Abstract
In this paper we propose a new technique for the solution of the image segmentation problem which is based on the concept of a piecewise smooth approximation of some target functional. We discuss in details the consistency of the new statement of segmentation problem and its solvability. We focus our main intension on the rigor mathematical substantiation of the proposed approach, deriving the corresponding optimality conditions, and show that the new optimization problem is rather flexible and powerful model to the study of variational image segmentation problems. We illustrate the accuracy and efficiency of the proposed algorithm by numerical experiences.
Highlights
In this paper we discuss a new coupled variational problem which is suggested by applications to satellite image segmentation
From practical point of view, image segmentation is the process of dividing an image into several areas with features and extracting the target of interest. in particular, in agricultural crop field classification, one of a fundamental problem is to provide a disjunctive decomposition of a fixed domain Ω ⊂ R2 onto finite number of nonempty subsets Ω = Ω1 ∪ Ω2 ∪ · · · ∪ ΩK such that each of these subsets could be associated with a crop that is grown in this area, or with a forest regions, or water zones, and so on, and this correspondence must be established at rather high level of accuracy
The following embedding results for BV -function is very useful in connection with variational problem that we study in this paper
Summary
In this paper we discuss a new coupled variational problem which is suggested by applications to satellite image segmentation. UoMpt T of the problems (1.1)–(1.2) to their ’locally smoothed’ versions We describe this passage by introduction of some nonlinear sequentially continuous operators Vi : BV (Ω) → BV (Ω), i.e. uo1pt, uo2pt, . We show that this problem can be considered as a particular case of the proposed couple optimization problem. We give the results of numerical simulation with the real-life satellite images which illustrate the accuracy and efficiency of the proposed algorithm
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