Using simulated annealing algorithm to move clod boundaries on seedbed digital elevation model

• Refine clods boundaries on a seedbed surface digital elevation model (DEM).
• Definition of new cost function of clod characteristics boundaries.
• Geometric method for estimation of cost function weight.
• Application of simulated annealing for cost function minimization and moving boundary.
• Study of algorithm performance.

A seedbed has a cloddy structure that is highly connected to its random roughness. Identifying and characterizing the clods is thus a preliminary step in surface roughness measurement and modelling. The aim of this paper is to propose an algorithm, based on the simulated annealing optimization, to refine the clod delineation estimated on a seedbed surface Digital Elevation Model (DEM). In our case, the DEM image was recorded on a real seedbed immediately after tillage, and we assume an initialization for the clods boundaries. The proposed method is based on a cost function to minimize, introducing four main characteristics of the clod boundary, respectively related to the mean of the DEM gradient norms on the boundary (f1f1), the standard deviation of the DEM gradient norms on the boundary (f2f2), the standard deviation of the DEM values on the boundary (f3f3) and L2-norm of the DEM values on the boundary (f4f4). In our case, the relative weights of previous criteria have been learned using a target reference that is a manual delineation of individual clods completed by a soil scientist on a sub-part of the DEM image. The cost function minimization is then achieved using the simulated annealing technics. The result performance is measured in term of the overlap rate. Further study shows the key feature of the f4 criterion. Then, the influence of the weighting coefficients was studied using (f1,f2,f4) based new cost function. We finally conclude on the possibility of improving the clod boundaries of a large surface using the cost function parameters learned on a training sub-surface.