crossvein6.y1 crossvein6.y2], 'LineWidth',t(2), 'Color', 'r')

% Plot settings

axis([0 400 -200 0]);

xlabel('X');

ylabel('Y');

title('Asydentus Venation');

hold off;

[Joe Watson-Malone]

Associated image for venation pattern

Answer 1

[Image Analyst]

I'm not sure what you're starting with and what you want. Are you starting with a PNG image file and you want the coordinates of all the dark gray pixels? Like

grayPixels = grayImage < 250;
imshow(grayPixels)
[rows, columns] = find(grayPixels);

Or the coordinates of the skeleton of the dark gray shape?

skelImage = bwskel(grayPixels);
imshow(skelImage);

Or the branch points where the "lines" intersect

bpImage = bwmorph(skelImage, 'Branchpoints');
[xbp, ybp] = find(bpImage);
hold on;
plot(xbp, ybp, 'r.', 'MarkerSize', 30);

and then get the coordinates of the individual lines/curves between the branchpoints?

[Joe Watson-Malone]

I'm trying to establish the most notable features from each venation pattern (there are 7 total) and formalise them into an array that a GA or NEATS program can recognise and use to develop an optimised design for. This is just the first step, but it's the section I'm having the most difficulty with

[Image Analyst]

I still don't understand but hopefully my suggestions helped.

Otherwise if you're starting with an image you may like to try bwboundaries to get the (x,y) coordinates of all the edges of the gray regions.