The dissertation presents a constrained optimization approach to contour energy minimization problems for deformable contour methods. The approach introduces a constraint of region features into the boundary based contour energy minimization framework. In this approach, the contour energy to be minimized can be arbitrary function characterizing target boundary and the constraint can be functions of any region features characterizing the contour interiors. Three deformable contour methods, respectively derived from evolution strategy, variational method, and divide and conquer approaches are proposed to solve the constrained contour energy minimization problem. Among the three deformable contour methods, evolution strategy iteratively generates a population of contour individuals by adding stochastic perturbations to contour evolutions and selects the optimal solutions; Variational method takes a Lagrange approach and minimizes the Lagrange function by a derivative based approach; Divide and conquer approach divides the contour into segments, and then iteratively deforms each contour segment under the region constraint and select the contour with minimum contour energy. The methods are successfully applied to MRI brain, ultrasound pig heart, CT abdominal, and microscopic blood cell images with contours having gaps, blur segments, complex shape, and inhomogeneous interiors. More favorable results comparing to other conventional deformable contour methods are also demonstrated.
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