Sensor orientation via RPCs

https://doi.org/10.1016/j.isprsjprs.2005.11.001Get rights and content

Abstract

The adoption of rational functions as a preferred sensor orientation model for narrow field of view line scanner imagery accompanied the introduction of commercial high-resolution satellite imagery (HRSI) at the turn of the millennium. This paper reviews the developments in ground point determination from HRSI via the model of terrain independent rational polynomial coefficients (RPCs). A brief mathematical background to rational functions is first presented, along with a review of the models for generating RPCs from a rigorous sensor orientation, and for geopositioning via either forward intersection or monoplotting. The concept of RPC block adjustment with compensation for exterior orientation biases is then discussed, as is the means to enhance the original RPCs through a bias correction procedure. The potential for RPC block adjustment to yield sub-pixel geopositioning accuracy from HRSI is illustrated using results from experimental testing with two Quickbird stereo image pairs and three multi-image IKONOS blocks. Finally, error propagation issues in RPC block adjustment of HRSI are considered.

Introduction

In spite of some early angst within the photogrammetric community prior to and immediately after the launch in 1999 of the IKONOS II satellite, the rational polynomial coefficient (RPC) model has been universally accepted, and validated, as an alternative sensor orientation model for high-resolution satellite imagery (HRSI). The motivation for adoption of the RPC model for HRSI can be traced to a number of factors. These include its widespread use within the defence mapping sector, circumvention of the need to release complex camera model information and metadata relating to ephemeris and satellite attitude, and the fact that it is ideally suited to narrow-angle imaging sensors. Conversely, concerns relating to the RPC model have often centred upon two perceptions: firstly, that RPCs represent an empirically derived approximation to the rigorous sensor orientation model, rather than a comprehensive re-parameterization of that model; and, secondly, that RPCs are not amenable to enhancement. The latter concern, expressed another way, is simply that the orientation will only be as good as the RPCs and that there is no practical way to improve upon the sensor orientation via analytical means. As regards the former perception, third-order rational functions can be empirically generated from ground control, but this generally represents an impractical and undesirable approach, which is not recommended for metric applications of HRSI. As it happens, first-order empirical functions can often suffice, but this paper will confine the discussion, and the references, to the terrain-independent RPCs provided by the imagery supplier, which have been generated through a fully verified determination process (Grodecki, 2001). The RPC generation process will be summarised in a following section, as it offers useful insights into the integrity of the rational function model for HRSI.

HRSI technology has now been with us for just over five years and it is useful to reflect on advances that have been made since its adoption for 3D spatial information generation. One of the principal areas of focus in relation to metric exploitation is sensor orientation, for single-, stereo- and multi-image configurations. This paper is aimed at reviewing developments related to the RPC model. Initially, a brief mathematical background to the RPC model for object-to-image space transformation is summarised, and the model for ground point determination via either forward intersection or monoplotting is reviewed. The subject of positioning biases is then addressed and the formulation of a bias-compensated RPC block adjustment is outlined. Results of experimental applications of RPC block adjustments are then summarised and the generation of bias-corrected RPCs is discussed. Finally, error propagation in RPC block adjustment is considered. The authors will attempt to give a coverage that is representative for current HRSI, though accounts of experimental testing and evaluation are confined to IKONOS and Quickbird imagery.

Section snippets

The modified collinearity model

The sensor orientation model for pushbroom HRSI scanners must accommodate the fact that within the plane formed by the linear CCD array and camera perspective centre the projection is central perspective, whereas for the adjacent scan lines in the along-track direction a parallel projection applies (assuming the angle between the velocity vector and the camera axis remains constant). An appropriate model to relate image- and object-space coordinates for such a case remains the well-known

Computation of RPCs

Early in the paper we implied that potential users of HRSI should not contemplate generating their own RPCs. We need to be more specific and say that users should not consider the estimation of RPCs from ground control points via the so-called terrain-dependent approach (Tao and Hu, 2001, Di et al., 2003). The need to generate alternative RPCs when you already have a set of rational function coefficients might arise. For example, ‘standard’ HRSI RPCs map geographic coordinates to image

