c++ - How to determine the area of a polygon in an Image -

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if having convex polygon vertices, area calculation in image not coming accurate standard formula.

(for simiplicity) if having 3x3 square, , vertices (1,1) (1,3) (3,3) (3,1)

enter image description here

by polygon area calculation method depicted here

enter image description here

and dividing summation 2 area.

so 3 x 3 data above, we'll area 4 instead of 9.

enter image description here

this happening because vertices not points pixel.

this corresponding code. coordinates cyclic.

int x[] = { 1, 1, 3, 3, 1}; int y[] = { 1, 3, 3, 1, 1}; double sum1 = 0; double sum2 = 0; int numelements = 5;      (int k = 0; k < numelements-1; k++)     {         sum1 += x[k] * y[k + 1];         sum2 += y[k] * x[k + 1];     }      double area = std::abs((double)(sum1 - sum2))/2;

for square, can +1 width , height , area correct. irregular polygons in image? hope question makes sense.

if don't want work pixel corners vertices, consider next method (works simple figures - convex ones, concave ones):

enter image description here

add additional fake pixel @ right side of every right-border pixel, @ bottom side of every bottom-border pixel, @ right-bottom of right-bottom corner pixel. here gray pixels initial, light blues ones - fake.


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