Modified support theorem and its application in estimation of vessel cross-sectional shape

Modified support theorem is proposed and applied to estimate vessel cross-sectional shape from noisy data. Based on the fact that the boundary of regular convex set is smooth, a kind of prior information λ is defined which describes the minimum local smoothness of the boundary. At the same time, λ will decrease with the increase of the number of support values. Considering prior information λ, one can get a modified support theorem that enforces the constraint of support vector. Under the constraint of modified support theorem, a maximum likelihood estimation form of vessel cross-sectional shape is constructed which can be solved by quadratic programming methods. Experimental results show that the modified support theorem can improve estimation precision.