Bias compensated RPC block adjustment

The RPCs constitute a re-parameterization of the rigorous sensor orientation model. Errors in sensor interior and exterior orientation thus give rise to errors in the RPCs. The calibration of camera interior orientation is determined to very high accuracy using well controlled test range imagery (Grodecki and Dial, 2002), whereas sensor exterior orientation, comprising position and attitude data, is directly observed using on-board GPS receivers, gyros and star trackers. The satellite ephemeris

Regeneration of RPCs

The ability to determine the bias parameters in an RPC block adjustment, or even for a single image, would be largely academic were it not for the fact that the user can correct the originally supplied RPCs for this bias. For the most common case, where only the shift terms A0 and B0 are employed, the bias-corrected RPCs are generated as (Fraser and Hanley, 2003):NumLC(U,V,W)=(a1b1A0/LS)+(a2b2A0/LS)V+(a3b3A0/LS)U++(a20b20A0/LS)W3NumSC(U,V,W)=(c1d1B0/SS)+(c2d2B0/SS)V+(c3d3B0/Ss)

Test range data

Over the past few years there have been a number of experimental evaluations of RPC block adjustment reported in the literature. These have generally involved analysis of IKONOS stereo pairs or triplets, and Quickbird stereo pairs. There has also been testing of the bias compensation approach for multi-strip blocks of IKONOS mono and stereo imagery. In order to illustrate the metric accuracy potential of RPC block adjustment for HRSI, we will briefly summarise the results of experimental

Error propagation

In this section we use a simplified error propagation to predict how accuracy changes as a function of the number of GCPs and of their accuracy.

Concluding remarks

The aim of this paper has been essentially two-fold, firstly to provide an overview of the RPC model for HRSI, and secondly to highlight both the practicability and accuracy potential of RPC block adjustment. It has been demonstrated that bias-compensated RPC block adjustment can yield sub-pixel accuracy, which for the case of both IKONOS and Quickbird imagery, translates to a sub-metre geopositioning capability. Moreover, the attainment of such accuracy via bias-corrected RPCs in subsequent

References (29)

  • C.S. Fraser et al.

    Insights into the affine model for satellite sensor orientation

    ISPRS Journal of Photogrammetry and Remote Sensing

    (2004)
  • P.V. Radhadevi et al.

    Precision rectification of IRS-1C PAN data using an orbit attitude model

    ISPRS Journal of Photogrammetry and Remote Sensing

    (1998)
  • Ager, T.P., 2003. Evaluation of the geometric accuracy of IKONOS imagery. SPIE 2003 AeroSense Conference, Orlando,...
  • Baltsavias, E., Pateraki, M., Zhang, L., 2001. Radiometric and geometric evaluation of IKONOS Geo images and their use...
  • Baltsavias, E., Zhang, L., Eisenbeiss, H., 2005. DSM generation and interior orientation determination of IKONOS images...
  • K. Di et al.

    Rational functions and potential for rigorous sensor model recovery

    Photogrammetric Engineering and Remote Sensing

    (2003)
  • Dial, G., Grodecki, J., 2002a. Block adjustment with rational polynomial camera models. Proceedings of ASPRS Annual...
  • Dial, G., Grodecki, J., 2002b. IKONOS accuracy without ground control. International Archives of Photogrammetry and...
  • H. Ebner et al.

    A simulation study on point determination for the MOMS-02/D2 space project using an extended functional model

    International Archives of Photogrammetry and Remote Sensing

    (1992)
  • H. Eisenbeiss et al.

    Potential of IKONOS and Quickbird imagery accurate 3D-point positioning, orthoimage and DSM generation

    International Archives of Photogrammetry, Remote Sensing and Spatial Information Sciences

    (2004)
  • C.S. Fraser et al.

    Bias compensation in rational functions for IKONOS satellite imagery

    Photogrammetric Engineering and Remote Sensing

    (2003)
  • C.S. Fraser et al.

    Bias compensated RPCs for sensor orientation of high-resolution satellite imagery

    Photogrammetric Engineering and Remote Sensing

    (2005)
  • Fraser, C.S., Hanley, H.B., Yamakawa, T., 2002. High-precision geopositioning from IKONOS satellite imagery....
  • Grodecki, J., 2001. IKONOS stereo feature extraction—RPC approach. Proceedings ASPRS Annual Conference, St. Louis,...
  • Cited by (0)

    View full text