By Ayman S El-Baz; et al
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Extra info for Multi modality state-of-the-art medical image segmentation and registration methodologies Volume 2
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M, the integer index m being generalized into a real number in the interval M ¼ ½1; Mto indicate continuous positions rm from r1 to rM around the curve. 3) m2M where, zint ðrm Þ and zext ðrm Þ denote the internal and external forces, respectively, that control the point-wise movements of the point rm ¼ ðxm ; ym Þ along the curve. The internal energy term keeps the curve as a single continuous unit and the external energy term attracts the model to the goal object boundary. The total internal force is typically defined as zint ðrm Þ ¼ aint jr0m j2 þ bint jr00m j2 , where the weights aint and bint control the curve’s tension and rigidity, respectively, and r0m and r00m denote the first and second derivatives of the curve in the point rm by the positional parameter m.