# Mapping with Pleiades--End-to-End Workflow
## 2 Related Work
### Digital Surface Model Generation
#### 2.2.2 Stereo Matching  
Within the standard processing chain, the most challenging part is the correspondence problem, where in the dense case for each pixel coordinate in the first image the corresponding pixel coordinate in the second image which holds the same object has to be determined. The process of finding those parallaxes, shift vectors or disparities is called image matching. In principle, the matching problem determines the column and line shifts for each pixel and thus is based on a 2D search space. However, using the epipolar rectification for each pixel in the first image the corresponding pixel in the second image is located on a horizontal line. In this case, the search space in image matching becomes one-dimensional, thus enabling faster and more accurate matching algorithms. A very good benchmark of 1D matching methods can be found in Reference [62]. Having epipolar rectified images a standard procedure in photogrammetry and remote sensing is to apply the semi-global matching (SGM) introduced by Reference [61]. This matching scheme is able to achieve very good results, comparable to methods based on global optimization, for example, graph cut [63] or total variation [64]. Moreover, it is computationally very efficient. Currently many commercial packages for processing satellite data use epipolar rectification and SGM for DSM generation, for example, Erdas Imagine ([[http://www.hexagongeospatial.com/products/remote-sensing/erdas-imagine/overview](http://www.hexagongeospatial.com/products/remote-sensing/erdas-imagine/overview)]([http://www.hexagongeospatial.com/products/remote-sensing/erdas-imagine/overview](http://www.hexagongeospatial.com/products/remote-sensing/erdas-imagine/overview))), PCI Geomatica ([[http://www.pcigeomatics.com](http://www.pcigeomatics.com)]([http://www.pcigeomatics.com](http://www.pcigeomatics.com))), Trimble Inpho with Match-T or MATCH-3 DX ([[http://www.trimble.com/imaging/inpho.aspx](http://www.trimble.com/imaging/inpho.aspx)]([http://www.trimble.com/imaging/inpho.aspx](http://www.trimble.com/imaging/inpho.aspx))), 82p ([[http://devi.polim/~carlo/s2p/](http://devi.polim/~carlo/s2p/)]([http://devi.polim/~carlo/s2p/](http://devi.polim/~carlo/s2p/))), SURE ([[http://nframes.com/](http://nframes.com/)]([http://nframes.com/](http://nframes.com/))) (only works with perspective images [65]), MicMac ([[http://micmac.ensg.eu](http://micmac.ensg.eu)]([http://micmac.ensg.eu](http://micmac.ensg.eu))) [66], RPC Stereo Processor ([[http://u.osu.edu/qin.324/rsp/](http://u.osu.edu/qin.324/rsp/)]([http://u.osu.edu/qin.324/rsp/](http://u.osu.edu/qin.324/rsp/))) [67] and also the Remote Sensing Software Graz ([[http://www.remotesensing.at/en/remote-sensing-software.html](http://www.remotesensing.at/en/remote-sensing-software.html)]([http://www.remotesensing.at/en/remote-sensing-software.html](http://www.remotesensing.at/en/remote-sensing-software.html))). Recent research reports on different variants of SGM, such as Reference [65] and extensions like those in References [68; 69; 70; 71]. As underlying cost function most algorithms apply the Hamming distance of the Census transform [72] due to its robustness [73]. Alternatively, the so-called modified Census Transform [74; 75] is used. Also a weighting can be incorporated based on the radiometric or the geometric distance (similarity and proximity weighting) [75; 76]. Optimizing the stereo matching technique is always an important research topic. In particular, a combined cost-function of Census transform and absolute difference measure is envisaged but also the replacement of Census transform with generalized Census transform [77; 78] is an issue. The most recent step is to train the cost-function via deep learning of a convolutional neural network [79; 80; 81; 82].