Abstract

Abstract. This paper proposes an algorithm for fusing digital surface models (DSM) obtained by heterogenous sensors. Based upon prior confidence knowledge, each DSM can be weighted locally adaptively and therefore strengthen or lessen its influence on the fused result. The proposed algorithm is based on variational methods of first and second order, minimizing a global energy functional comprising of a data term forcing the resulting DSM being similar to all of the input height information and incorporating additional local smoothness constraints. By applying these additional constraints in the form of favoring low gradients in the spatial direction, the surface model is forced to be locally smooth and in contrast to simple mean or median based fusion of the height information, this global formulation of context-awareness reduced the noise level of the result significantly. Minimization of the global energy functional is done with respect to the L1 norm and therefore is robust to large height differences in the data, which preserves sharp edges and fine details in the fused surface model, which again simple mean- and median-based methods are not able to do in comparable quality. Due to the convexity of the framed energy functional, the solution furthermore is guaranteed to converge towards the global energy minimum. The accuracy of the algorithms and the quality of the resulting fused surface models is evaluated using synthetic datasets and real world spaceborne datasets from different optical satellite sensors.

Highlights

  • Digital surface models (DSM) are a basic component for many applications, such as orthophoto creation, mapping, visualisation and 3D planing in many application fields

  • Total Variation based methods (TV) for minimizing energy functionals have seen a lot of attention in the research community

  • Five of these noisy digital surface models (DSM) are given as input to the fusion algorithms and the accuracy of the output DSM u is measured by the logarithmic signal-to-noise ratio: SN R = 10 log10

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Summary

INTRODUCTION

Digital surface models (DSM) are a basic component for many applications, such as orthophoto creation, mapping, visualisation and 3D planing in many application fields. A comparison between weighted averaging and sparse representations (Schindler et al, 2011) found that the quality of the fused DSMs is mostly determined by the quality of these pixel based error maps. Another direction of work (Pock et al, 2011) aims to formulate a global energy function, minimizing the distance of the fused result to all input DSMs simultaneously and incorporates the assumption of the world being locally planar. Due to its simple structure and theoretically well founded minimization procedure, we build upon this work and extend it to a weighted, multi-resolution, fusion framework The peer-review was conducted on the basis of the abstract

METHOD
TV-L1 Fusion
TGV-L1 Fusion
Weighted TGV-L1 Fusion
ALGORITHM
Artificial Tests
Unimodal DSM fusion
Multimodal DSM fusion
CONCLUSION

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