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Pitiot A, Toga AW, Thompson PM (2002) Adaptive elastic segmentation of brain MRI via Shape-model-guided evolutionary programming. IEEE Trans Med Imaging 21(8):910–923 55. Behiels G, Maes F, Vandermeulen D, Suetens P (2002) Deformable evaluation of image features and search strategies for segmentation of bone structures in radiographs using active shape models. Med Image Anal 6(1):47–62 56. Davatzikos C, Tao X, Shen D (2003) Hierarchical active shape models, using the wavelet transform. IEEE Trans Med Imaging 22(3):414–423 57.

IEEE Trans Image Process 16(1): 153–161 49. Duta N, Sonka M (1998) Segmentation and interpretation of MR brain images: an improved active shape model. IEEE Trans Med Imaging 17(6):1049–1062 50. Shen D, Herskovits EH, Davatzikos C (2001) An adaptive-focus statistical shape model for segmentation and shape modeling of 3-D brain structures. IEEE Trans Med Imaging 20(4): 257–270 51. Tao X, Prince JL, Davatzikos C (2002) Using a statistical shape model to extract sulcal curves on the outer cortex of the human brain.

MŠ, the integer index m being generalized into a real number in the interval M ¼ ½1; MŠto 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.

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