Let R be the region of interest on the 2D image and it is tessellated by set of unit triangles T={T_i}. By unit triangle we refer to isosceles right triangle that the two equal sides have one pixel distance (4-connected neighbors). The area of the region of interest can be computed as the sum of partial areas of the unit triangles in 3D. Let { a_i , b_i , c_i } be the 3D coordinates of the three points of unit triangle T_i . The 3D area of this triangle is

and the total area of R is:

Where (‖ … ‖) and ( x ) refer to the magnitude and cross product, respectively.

Consider that a_i , b_i and c_i are the 3D coordinates not the 2D indices of the unit triangle points on the image.