Image processing: flows under min/max curvature and mean curvature
Graphical Models and Image Processing
Shapes and geometries: analysis, differential calculus, and optimization
Shapes and geometries: analysis, differential calculus, and optimization
Minimizing within Convex Bodies Using a Convex Hull Method
SIAM Journal on Optimization
The Flexible, Extensible and Efficient Toolbox of Level Set Methods
Journal of Scientific Computing
Approximating optimization problems over convex functions
Numerische Mathematik
Hi-index | 0.00 |
We consider a shape identification problem of growing crystals. The shape of the crystal is to be constructed from a single interferometer measurement. This is an ill-posed inverse problem. The forward problem of interferogram from shape is injective if we restrict the problem to convex shapes with known boundary. The problem is formulated as a shape optimization problem. Our aim is to solve this numerically using the gradient descent method. In the numerical computations of this paper we study the behavior of the approach in simplified cases. Using H 1-gradients (inner products) acts as a regularization method. Methods for enforcing the convexity of shapes are discussed.