Non Differentiable Optimization Applied to Min-Max Gradient Surface Reconstruction

D'AMATO JUAN PABLO; PARENTE LISANDRO; LOTITO PABLO; ARAGONE LAURA

Buenos Aires

Conferencia; IFIP TC 7 Conference on System Modeling and Optimization; 2009

In this work we study surface reconstruction as a kind of interpolation of given data at some points in a 2D-grid. The application we have in mind is river bed reconstruction from batimetry. The knowledge of the river bed surface is very important in many applications as the study of sedimentary processes and the design of optimal navigation routes. In order to obtain the interpolated data at the non measured grid points we solve the optimization problem of minimizing a criterium that depends on the missing heights. The objective function we study here is the global maximum of the gradient norm. More precisely we minimize the maximum for every mesh point of the norm of the gradient. As the objective function is the maximum of many functions, it is a non differentiable function, and to numerically solve the problem we apply a bundle like algorithm (see [1, 2]) we devised for this case. Typically, when we set the river in a n × n grid, the rate of points outside the river is high and no interest is given to these points. In order to reduce the computational cost we preprocess the data to decide whether a grid point belongs to the river. This is accomplished with a growing like method. We present the numerical results obtained with real data. We present the numerical results obtained with real data. n × n grid, the rate of points outside the river is high and no interest is given to these points. In order to reduce the computational cost we preprocess the data to decide whether a grid point belongs to the river. This is accomplished with a growing like method. We present the numerical results obtained with real data.