PEER.REVIEWED ARTICIE Incorporation of Relief in Polynomial-Based Geometric Gorrections Viceng Pali and Xavier Pons Abstract This study focuses on the geometricd deformations intro- duced by relief in images captured by the TM sensor of Land- sat satellites and by the Hnv senso-r of seor satellites. Different correction alternatives are prcsented in order to in- coiporate altitude data into cotection procedures basedon first-degree polynomial models. Column and row determina- tions from the cotesponding map coordinates are carried out independently. Three different models for columns and two for rows are proposed. The results have been contrasted with those obtained using dassic first- and second-degree polynomial calculations, and with those obtained using an orbital model (for snor images). The models presented are easy to implement and provide a hevelof precision similar to that of the orbital model used, while they are much more ef- ficient in calculation time. In view of the results, the model which integrates altimetric data into a single first-degree pol- ynomial seems of pafticular interest. Introduction Due to the complex characteristics of the Earth-sensor sys- tem, images obtained from resource observation satellites suf- fer from several distortions that make them not directly superimposable on a map. Among those characteristics, we might mention the deformation produced by the conical per- spective in which the images are captured, aggravated by Earth curvature and relief, the simultaneous movements of terrestrial rotation and satellite orbit during image capture, and the attitude of the sensor in space, which, whether in- voluntarily or intentionally, does not always have a view perpendicular to the terrain surface at the center of the im- age. This last factor is of particular importance in the SPoT satellite, capable of taking images with a lateral inclination angle up Io + 27". Classically, the process of geometric correction of images has been approached by employing two different methods (Billingsley, 1983), each of which requires knowledge of one or more ground control points (ccps). The first one is based on orbital models, deliberately physical in conception, which aim to grasp and model the distortions in order to lead them back towards the desired cartographic projection. The second method, more empirical in conception, aims to convert the image into a map by finding transformation polynomials; this method usually requires a higher number of ccps, V. Pald is with the Institut Cartogrdfic de Catalunya, Balmes 209-211, 08006 Barcelona, Catalonia, Spain. X. Pons is with the Centre de Recerca Ecoldgica i Aplica- cions Forestals ICREAF), and Unitat de Botdnica, Fac. Cidn- cies, Universitat Autbnoma de Barcelona, 08193 Bellaterra, Catalonia, Spain. In this study, we aim to o incorporatethe effect of relief into polynomial-based geomet- ric correction models and apply them to rna (Landsat) and snv (spor) images (the models have a different geometric fi- delity, and they will be comparativelytested); and o make an exnerimentalcheck on the improvementsachieved by these -"ihodr, comparing the resulti to those obtained us- ing the classicpolynomial models - in which account is not taken of relief- and to an orbital model (for spor only). Obital Models, Conection of SPOT lmages, andOdital Model Used The ideal situation implementing a correction process based on ohvsical models demands that the data be in a raw state, i.e., ai captured at the sensor. In this situation, which we may consider equivalent to that of spot level tA, the pixels have the nominal size (e.g., 10 m, 20 m, etc.) only at the na- dir, while they are "bigger" the further we move to the sides of the image. In addition, other deformations must be taken into account, such as Earth curvature and rotation, orbital movement of the satellite, attitude of the sensor, non-linear- ity of sensor movement in the exploration devices (multis- pectral scanners), relief, etc. Orbital models try to correct the image by taking into ac- count the maximum number of these parameters and inte- grating them into a geocentric reference system (Labovitz and Marvin, 1986; Salamonowicz, 1986; Light, 1986; Marvin ef al., tg\z; Gugan, 1987; Rodrigtez et al.,19BB; Kratky, 19BB). If we have a digital elevation model (onrra), we can correct for the effect of relief by means of the collinearity equations, that relate the position of each point of the territory (defined by its three Cartesian coordinates in the corresponding geo- metric space) with that of the sensor (also three coordinates). These equations require knowledge of the sensor attitude, de- fined by the three angles yaw (rc),roll (ro), and pitch (d) (Wong, 1986). Various approaches can be taken in order to simplify the process, such as assuming that the attitude of the sensor is constant, or allowing that some parameter, such as pitch, changes linearly with time. The main advantage of orbital models is their high preci- sion and robustness, as a consequence of their physical foun- dations, while their chief disadvantages lie in their imple- mentation complexity and, above all, the amount of calculation time reouired. Although raw data correction by using orbital models may seem optimum, this is not the type of material that com- mon users of high spatial resolution satellites usually re- Photogrammetric Engineering & Remote Sensing, Vol. 0r, No. 7, July 1995, pp. 935-944. 00s9-11 1 2/S5/6107-935$3.00/O O 1995 American Society for Photogrammetry and Remote Sensing