Z Points IceSat Points

on them. As a consequence, the method based on SURF points exposed in §2.3 had to be adapted. SURF methods are usually robust to scale variation and rotation. Nevertheless, in our cases the scale difference is so big that we have to transform the GCIs to the resolution of the HRS one. Moreover, the HRS MTF Modulation Transfer Function is often poorer than the GCIs: as a consequence, a filter on the VHR image has to be applied before looking for tie points. Finally 30 to 100 tie points usually link GCIs to the rest of the block. These points often have a multiplicity greater than 4. Fig. 5: Homologous points automatically measured on a HRS couple from 2002 and two WorldView images from 2010. ©CNES, 2002, Distribution Spot Image. ©Digital Globe, 2010. 2.5.4 Precautions of use GCIs usually are very high resolution images pixel around 0.5m, and the roll angle can be important, sometimes more than 35°. As a consequence, these images should be used with care because a planimetric error is proportional to the tangent of the angle, as shown below. 6 Fig. 6: Error of location according the roll angle Nevertheless, internal studies show that up to a roll angle of 25° the influence is very low. As a consequence, we recommend to use images as GCPs when the roll angle is less than 25°. What should also be taken into account is the influence of the vegetation andor the relief. Other tests show that the influence on the location of the block was less than 1m between areas with and without forests.

2.6 Planning of new Ground Control Data

In order to anticipate our future computations of the global block and places where the location could be improved with new GCPs or images, simulation maps of accuracy were achieved. In these raster maps, the different constraints and recommendations to make spatiotriangulation are included. All the formulas presented here are empirically generated and are directly linked to the nominal parameters entered in the computation. They were checked by making comparisons with real blocks of smaller size. The main idea of this model is to estimate the accuracy of every pixel of 1 deg 2 in the map. Thus, the influence of one GCP or an image on one pixel is given by: σ GCP → pixel = σ GCP 2 + σ Pr opagation 2 where σ Pr opagation d = 15.1- exp d2000 and d is the distance in kilometres between the pixel and the GCP. Each GCP has an influence on the accuracy of a pixel. As a consequence, the accuracy on a pixel of 1 deg 2 is determined by: σ pixel = p i . σ GCP → pixel 2 i=1 n ∑ p i 2 i=1 n ∑ with p i = 1 d i This only means that the weight granted to each GCP is inversely proportional to the square distance of the pixel. The simple modelisation of the distance could not take into account constraints of landscape as seas for example. Indeed, with such a distance, every GCP has the same role whether they are separated by the sea or not, and whether images are linked together or not. To avoid this problem, a parameter of viscosity was introduced in the computation of the distance, in order to virtually increase distances between GCPs and pixels when they are separated by seas. Finally, a global map of accuracy was computed by taking into account these algorithms and the equipment. The next figure presents the equipment needed to reach an accuracy compatible with future positioning systems. Around 700 GCPs including images are needed. Fig. 7: Ideal equipment needed to reach a performing location green to yellow

2.7 Z Points IceSat Points

The introduction of Z points in our bundle adjustment has been done recently, in order to get many different external sources of reliable information. Z points can be considered as GCPs in which we don’t trust planimetric information. Indeed, as they are extracted from IceSat spatial mission, these points have a very accurate height measurement but the planimetric information has only an accuracy of 30m. XXII ISPRS Congress, 25 August – 01 September 2012, Melbourne, Australia 254 2.7.1 Filters All IceSat measurements are not included in the spatiotriangulation, because some points are not reliable. A quite simple filter is applied on metadata of quality of the points and the number of echoes. This filter is based on an efficient quality flag including metadata and on the number of echoes. The effect is that points on cloudy areas, forests and mountain zones are filtered. Finally, around 160,000 IceSat points have been included in the computation: it means that in average there are more than 10 IceSat points on each HRS image. Fig. 8: Active IceSat points green on India block 3. AN IMPROVED BUNDLE ADJUSTMENT TOOL 3.1 Generalities IGN has been involved in spatiotriangulation since the early eighties with the arrival of SPOT1 and took part in the development of a spatiotriangulation engine called Delta which has now become Euclidium developed and maintained by Magellium company. Although Euclidium is correctly designed to take into account most types of satellite images it has proved limited in terms of quantity of data it can process: blocks up to 1000 images are a limit. Thus for larger blocks, we had to improve our solving methods while sticking to the principles of Euclidium for the physical models and blocks management.

3.2 A generic tool

Fully automatic methods for tie points measurement generally generate numbers of outliers mismatched points and the elimination of those mismatched points is particularly critical. The outliers elimination is performed through iterative resolution of a least squares system and may be very costly. A first improvement of our software aims at minimizing the cost of outliers elimination: any computation linked to unchanged data is kept unchanged. This is done by splitting upstream computations such as partial derivatives computed once for all iterations and downstream computations least squares solver into 2 different software. Furthermore, this separation allows to input into the least squares solving software data from various origin Euclidium formalism, aerial photographs…. A second improvement concerns the optimization of the least squares solver itself. We adopted a solution based on Jacobi preconditioned conjugate gradient after normalization of the unkwowns.

3.3 Inputs

All the data listed below are used as an input data, sometimes in a modified form. 3.3.1 GCPs and tie points Equations about GCPs are expressed in ground coordinate system, and can be written as follows: 1 σ obs ∂ loc ∂ Param ⋅ d Param Param ∑       = loc measured − loc estimated where ∂ loc ∂ Param is a partial derivative of location according to a differential variation of a parameter, d Param is the variation of a parameter of the system to estimate, loc measured is the coordinates of the GCP and loc estimated is the estimated location of the point with initial parameters. 3.3.2 Constraint equations In order to force the system to be solved to converge to a value near the initial solution, constraint equations on points and parameters are added. They can be written as follows: 1 σ Param d Param i + Δ Param i−1 = 0 , where d Param i is the parameter to estimate on iteration i, Δ Param i −1 is the variation of the parameter estimated on iteration i-1, so that the more accurate σ Param is, the more constrained d Param i is. 3.3.3 Partial derivatives calculation Partial derivatives are not computed by this engine but elsewhere in the process. They must be brought as an input of the system. This process requires a lot of calculation time for a global block. 3.4 Solving the system

3.4.1 Normalization of the parameters

Parameters used in the system can have very different orders of magnitude. As a consequence, every parameter is normalized in the system before being used. Thus, the normalization removes this effect, and allows us to use homogeneous parameters. Finally, for each equation, each parameter to estimate d Param is replaced by d Param ⋅ max Param ∂ loc ∂ Param . 3.4.2 System to solve The system to solve can be presented as follows, where A is an almost diagonal matrix, and mainly sparse. A 1 ...       … A n             X 1  X n             = B 1  B n             , where X 1 is a vector of parameters to estimate for image 1, B 1 are the residual values concerning image 1… XXII ISPRS Congress, 25 August – 01 September 2012, Melbourne, Australia 255